diff --git a/challenges/08-coding-interview-questions-and-take-home-assignments/project-euler-problems.json b/challenges/08-coding-interview-questions-and-take-home-assignments/project-euler-problems.json index e0a9c72573..792dadf31a 100644 --- a/challenges/08-coding-interview-questions-and-take-home-assignments/project-euler-problems.json +++ b/challenges/08-coding-interview-questions-and-take-home-assignments/project-euler-problems.json @@ -5,7 +5,7 @@ "helpRoom": "HelpJavaScript", "challenges": [ { - "_id": "5900f36e1000cf542c50fe80", + "id": "5900f36e1000cf542c50fe80", "challengeType": 5, "type": "bonfire", "title": "Problem 1: Multiples of 3 and 5", @@ -31,7 +31,7 @@ ] }, { - "_id": "5900f36e1000cf542c50fe81", + "id": "5900f36e1000cf542c50fe81", "challengeType": 5, "type": "bonfire", "title": "Problem 2: Even Fibonacci Numbers", @@ -59,7 +59,7 @@ ] }, { - "_id": "5900f36f1000cf542c50fe82", + "id": "5900f36f1000cf542c50fe82", "challengeType": 5, "type": "bonfire", "title": "Problem 3: Largest prime factor", @@ -89,7 +89,7 @@ ] }, { - "_id": "5900f3701000cf542c50fe83", + "id": "5900f3701000cf542c50fe83", "challengeType": 5, "type": "bonfire", "title": "Problem 4: Largest palindrome product", @@ -115,7 +115,7 @@ ] }, { - "_id": "5900f3711000cf542c50fe84", + "id": "5900f3711000cf542c50fe84", "challengeType": 5, "type": "bonfire", "title": "Problem 5: Smallest multiple", @@ -140,7 +140,7 @@ ] }, { - "_id": "5900f3721000cf542c50fe85", + "id": "5900f3721000cf542c50fe85", "challengeType": 5, "type": "bonfire", "title": "Problem 6: Sum square difference", @@ -171,7 +171,7 @@ ] }, { - "_id": "5900f3731000cf542c50fe86", + "id": "5900f3731000cf542c50fe86", "challengeType": 5, "type": "bonfire", "title": "Problem 7: 10001st prime", @@ -200,7 +200,7 @@ ] }, { - "_id": "5900f3741000cf542c50fe87", + "id": "5900f3741000cf542c50fe87", "challengeType": 5, "type": "bonfire", "title": "Problem 8: Largest product in a series", @@ -248,7 +248,7 @@ ] }, { - "_id": "5900f3761000cf542c50fe88", + "id": "5900f3761000cf542c50fe88", "challengeType": 5, "type": "bonfire", "title": "Problem 9: Special Pythagorean triplet", @@ -276,7 +276,7 @@ ] }, { - "_id": "5900f3761000cf542c50fe89", + "id": "5900f3761000cf542c50fe89", "challengeType": 5, "type": "bonfire", "title": "Problem 10: Summation of primes", @@ -302,7 +302,7 @@ ] }, { - "_id": "5900f3781000cf542c50fe8a", + "id": "5900f3781000cf542c50fe8a", "challengeType": 5, "type": "bonfire", "title": "Problem 11: Largest product in a grid", @@ -381,7 +381,7 @@ ] }, { - "_id": "5900f3781000cf542c50fe8b", + "id": "5900f3781000cf542c50fe8b", "challengeType": 5, "type": "bonfire", "title": "Problem 12: Highly divisible triangular number", @@ -416,7 +416,7 @@ ] }, { - "_id": "5900f37a1000cf542c50fe8c", + "id": "5900f37a1000cf542c50fe8c", "challengeType": 5, "type": "bonfire", "title": "Problem 13: Large sum", @@ -539,7 +539,7 @@ ] }, { - "_id": "5900f37a1000cf542c50fe8d", + "id": "5900f37a1000cf542c50fe8d", "challengeType": 5, "type": "bonfire", "title": "Problem 14: Longest Collatz sequence", @@ -567,7 +567,7 @@ ] }, { - "_id": "5900f37b1000cf542c50fe8e", + "id": "5900f37b1000cf542c50fe8e", "challengeType": 5, "type": "bonfire", "title": "Problem 15: Lattice paths", @@ -592,7 +592,7 @@ ] }, { - "_id": "5900f37d1000cf542c50fe8f", + "id": "5900f37d1000cf542c50fe8f", "challengeType": 5, "type": "bonfire", "title": "Problem 16: Power digit sum", @@ -615,7 +615,7 @@ ] }, { - "_id": "5900f37d1000cf542c50fe90", + "id": "5900f37d1000cf542c50fe90", "challengeType": 5, "type": "bonfire", "title": "Problem 17: Number letter counts", @@ -639,7 +639,7 @@ ] }, { - "_id": "5900f37e1000cf542c50fe91", + "id": "5900f37e1000cf542c50fe91", "challengeType": 5, "type": "bonfire", "title": "Problem 18: Maximum path sum I", @@ -682,7 +682,7 @@ ] }, { - "_id": "5900f37f1000cf542c50fe92", + "id": "5900f37f1000cf542c50fe92", "challengeType": 5, "type": "bonfire", "title": "Problem 19: Counting Sundays", @@ -713,7 +713,7 @@ ] }, { - "_id": "5900f3801000cf542c50fe93", + "id": "5900f3801000cf542c50fe93", "challengeType": 5, "type": "bonfire", "title": "Problem 20: Factorial digit sum", @@ -741,7 +741,7 @@ ] }, { - "_id": "5900f3811000cf542c50fe94", + "id": "5900f3811000cf542c50fe94", "challengeType": 5, "type": "bonfire", "title": "Problem 21: Amicable numbers", @@ -769,7 +769,7 @@ ] }, { - "_id": "5a51eabcad78bf416f316e2a", + "id": "5a51eabcad78bf416f316e2a", "challengeType": 5, "type": "bonfire", "title": "Problem 22: Names scores", @@ -802,7 +802,7 @@ ] }, { - "_id": "5900f3831000cf542c50fe96", + "id": "5900f3831000cf542c50fe96", "challengeType": 5, "type": "bonfire", "title": "Problem 23: Non-abundant sums", @@ -831,7 +831,7 @@ ] }, { - "_id": "5900f3841000cf542c50fe97", + "id": "5900f3841000cf542c50fe97", "challengeType": 5, "type": "bonfire", "title": "Problem 24: Lexicographic permutations", @@ -858,7 +858,7 @@ ] }, { - "_id": "5900f3851000cf542c50fe98", + "id": "5900f3851000cf542c50fe98", "challengeType": 5, "type": "bonfire", "title": "Problem 25: 1000-digit Fibonacci number", @@ -899,7 +899,7 @@ ] }, { - "_id": "5900f3861000cf542c50fe99", + "id": "5900f3861000cf542c50fe99", "challengeType": 5, "type": "bonfire", "title": "Problem 26: Reciprocal cycles", @@ -937,7 +937,7 @@ ] }, { - "_id": "5900f3871000cf542c50fe9a", + "id": "5900f3871000cf542c50fe9a", "challengeType": 5, "type": "bonfire", "title": "Problem 27: Quadratic primes", @@ -970,7 +970,7 @@ ] }, { - "_id": "5900f3881000cf542c50fe9b", + "id": "5900f3881000cf542c50fe9b", "challengeType": 5, "type": "bonfire", "title": "Problem 28: Number spiral diagonals", @@ -1002,7 +1002,7 @@ ] }, { - "_id": "5900f3891000cf542c50fe9c", + "id": "5900f3891000cf542c50fe9c", "challengeType": 5, "type": "bonfire", "title": "Problem 29: Distinct powers", @@ -1034,7 +1034,7 @@ ] }, { - "_id": "5900f38a1000cf542c50fe9d", + "id": "5900f38a1000cf542c50fe9d", "challengeType": 5, "type": "bonfire", "title": "Problem 30: Digit n powers", @@ -1065,7 +1065,7 @@ ] }, { - "_id": "5900f38b1000cf542c50fe9e", + "id": "5900f38b1000cf542c50fe9e", "challengeType": 5, "type": "bonfire", "title": "Problem 31: Coin sums", @@ -1094,7 +1094,7 @@ ] }, { - "_id": "5900f38c1000cf542c50fe9f", + "id": "5900f38c1000cf542c50fe9f", "challengeType": 5, "type": "bonfire", "title": "Problem 32: Pandigital products", @@ -1122,7 +1122,7 @@ ] }, { - "_id": "5900f38d1000cf542c50fea0", + "id": "5900f38d1000cf542c50fea0", "challengeType": 5, "type": "bonfire", "title": "Problem 33: Digit cancelling fractions", @@ -1147,7 +1147,7 @@ ] }, { - "_id": "5900f38e1000cf542c50fea1", + "id": "5900f38e1000cf542c50fea1", "challengeType": 5, "type": "bonfire", "title": "Problem 34: Digit factorials", @@ -1173,7 +1173,7 @@ ] }, { - "_id": "5900f38f1000cf542c50fea2", + "id": "5900f38f1000cf542c50fea2", "challengeType": 5, "type": "bonfire", "title": "Problem 35: Circular primes", @@ -1202,7 +1202,7 @@ ] }, { - "_id": "5900f3901000cf542c50fea3", + "id": "5900f3901000cf542c50fea3", "challengeType": 5, "type": "bonfire", "title": "Problem 36: Double-base palindromes", @@ -1229,7 +1229,7 @@ ] }, { - "_id": "5900f3911000cf542c50fea4", + "id": "5900f3911000cf542c50fea4", "challengeType": 5, "type": "bonfire", "title": "Problem 37: Truncatable primes", @@ -1256,7 +1256,7 @@ ] }, { - "_id": "5900f3931000cf542c50fea5", + "id": "5900f3931000cf542c50fea5", "challengeType": 5, "type": "bonfire", "title": "Problem 38: Pandigital multiples", @@ -1284,7 +1284,7 @@ ] }, { - "_id": "5900f3931000cf542c50fea6", + "id": "5900f3931000cf542c50fea6", "challengeType": 5, "type": "bonfire", "title": "Problem 39: Integer right triangles", @@ -1311,7 +1311,7 @@ ] }, { - "_id": "5900f3941000cf542c50fea7", + "id": "5900f3941000cf542c50fea7", "challengeType": 5, "type": "bonfire", "title": "Problem 40: Champernowne's constant", @@ -1337,7 +1337,7 @@ ] }, { - "_id": "5900f3951000cf542c50fea8", + "id": "5900f3951000cf542c50fea8", "challengeType": 5, "type": "bonfire", "title": "Problem 41: Pandigital prime", @@ -1363,7 +1363,7 @@ ] }, { - "_id": "5900f3961000cf542c50fea9", + "id": "5900f3961000cf542c50fea9", "challengeType": 5, "type": "bonfire", "title": "Problem 42: Coded triangle numbers", @@ -1394,7 +1394,7 @@ ] }, { - "_id": "5900f3971000cf542c50feaa", + "id": "5900f3971000cf542c50feaa", "challengeType": 5, "type": "bonfire", "title": "Problem 43: Sub-string divisibility", @@ -1425,7 +1425,7 @@ ] }, { - "_id": "5900f3981000cf542c50feab", + "id": "5900f3981000cf542c50feab", "challengeType": 5, "type": "bonfire", "title": "Problem 44: Pentagon numbers", @@ -1450,7 +1450,7 @@ ] }, { - "_id": "5900f3991000cf542c50feac", + "id": "5900f3991000cf542c50feac", "challengeType": 5, "type": "bonfire", "title": "Problem 45: Triangular, pentagonal, and hexagonal", @@ -1489,7 +1489,7 @@ ] }, { - "_id": "5900f39a1000cf542c50fead", + "id": "5900f39a1000cf542c50fead", "challengeType": 5, "type": "bonfire", "title": "Problem 46: Goldbach's other conjecture", @@ -1519,7 +1519,7 @@ ] }, { - "_id": "5900f39c1000cf542c50feae", + "id": "5900f39c1000cf542c50feae", "challengeType": 5, "type": "bonfire", "title": "Problem 47: Distinct primes factors", @@ -1545,7 +1545,7 @@ ] }, { - "_id": "5900f39c1000cf542c50feaf", + "id": "5900f39c1000cf542c50feaf", "challengeType": 5, "type": "bonfire", "title": "Problem 48: Self powers", @@ -1568,7 +1568,7 @@ ] }, { - "_id": "5900f39d1000cf542c50feb0", + "id": "5900f39d1000cf542c50feb0", "challengeType": 5, "type": "bonfire", "title": "Problem 49: Prime permutations", @@ -1592,7 +1592,7 @@ ] }, { - "_id": "5900f39e1000cf542c50feb1", + "id": "5900f39e1000cf542c50feb1", "challengeType": 5, "type": "bonfire", "title": "Problem 50: Consecutive prime sum", @@ -1618,7 +1618,7 @@ ] }, { - "_id": "5900f39f1000cf542c50feb2", + "id": "5900f39f1000cf542c50feb2", "challengeType": 5, "type": "bonfire", "title": "Problem 51: Prime digit replacements", @@ -1642,7 +1642,7 @@ ] }, { - "_id": "5900f3a01000cf542c50feb3", + "id": "5900f3a01000cf542c50feb3", "challengeType": 5, "type": "bonfire", "title": "Problem 52: Permuted multiples", @@ -1665,7 +1665,7 @@ ] }, { - "_id": "5900f3a11000cf542c50feb4", + "id": "5900f3a11000cf542c50feb4", "challengeType": 5, "type": "bonfire", "title": "Problem 53: Combinatoric selections", @@ -1697,7 +1697,7 @@ ] }, { - "_id": "5900f3a21000cf542c50feb5", + "id": "5900f3a21000cf542c50feb5", "challengeType": 5, "type": "bonfire", "title": "Problem 54: Poker hands", @@ -1742,7 +1742,7 @@ ] }, { - "_id": "5900f3a31000cf542c50feb6", + "id": "5900f3a31000cf542c50feb6", "challengeType": 5, "type": "bonfire", "title": "Problem 55: Lychrel numbers", @@ -1773,7 +1773,7 @@ ] }, { - "_id": "5900f3a41000cf542c50feb7", + "id": "5900f3a41000cf542c50feb7", "challengeType": 5, "type": "bonfire", "title": "Problem 56: Powerful digit sum", @@ -1796,7 +1796,7 @@ ] }, { - "_id": "5900f3a51000cf542c50feb8", + "id": "5900f3a51000cf542c50feb8", "challengeType": 5, "type": "bonfire", "title": "Problem 57: Square root convergents", @@ -1826,7 +1826,7 @@ ] }, { - "_id": "5900f3a61000cf542c50feb9", + "id": "5900f3a61000cf542c50feb9", "challengeType": 5, "type": "bonfire", "title": "Problem 58: Spiral primes", @@ -1856,7 +1856,7 @@ ] }, { - "_id": "5900f3a81000cf542c50feba", + "id": "5900f3a81000cf542c50feba", "challengeType": 5, "type": "bonfire", "title": "Problem 59: XOR decryption", @@ -1882,7 +1882,7 @@ ] }, { - "_id": "5900f3a81000cf542c50febb", + "id": "5900f3a81000cf542c50febb", "challengeType": 5, "type": "bonfire", "title": "Problem 60: Prime pair sets", @@ -1905,7 +1905,7 @@ ] }, { - "_id": "5900f3a91000cf542c50febc", + "id": "5900f3a91000cf542c50febc", "challengeType": 5, "type": "bonfire", "title": "Problem 61: Cyclical figurate numbers", @@ -1962,7 +1962,7 @@ ] }, { - "_id": "5900f3aa1000cf542c50febd", + "id": "5900f3aa1000cf542c50febd", "challengeType": 5, "type": "bonfire", "title": "Problem 62: Cubic permutations", @@ -1985,7 +1985,7 @@ ] }, { - "_id": "5900f3ab1000cf542c50febe", + "id": "5900f3ab1000cf542c50febe", "challengeType": 5, "type": "bonfire", "title": "Problem 63: Powerful digit counts", @@ -2008,7 +2008,7 @@ ] }, { - "_id": "5900f3ac1000cf542c50febf", + "id": "5900f3ac1000cf542c50febf", "challengeType": 5, "type": "bonfire", "title": "Problem 64: Odd period square roots", @@ -2153,7 +2153,7 @@ ] }, { - "_id": "5900f3ad1000cf542c50fec0", + "id": "5900f3ad1000cf542c50fec0", "challengeType": 5, "type": "bonfire", "title": "Problem 65: Convergents of e", @@ -2264,7 +2264,7 @@ ] }, { - "_id": "5900f3ae1000cf542c50fec1", + "id": "5900f3ae1000cf542c50fec1", "challengeType": 5, "type": "bonfire", "title": "Problem 66: Diophantine equation", @@ -2296,7 +2296,7 @@ ] }, { - "_id": "5900f3b01000cf542c50fec2", + "id": "5900f3b01000cf542c50fec2", "challengeType": 5, "type": "bonfire", "title": "Problem 67: Maximum path sum II", @@ -2324,7 +2324,7 @@ ] }, { - "_id": "5900f3b01000cf542c50fec3", + "id": "5900f3b01000cf542c50fec3", "challengeType": 5, "type": "bonfire", "title": "Problem 68: Magic 5-gon ring", @@ -2363,7 +2363,7 @@ ] }, { - "_id": "5900f3b11000cf542c50fec4", + "id": "5900f3b11000cf542c50fec4", "challengeType": 5, "type": "bonfire", "title": "Problem 69: Totient maximum", @@ -2429,7 +2429,7 @@ ] }, { - "_id": "5900f3b21000cf542c50fec5", + "id": "5900f3b21000cf542c50fec5", "challengeType": 5, "type": "bonfire", "title": "Problem 70: Totient permutation", @@ -2453,7 +2453,7 @@ ] }, { - "_id": "5900f3b31000cf542c50fec6", + "id": "5900f3b31000cf542c50fec6", "challengeType": 5, "type": "bonfire", "title": "Problem 71: Ordered fractions", @@ -2479,7 +2479,7 @@ ] }, { - "_id": "5900f3b41000cf542c50fec7", + "id": "5900f3b41000cf542c50fec7", "challengeType": 5, "type": "bonfire", "title": "Problem 72: Counting fractions", @@ -2505,7 +2505,7 @@ ] }, { - "_id": "5900f3b61000cf542c50fec8", + "id": "5900f3b61000cf542c50fec8", "challengeType": 5, "type": "bonfire", "title": "Problem 73: Counting fractions in a range", @@ -2531,7 +2531,7 @@ ] }, { - "_id": "5900f3b61000cf542c50fec9", + "id": "5900f3b61000cf542c50fec9", "challengeType": 5, "type": "bonfire", "title": "Problem 74: Digit factorial chains", @@ -2564,7 +2564,7 @@ ] }, { - "_id": "5900f3b71000cf542c50feca", + "id": "5900f3b71000cf542c50feca", "challengeType": 5, "type": "bonfire", "title": "Problem 75: Singular integer right triangles", @@ -2590,7 +2590,7 @@ ] }, { - "_id": "5900f3b81000cf542c50fecb", + "id": "5900f3b81000cf542c50fecb", "challengeType": 5, "type": "bonfire", "title": "Problem 76: Counting summations", @@ -2619,7 +2619,7 @@ ] }, { - "_id": "5900f3b91000cf542c50fecc", + "id": "5900f3b91000cf542c50fecc", "challengeType": 5, "type": "bonfire", "title": "Problem 77: Prime summations", @@ -2647,7 +2647,7 @@ ] }, { - "_id": "5900f3ba1000cf542c50fecd", + "id": "5900f3ba1000cf542c50fecd", "challengeType": 5, "type": "bonfire", "title": "Problem 78: Coin partitions", @@ -2679,7 +2679,7 @@ ] }, { - "_id": "5900f3bb1000cf542c50fece", + "id": "5900f3bb1000cf542c50fece", "challengeType": 5, "type": "bonfire", "title": "Problem 79: Passcode derivation", @@ -2703,7 +2703,7 @@ ] }, { - "_id": "5900f3bc1000cf542c50fecf", + "id": "5900f3bc1000cf542c50fecf", "challengeType": 5, "type": "bonfire", "title": "Problem 80: Square root digital expansion", @@ -2727,7 +2727,7 @@ ] }, { - "_id": "5900f3bd1000cf542c50fed0", + "id": "5900f3bd1000cf542c50fed0", "challengeType": 5, "type": "bonfire", "title": "Problem 81: Path sum: two ways", @@ -2761,7 +2761,7 @@ ] }, { - "_id": "5900f3be1000cf542c50fed1", + "id": "5900f3be1000cf542c50fed1", "challengeType": 5, "type": "bonfire", "title": "Problem 82: Path sum: three ways", @@ -2796,7 +2796,7 @@ ] }, { - "_id": "5900f3bf1000cf542c50fed2", + "id": "5900f3bf1000cf542c50fed2", "challengeType": 5, "type": "bonfire", "title": "Problem 83: Path sum: four ways", @@ -2832,7 +2832,7 @@ ] }, { - "_id": "5900f3c11000cf542c50fed3", + "id": "5900f3c11000cf542c50fed3", "challengeType": 5, "type": "bonfire", "title": "Problem 84: Monopoly odds", @@ -2928,7 +2928,7 @@ ] }, { - "_id": "5900f3c11000cf542c50fed4", + "id": "5900f3c11000cf542c50fed4", "challengeType": 5, "type": "bonfire", "title": "Problem 85: Counting rectangles", @@ -2953,7 +2953,7 @@ ] }, { - "_id": "5900f3c31000cf542c50fed5", + "id": "5900f3c31000cf542c50fed5", "challengeType": 5, "type": "bonfire", "title": "Problem 86: Cuboid route", @@ -2980,7 +2980,7 @@ ] }, { - "_id": "5900f3c51000cf542c50fed8", + "id": "5900f3c51000cf542c50fed8", "challengeType": 5, "type": "bonfire", "title": "Problem 87: Prime power triples", @@ -3007,7 +3007,7 @@ ] }, { - "_id": "5900f3c51000cf542c50fed6", + "id": "5900f3c51000cf542c50fed6", "challengeType": 5, "type": "bonfire", "title": "Problem 88: Product-sum numbers", @@ -3035,7 +3035,7 @@ ] }, { - "_id": "5900f3c51000cf542c50fed7", + "id": "5900f3c51000cf542c50fed7", "challengeType": 5, "type": "bonfire", "title": "Problem 89: Roman numerals", @@ -3068,7 +3068,7 @@ ] }, { - "_id": "5900f3c61000cf542c50fed9", + "id": "5900f3c61000cf542c50fed9", "challengeType": 5, "type": "bonfire", "title": "Problem 90: Cube digit pairs", @@ -3110,7 +3110,7 @@ ] }, { - "_id": "5900f3c71000cf542c50feda", + "id": "5900f3c71000cf542c50feda", "challengeType": 5, "type": "bonfire", "title": "Problem 91: Right triangles with integer coordinates", @@ -3142,7 +3142,7 @@ ] }, { - "_id": "5900f3c81000cf542c50fedb", + "id": "5900f3c81000cf542c50fedb", "challengeType": 5, "type": "bonfire", "title": "Problem 92: Square digit chains", @@ -3169,7 +3169,7 @@ ] }, { - "_id": "5900f3ca1000cf542c50fedc", + "id": "5900f3ca1000cf542c50fedc", "challengeType": 5, "type": "bonfire", "title": "Problem 93: Arithmetic expressions", @@ -3199,7 +3199,7 @@ ] }, { - "_id": "5900f3ca1000cf542c50fedd", + "id": "5900f3ca1000cf542c50fedd", "challengeType": 5, "type": "bonfire", "title": "Problem 94: Almost equilateral triangles", @@ -3223,7 +3223,7 @@ ] }, { - "_id": "5900f3cc1000cf542c50fede", + "id": "5900f3cc1000cf542c50fede", "challengeType": 5, "type": "bonfire", "title": "Problem 95: Amicable chains", @@ -3250,7 +3250,7 @@ ] }, { - "_id": "5900f3cc1000cf542c50fedf", + "id": "5900f3cc1000cf542c50fedf", "challengeType": 5, "type": "bonfire", "title": "Problem 96: Su Doku", @@ -3300,7 +3300,7 @@ ] }, { - "_id": "5900f3ce1000cf542c50fee0", + "id": "5900f3ce1000cf542c50fee0", "challengeType": 5, "type": "bonfire", "title": "Problem 97: Large non-Mersenne prime", @@ -3324,7 +3324,7 @@ ] }, { - "_id": "5900f3cf1000cf542c50fee1", + "id": "5900f3cf1000cf542c50fee1", "challengeType": 5, "type": "bonfire", "title": "Problem 98: Anagramic squares", @@ -3349,7 +3349,7 @@ ] }, { - "_id": "5900f3d01000cf542c50fee2", + "id": "5900f3d01000cf542c50fee2", "challengeType": 5, "type": "bonfire", "title": "Problem 99: Largest exponential", @@ -3374,7 +3374,7 @@ ] }, { - "_id": "5900f3d01000cf542c50fee3", + "id": "5900f3d01000cf542c50fee3", "challengeType": 5, "type": "bonfire", "title": "Problem 100: Arranged probability", @@ -3398,7 +3398,7 @@ ] }, { - "_id": "5900f3d21000cf542c50fee4", + "id": "5900f3d21000cf542c50fee4", "challengeType": 5, "type": "bonfire", "title": "Problem 101: Optimum polynomial", @@ -3440,7 +3440,7 @@ ] }, { - "_id": "5900f3d21000cf542c50fee5", + "id": "5900f3d21000cf542c50fee5", "challengeType": 5, "type": "bonfire", "title": "Problem 102: Triangle containment", @@ -3468,7 +3468,7 @@ ] }, { - "_id": "5900f3d61000cf542c50fee7", + "id": "5900f3d61000cf542c50fee7", "challengeType": 5, "type": "bonfire", "title": "Problem 103: Special subset sums: optimum", @@ -3498,7 +3498,7 @@ ] }, { - "_id": "5900f3d51000cf542c50fee6", + "id": "5900f3d51000cf542c50fee6", "challengeType": 5, "type": "bonfire", "title": "Problem 104: Pandigital Fibonacci ends", @@ -3523,7 +3523,7 @@ ] }, { - "_id": "5900f3d61000cf542c50fee8", + "id": "5900f3d61000cf542c50fee8", "challengeType": 5, "type": "bonfire", "title": "Problem 105: Special subset sums: testing", @@ -3550,7 +3550,7 @@ ] }, { - "_id": "5900f3d71000cf542c50fee9", + "id": "5900f3d71000cf542c50fee9", "challengeType": 5, "type": "bonfire", "title": "Problem 106: Special subset sums: meta-testing", @@ -3578,7 +3578,7 @@ ] }, { - "_id": "5900f3d91000cf542c50feea", + "id": "5900f3d91000cf542c50feea", "challengeType": 5, "type": "bonfire", "title": "Problem 107: Minimal network", @@ -3615,7 +3615,7 @@ ] }, { - "_id": "5900f3d91000cf542c50feeb", + "id": "5900f3d91000cf542c50feeb", "challengeType": 5, "type": "bonfire", "title": "Problem 108: About Project Euler", @@ -3637,7 +3637,7 @@ ] }, { - "_id": "5900f3db1000cf542c50feec", + "id": "5900f3db1000cf542c50feec", "challengeType": 5, "type": "bonfire", "title": "Problem 109: Darts", @@ -3705,7 +3705,7 @@ ] }, { - "_id": "5900f3db1000cf542c50feed", + "id": "5900f3db1000cf542c50feed", "challengeType": 5, "type": "bonfire", "title": "Problem 110: About Project Euler", @@ -3727,7 +3727,7 @@ ] }, { - "_id": "5900f3db1000cf542c50feee", + "id": "5900f3db1000cf542c50feee", "challengeType": 5, "type": "bonfire", "title": "Problem 111: Primes with runs", @@ -3801,7 +3801,7 @@ ] }, { - "_id": "5900f3dd1000cf542c50feef", + "id": "5900f3dd1000cf542c50feef", "challengeType": 5, "type": "bonfire", "title": "Problem 112: Bouncy numbers", @@ -3828,7 +3828,7 @@ ] }, { - "_id": "5900f3dd1000cf542c50fef0", + "id": "5900f3dd1000cf542c50fef0", "challengeType": 5, "type": "bonfire", "title": "Problem 113: Non-bouncy numbers", @@ -3854,7 +3854,7 @@ ] }, { - "_id": "5900f3e01000cf542c50fef2", + "id": "5900f3e01000cf542c50fef2", "challengeType": 5, "type": "bonfire", "title": "Problem 114: Counting block combinations I", @@ -3979,7 +3979,7 @@ ] }, { - "_id": "5900f3df1000cf542c50fef1", + "id": "5900f3df1000cf542c50fef1", "challengeType": 5, "type": "bonfire", "title": "Problem 115: Counting block combinations II", @@ -4007,7 +4007,7 @@ ] }, { - "_id": "5900f3e01000cf542c50fef3", + "id": "5900f3e01000cf542c50fef3", "challengeType": 5, "type": "bonfire", "title": "Problem 116: Red, green or blue tiles", @@ -4102,7 +4102,7 @@ ] }, { - "_id": "5900f3e21000cf542c50fef4", + "id": "5900f3e21000cf542c50fef4", "challengeType": 5, "type": "bonfire", "title": "Problem 117: Red, green, and blue tiles", @@ -4205,7 +4205,7 @@ ] }, { - "_id": "5900f3e21000cf542c50fef5", + "id": "5900f3e21000cf542c50fef5", "challengeType": 5, "type": "bonfire", "title": "Problem 118: Pandigital prime sets", @@ -4228,7 +4228,7 @@ ] }, { - "_id": "5900f3e41000cf542c50fef6", + "id": "5900f3e41000cf542c50fef6", "challengeType": 5, "type": "bonfire", "title": "Problem 119: Digit power sum", @@ -4253,7 +4253,7 @@ ] }, { - "_id": "5900f3e41000cf542c50fef7", + "id": "5900f3e41000cf542c50fef7", "challengeType": 5, "type": "bonfire", "title": "Problem 120: Square remainders", @@ -4277,7 +4277,7 @@ ] }, { - "_id": "5900f3e51000cf542c50fef8", + "id": "5900f3e51000cf542c50fef8", "challengeType": 5, "type": "bonfire", "title": "Problem 121: Disc game prize fund", @@ -4302,7 +4302,7 @@ ] }, { - "_id": "5900f3e61000cf542c50fef9", + "id": "5900f3e61000cf542c50fef9", "challengeType": 5, "type": "bonfire", "title": "Problem 122: Efficient exponentiation", @@ -4331,7 +4331,7 @@ ] }, { - "_id": "5900f3e71000cf542c50fefa", + "id": "5900f3e71000cf542c50fefa", "challengeType": 5, "type": "bonfire", "title": "Problem 123: Prime square remainders", @@ -4356,7 +4356,7 @@ ] }, { - "_id": "5900f3e81000cf542c50fefb", + "id": "5900f3e81000cf542c50fefb", "challengeType": 5, "type": "bonfire", "title": "Problem 124: Ordered radicals", @@ -4420,7 +4420,7 @@ ] }, { - "_id": "5900f3e91000cf542c50fefc", + "id": "5900f3e91000cf542c50fefc", "challengeType": 5, "type": "bonfire", "title": "Problem 125: Palindromic sums", @@ -4444,7 +4444,7 @@ ] }, { - "_id": "5900f3ea1000cf542c50fefd", + "id": "5900f3ea1000cf542c50fefd", "challengeType": 5, "type": "bonfire", "title": "Problem 126: Cuboid layers", @@ -4473,7 +4473,7 @@ ] }, { - "_id": "5900f3ec1000cf542c50fefe", + "id": "5900f3ec1000cf542c50fefe", "challengeType": 5, "type": "bonfire", "title": "Problem 127: abc-hits", @@ -4507,7 +4507,7 @@ ] }, { - "_id": "5900f3ec1000cf542c50feff", + "id": "5900f3ec1000cf542c50feff", "challengeType": 5, "type": "bonfire", "title": "Problem 128: Hexagonal tile differences", @@ -4538,7 +4538,7 @@ ] }, { - "_id": "5900f3ef1000cf542c50ff01", + "id": "5900f3ef1000cf542c50ff01", "challengeType": 5, "type": "bonfire", "title": "Problem 129: Repunit divisibility", @@ -4563,7 +4563,7 @@ ] }, { - "_id": "5900f3ee1000cf542c50ff00", + "id": "5900f3ee1000cf542c50ff00", "challengeType": 5, "type": "bonfire", "title": "Problem 130: Composites with prime repunit property", @@ -4589,7 +4589,7 @@ ] }, { - "_id": "5900f3ef1000cf542c50ff02", + "id": "5900f3ef1000cf542c50ff02", "challengeType": 5, "type": "bonfire", "title": "Problem 131: Prime cube partnership", @@ -4614,7 +4614,7 @@ ] }, { - "_id": "5900f3f11000cf542c50ff03", + "id": "5900f3f11000cf542c50ff03", "challengeType": 5, "type": "bonfire", "title": "Problem 132: Large repunit factors", @@ -4638,7 +4638,7 @@ ] }, { - "_id": "5900f3f21000cf542c50ff04", + "id": "5900f3f21000cf542c50ff04", "challengeType": 5, "type": "bonfire", "title": "Problem 133: Repunit nonfactors", @@ -4663,7 +4663,7 @@ ] }, { - "_id": "5900f3f21000cf542c50ff05", + "id": "5900f3f21000cf542c50ff05", "challengeType": 5, "type": "bonfire", "title": "Problem 134: Prime pair connection", @@ -4687,7 +4687,7 @@ ] }, { - "_id": "5900f3f31000cf542c50ff06", + "id": "5900f3f31000cf542c50ff06", "challengeType": 5, "type": "bonfire", "title": "Problem 135: Same differences", @@ -4712,7 +4712,7 @@ ] }, { - "_id": "5900f3f51000cf542c50ff07", + "id": "5900f3f51000cf542c50ff07", "challengeType": 5, "type": "bonfire", "title": "Problem 136: Singleton difference", @@ -4737,7 +4737,7 @@ ] }, { - "_id": "5900f3f51000cf542c50ff08", + "id": "5900f3f51000cf542c50ff08", "challengeType": 5, "type": "bonfire", "title": "Problem 137: Fibonacci golden nuggets", @@ -4780,7 +4780,7 @@ ] }, { - "_id": "5900f3f61000cf542c50ff09", + "id": "5900f3f61000cf542c50ff09", "challengeType": 5, "type": "bonfire", "title": "Problem 138: Special isosceles triangles", @@ -4807,7 +4807,7 @@ ] }, { - "_id": "5900f3f71000cf542c50ff0a", + "id": "5900f3f71000cf542c50ff0a", "challengeType": 5, "type": "bonfire", "title": "Problem 139: Pythagorean tiles", @@ -4834,7 +4834,7 @@ ] }, { - "_id": "5900f3fa1000cf542c50ff0c", + "id": "5900f3fa1000cf542c50ff0c", "challengeType": 5, "type": "bonfire", "title": "Problem 140: Modified Fibonacci golden nuggets", @@ -4868,7 +4868,7 @@ ] }, { - "_id": "5900f3f91000cf542c50ff0b", + "id": "5900f3f91000cf542c50ff0b", "challengeType": 5, "type": "bonfire", "title": "Problem 141: Investigating progressive numbers, n, which are also square", @@ -4894,7 +4894,7 @@ ] }, { - "_id": "5900f3fa1000cf542c50ff0d", + "id": "5900f3fa1000cf542c50ff0d", "challengeType": 5, "type": "bonfire", "title": "Problem 142: Perfect Square Collection", @@ -4916,7 +4916,7 @@ ] }, { - "_id": "5900f3fc1000cf542c50ff0e", + "id": "5900f3fc1000cf542c50ff0e", "challengeType": 5, "type": "bonfire", "title": "Problem 143: Investigating the Torricelli point of a triangle", @@ -4943,7 +4943,7 @@ ] }, { - "_id": "5900f3fc1000cf542c50ff0f", + "id": "5900f3fc1000cf542c50ff0f", "challengeType": 5, "type": "bonfire", "title": "Problem 144: Investigating multiple reflections of a laser beam", @@ -4974,7 +4974,7 @@ ] }, { - "_id": "5900f3fd1000cf542c50ff10", + "id": "5900f3fd1000cf542c50ff10", "challengeType": 5, "type": "bonfire", "title": "Problem 145: How many reversible numbers are there below one-billion?", @@ -5000,7 +5000,7 @@ ] }, { - "_id": "5900f3fe1000cf542c50ff11", + "id": "5900f3fe1000cf542c50ff11", "challengeType": 5, "type": "bonfire", "title": "Problem 146: Investigating a Prime Pattern", @@ -5024,7 +5024,7 @@ ] }, { - "_id": "5900f3ff1000cf542c50ff12", + "id": "5900f3ff1000cf542c50ff12", "challengeType": 5, "type": "bonfire", "title": "Problem 147: Rectangles in cross-hatched grids", @@ -5057,7 +5057,7 @@ ] }, { - "_id": "5900f4021000cf542c50ff14", + "id": "5900f4021000cf542c50ff14", "challengeType": 5, "type": "bonfire", "title": "Problem 148: Exploring Pascal's triangle", @@ -5152,7 +5152,7 @@ ] }, { - "_id": "5900f4021000cf542c50ff13", + "id": "5900f4021000cf542c50ff13", "challengeType": 5, "type": "bonfire", "title": "Problem 149: Searching for a maximum-sum subsequence", @@ -5190,7 +5190,7 @@ ] }, { - "_id": "5900f4031000cf542c50ff15", + "id": "5900f4031000cf542c50ff15", "challengeType": 5, "type": "bonfire", "title": "Problem 150: Searching a triangular array for a sub-triangle having minimum-sum", @@ -5237,7 +5237,7 @@ ] }, { - "_id": "5900f4031000cf542c50ff16", + "id": "5900f4031000cf542c50ff16", "challengeType": 5, "type": "bonfire", "title": "Problem 151: Paper sheets of standard sizes: an expected-value problem", @@ -5266,7 +5266,7 @@ ] }, { - "_id": "5900f4041000cf542c50ff17", + "id": "5900f4041000cf542c50ff17", "challengeType": 5, "type": "bonfire", "title": "Problem 152: Writing 1/2 as a sum of inverse squares", @@ -5292,7 +5292,7 @@ ] }, { - "_id": "5900f4051000cf542c50ff18", + "id": "5900f4051000cf542c50ff18", "challengeType": 5, "type": "bonfire", "title": "Problem 153: Investigating Gaussian Integers", @@ -5358,7 +5358,7 @@ ] }, { - "_id": "5900f4071000cf542c50ff19", + "id": "5900f4071000cf542c50ff19", "challengeType": 5, "type": "bonfire", "title": "Problem 154: Exploring Pascal's pyramid", @@ -5387,7 +5387,7 @@ ] }, { - "_id": "5900f4081000cf542c50ff1a", + "id": "5900f4081000cf542c50ff1a", "challengeType": 5, "type": "bonfire", "title": "Problem 155: Counting Capacitor Circuits", @@ -5418,7 +5418,7 @@ ] }, { - "_id": "5900f4091000cf542c50ff1b", + "id": "5900f4091000cf542c50ff1b", "challengeType": 5, "type": "bonfire", "title": "Problem 156: Counting Digits", @@ -5472,7 +5472,7 @@ ] }, { - "_id": "5900f4091000cf542c50ff1c", + "id": "5900f4091000cf542c50ff1c", "challengeType": 5, "type": "bonfire", "title": "Problem 157: Solving the diophantine equation 1/a+1/b= p/10n", @@ -5516,7 +5516,7 @@ ] }, { - "_id": "5900f40a1000cf542c50ff1d", + "id": "5900f40a1000cf542c50ff1d", "challengeType": 5, "type": "bonfire", "title": "Problem 158: Exploring strings for which only one character comes lexicographically after its neighbour to the left", @@ -5545,7 +5545,7 @@ ] }, { - "_id": "5900f40c1000cf542c50ff1e", + "id": "5900f40c1000cf542c50ff1e", "challengeType": 5, "type": "bonfire", "title": "Problem 159: Digital root sums of factorisations", @@ -5592,7 +5592,7 @@ ] }, { - "_id": "5900f40d1000cf542c50ff1f", + "id": "5900f40d1000cf542c50ff1f", "challengeType": 5, "type": "bonfire", "title": "Problem 160: Factorial trailing digits", @@ -5619,7 +5619,7 @@ ] }, { - "_id": "5900f40d1000cf542c50ff20", + "id": "5900f40d1000cf542c50ff20", "challengeType": 5, "type": "bonfire", "title": "Problem 161: Triominoes", @@ -5655,7 +5655,7 @@ ] }, { - "_id": "5900f40e1000cf542c50ff21", + "id": "5900f40e1000cf542c50ff21", "challengeType": 5, "type": "bonfire", "title": "Problem 162: Hexadecimal numbers", @@ -5684,7 +5684,7 @@ ] }, { - "_id": "5900f40f1000cf542c50ff22", + "id": "5900f40f1000cf542c50ff22", "challengeType": 5, "type": "bonfire", "title": "Problem 163: Cross-hatched triangles", @@ -5713,7 +5713,7 @@ ] }, { - "_id": "5900f4111000cf542c50ff23", + "id": "5900f4111000cf542c50ff23", "challengeType": 5, "type": "bonfire", "title": "Problem 164: Numbers for which no three consecutive digits have a sum greater than a given value", @@ -5735,7 +5735,7 @@ ] }, { - "_id": "5900f4111000cf542c50ff24", + "id": "5900f4111000cf542c50ff24", "challengeType": 5, "type": "bonfire", "title": "Problem 165: Intersections", @@ -5774,7 +5774,7 @@ ] }, { - "_id": "5900f4131000cf542c50ff25", + "id": "5900f4131000cf542c50ff25", "challengeType": 5, "type": "bonfire", "title": "Problem 166: Criss Cross", @@ -5808,7 +5808,7 @@ ] }, { - "_id": "5900f4141000cf542c50ff26", + "id": "5900f4141000cf542c50ff26", "challengeType": 5, "type": "bonfire", "title": "Problem 167: Investigating Ulam sequences", @@ -5835,7 +5835,7 @@ ] }, { - "_id": "5900f4151000cf542c50ff27", + "id": "5900f4151000cf542c50ff27", "challengeType": 5, "type": "bonfire", "title": "Problem 168: Number Rotations", @@ -5860,7 +5860,7 @@ ] }, { - "_id": "5900f4151000cf542c50ff28", + "id": "5900f4151000cf542c50ff28", "challengeType": 5, "type": "bonfire", "title": "Problem 169: Exploring the number of different ways a number can be expressed as a sum of powers of 2", @@ -5888,7 +5888,7 @@ ] }, { - "_id": "5900f4161000cf542c50ff29", + "id": "5900f4161000cf542c50ff29", "challengeType": 5, "type": "bonfire", "title": "Problem 170: Find the largest 0 to 9 pandigital that can be formed by concatenating products", @@ -5919,7 +5919,7 @@ ] }, { - "_id": "5900f4181000cf542c50ff2a", + "id": "5900f4181000cf542c50ff2a", "challengeType": 5, "type": "bonfire", "title": "Problem 171: Finding numbers for which the sum of the squares of the digits is a square", @@ -5945,7 +5945,7 @@ ] }, { - "_id": "5900f4181000cf542c50ff2b", + "id": "5900f4181000cf542c50ff2b", "challengeType": 5, "type": "bonfire", "title": "Problem 172: Investigating numbers with few repeated digits", @@ -5967,7 +5967,7 @@ ] }, { - "_id": "5900f41a1000cf542c50ff2c", + "id": "5900f41a1000cf542c50ff2c", "challengeType": 5, "type": "bonfire", "title": "Problem 173: Using up to one million tiles how many different \"hollow\" square laminae can be formed?", @@ -5993,7 +5993,7 @@ ] }, { - "_id": "5900f41a1000cf542c50ff2d", + "id": "5900f41a1000cf542c50ff2d", "challengeType": 5, "type": "bonfire", "title": "Problem 174: Counting the number of \"hollow\" square laminae that can form one, two, three, ... distinct arrangements", @@ -6021,7 +6021,7 @@ ] }, { - "_id": "5900f41c1000cf542c50ff2e", + "id": "5900f41c1000cf542c50ff2e", "challengeType": 5, "type": "bonfire", "title": "Problem 175: Fractions involving the number of different ways a number can be expressed as a sum of powers of 2", @@ -6052,7 +6052,7 @@ ] }, { - "_id": "5900f41c1000cf542c50ff2f", + "id": "5900f41c1000cf542c50ff2f", "challengeType": 5, "type": "bonfire", "title": "Problem 176: Right-angled triangles that share a cathetus", @@ -6075,7 +6075,7 @@ ] }, { - "_id": "5900f41e1000cf542c50ff30", + "id": "5900f41e1000cf542c50ff30", "challengeType": 5, "type": "bonfire", "title": "Problem 177: Integer angled Quadrilaterals", @@ -6102,7 +6102,7 @@ ] }, { - "_id": "5900f41e1000cf542c50ff31", + "id": "5900f41e1000cf542c50ff31", "challengeType": 5, "type": "bonfire", "title": "Problem 178: Step Numbers", @@ -6129,7 +6129,7 @@ ] }, { - "_id": "5900f41f1000cf542c50ff32", + "id": "5900f41f1000cf542c50ff32", "challengeType": 5, "type": "bonfire", "title": "Problem 179: Consecutive positive divisors", @@ -6151,7 +6151,7 @@ ] }, { - "_id": "5900f4201000cf542c50ff33", + "id": "5900f4201000cf542c50ff33", "challengeType": 5, "type": "bonfire", "title": "Problem 180: Rational zeros of a function of three variables", @@ -6181,7 +6181,7 @@ ] }, { - "_id": "5900f4231000cf542c50ff34", + "id": "5900f4231000cf542c50ff34", "challengeType": 5, "type": "bonfire", "title": "Problem 181: Investigating in how many ways objects of two different colours can be grouped", @@ -6206,7 +6206,7 @@ ] }, { - "_id": "5900f4231000cf542c50ff35", + "id": "5900f4231000cf542c50ff35", "challengeType": 5, "type": "bonfire", "title": "Problem 182: RSA encryption", @@ -6242,7 +6242,7 @@ ] }, { - "_id": "5900f4231000cf542c50ff36", + "id": "5900f4231000cf542c50ff36", "challengeType": 5, "type": "bonfire", "title": "Problem 183: Maximum product of parts", @@ -6279,7 +6279,7 @@ ] }, { - "_id": "5900f4241000cf542c50ff37", + "id": "5900f4241000cf542c50ff37", "challengeType": 5, "type": "bonfire", "title": "Problem 184: Triangles containing the origin", @@ -6307,7 +6307,7 @@ ] }, { - "_id": "5900f4251000cf542c50ff38", + "id": "5900f4251000cf542c50ff38", "challengeType": 5, "type": "bonfire", "title": "Problem 185: Number Mind", @@ -6366,7 +6366,7 @@ ] }, { - "_id": "5900f4281000cf542c50ff39", + "id": "5900f4281000cf542c50ff39", "challengeType": 5, "type": "bonfire", "title": "Problem 186: Connectedness of a network", @@ -6400,7 +6400,7 @@ ] }, { - "_id": "5900f4291000cf542c50ff3a", + "id": "5900f4291000cf542c50ff3a", "challengeType": 5, "type": "bonfire", "title": "Problem 187: Semiprimes", @@ -6427,7 +6427,7 @@ ] }, { - "_id": "5900f4291000cf542c50ff3b", + "id": "5900f4291000cf542c50ff3b", "challengeType": 5, "type": "bonfire", "title": "Problem 188: The hyperexponentiation of a number", @@ -6454,7 +6454,7 @@ ] }, { - "_id": "5900f4291000cf542c50ff3c", + "id": "5900f4291000cf542c50ff3c", "challengeType": 5, "type": "bonfire", "title": "Problem 189: Tri-colouring a triangular grid", @@ -6488,7 +6488,7 @@ ] }, { - "_id": "5900f42b1000cf542c50ff3d", + "id": "5900f42b1000cf542c50ff3d", "challengeType": 5, "type": "bonfire", "title": "Problem 190: Maximising a weighted product", @@ -6514,7 +6514,7 @@ ] }, { - "_id": "5900f42b1000cf542c50ff3e", + "id": "5900f42b1000cf542c50ff3e", "challengeType": 5, "type": "bonfire", "title": "Problem 191: Prize Strings", @@ -6548,7 +6548,7 @@ ] }, { - "_id": "5900f42c1000cf542c50ff3f", + "id": "5900f42c1000cf542c50ff3f", "challengeType": 5, "type": "bonfire", "title": "Problem 192: Best Approximations", @@ -6577,7 +6577,7 @@ ] }, { - "_id": "5900f42f1000cf542c50ff41", + "id": "5900f42f1000cf542c50ff41", "challengeType": 5, "type": "bonfire", "title": "Problem 193: Squarefree Numbers", @@ -6601,7 +6601,7 @@ ] }, { - "_id": "5900f42f1000cf542c50ff40", + "id": "5900f42f1000cf542c50ff40", "challengeType": 5, "type": "bonfire", "title": "Problem 194: Coloured Configurations", @@ -6633,7 +6633,7 @@ ] }, { - "_id": "5900f4311000cf542c50ff43", + "id": "5900f4311000cf542c50ff43", "challengeType": 5, "type": "bonfire", "title": "Problem 195: Inscribed circles of triangles with one angle of 60 degrees", @@ -6661,7 +6661,7 @@ ] }, { - "_id": "5900f4301000cf542c50ff42", + "id": "5900f4301000cf542c50ff42", "challengeType": 5, "type": "bonfire", "title": "Problem 196: Prime triplets", @@ -6709,7 +6709,7 @@ ] }, { - "_id": "5900f4311000cf542c50ff44", + "id": "5900f4311000cf542c50ff44", "challengeType": 5, "type": "bonfire", "title": "Problem 197: Investigating the behaviour of a recursively defined sequence", @@ -6735,7 +6735,7 @@ ] }, { - "_id": "5900f4331000cf542c50ff45", + "id": "5900f4331000cf542c50ff45", "challengeType": 5, "type": "bonfire", "title": "Problem 198: Ambiguous Numbers", @@ -6763,7 +6763,7 @@ ] }, { - "_id": "5900f4341000cf542c50ff46", + "id": "5900f4341000cf542c50ff46", "challengeType": 5, "type": "bonfire", "title": "Problem 199: Iterative Circle Packing", @@ -6793,7 +6793,7 @@ ] }, { - "_id": "5900f4351000cf542c50ff47", + "id": "5900f4351000cf542c50ff47", "challengeType": 5, "type": "bonfire", "title": "Problem 200: Find the 200th prime-proof sqube containing the contiguous sub-string \"200\"", @@ -6822,7 +6822,7 @@ ] }, { - "_id": "5900f4361000cf542c50ff48", + "id": "5900f4361000cf542c50ff48", "challengeType": 5, "type": "bonfire", "title": "Problem 201: Subsets with a unique sum", @@ -6875,7 +6875,7 @@ ] }, { - "_id": "5900f4371000cf542c50ff49", + "id": "5900f4371000cf542c50ff49", "challengeType": 5, "type": "bonfire", "title": "Problem 202: Laserbeam", @@ -6906,7 +6906,7 @@ ] }, { - "_id": "5900f4381000cf542c50ff4a", + "id": "5900f4381000cf542c50ff4a", "challengeType": 5, "type": "bonfire", "title": "Problem 203: Squarefree Binomial Coefficients", @@ -6941,7 +6941,7 @@ ] }, { - "_id": "5900f4381000cf542c50ff4b", + "id": "5900f4381000cf542c50ff4b", "challengeType": 5, "type": "bonfire", "title": "Problem 204: Generalised Hamming Numbers", @@ -6970,7 +6970,7 @@ ] }, { - "_id": "5900f4391000cf542c50ff4c", + "id": "5900f4391000cf542c50ff4c", "challengeType": 5, "type": "bonfire", "title": "Problem 205: Dice Game", @@ -6997,7 +6997,7 @@ ] }, { - "_id": "5900f43a1000cf542c50ff4d", + "id": "5900f43a1000cf542c50ff4d", "challengeType": 5, "type": "bonfire", "title": "Problem 206: Concealed Square", @@ -7019,7 +7019,7 @@ ] }, { - "_id": "5900f43c1000cf542c50ff4e", + "id": "5900f43c1000cf542c50ff4e", "challengeType": 5, "type": "bonfire", "title": "Problem 207: Integer partition equations", @@ -7062,7 +7062,7 @@ ] }, { - "_id": "5900f43f1000cf542c50ff51", + "id": "5900f43f1000cf542c50ff51", "challengeType": 5, "type": "bonfire", "title": "Problem 208: Robot Walks", @@ -7091,7 +7091,7 @@ ] }, { - "_id": "5900f43e1000cf542c50ff4f", + "id": "5900f43e1000cf542c50ff4f", "challengeType": 5, "type": "bonfire", "title": "Problem 209: Circular Logic", @@ -7123,7 +7123,7 @@ ] }, { - "_id": "5900f43e1000cf542c50ff50", + "id": "5900f43e1000cf542c50ff50", "challengeType": 5, "type": "bonfire", "title": "Problem 210: Obtuse Angled Triangles", @@ -7150,7 +7150,7 @@ ] }, { - "_id": "5900f43f1000cf542c50ff52", + "id": "5900f43f1000cf542c50ff52", "challengeType": 5, "type": "bonfire", "title": "Problem 211: Divisor Square Sum", @@ -7174,7 +7174,7 @@ ] }, { - "_id": "5900f4411000cf542c50ff53", + "id": "5900f4411000cf542c50ff53", "challengeType": 5, "type": "bonfire", "title": "Problem 212: Combined Volume of Cuboids", @@ -7210,7 +7210,7 @@ ] }, { - "_id": "5900f4411000cf542c50ff54", + "id": "5900f4411000cf542c50ff54", "challengeType": 5, "type": "bonfire", "title": "Problem 213: Flea Circus", @@ -7235,7 +7235,7 @@ ] }, { - "_id": "5900f4421000cf542c50ff55", + "id": "5900f4421000cf542c50ff55", "challengeType": 5, "type": "bonfire", "title": "Problem 214: Totient Chains", @@ -7276,7 +7276,7 @@ ] }, { - "_id": "5900f4431000cf542c50ff56", + "id": "5900f4431000cf542c50ff56", "challengeType": 5, "type": "bonfire", "title": "Problem 215: Crack-free Walls", @@ -7307,7 +7307,7 @@ ] }, { - "_id": "5900f4451000cf542c50ff57", + "id": "5900f4451000cf542c50ff57", "challengeType": 5, "type": "bonfire", "title": "Problem 216: Investigating the primality of numbers of the form 2n2-1", @@ -7334,7 +7334,7 @@ ] }, { - "_id": "5900f4461000cf542c50ff58", + "id": "5900f4461000cf542c50ff58", "challengeType": 5, "type": "bonfire", "title": "Problem 217: Balanced Numbers", @@ -7360,7 +7360,7 @@ ] }, { - "_id": "5900f4461000cf542c50ff59", + "id": "5900f4461000cf542c50ff59", "challengeType": 5, "type": "bonfire", "title": "Problem 218: Perfect right-angled triangles", @@ -7396,7 +7396,7 @@ ] }, { - "_id": "5900f4481000cf542c50ff5a", + "id": "5900f4481000cf542c50ff5a", "challengeType": 5, "type": "bonfire", "title": "Problem 219: Skew-cost coding", @@ -7430,7 +7430,7 @@ ] }, { - "_id": "5900f4481000cf542c50ff5b", + "id": "5900f4481000cf542c50ff5b", "challengeType": 5, "type": "bonfire", "title": "Problem 220: Heighway Dragon", @@ -7467,7 +7467,7 @@ ] }, { - "_id": "5900f4491000cf542c50ff5c", + "id": "5900f4491000cf542c50ff5c", "challengeType": 5, "type": "bonfire", "title": "Problem 221: Alexandrian Integers", @@ -7508,7 +7508,7 @@ ] }, { - "_id": "5900f44b1000cf542c50ff5d", + "id": "5900f44b1000cf542c50ff5d", "challengeType": 5, "type": "bonfire", "title": "Problem 222: Sphere Packing", @@ -7532,7 +7532,7 @@ ] }, { - "_id": "5900f44b1000cf542c50ff5e", + "id": "5900f44b1000cf542c50ff5e", "challengeType": 5, "type": "bonfire", "title": "Problem 223: Almost right-angled triangles I", @@ -7556,7 +7556,7 @@ ] }, { - "_id": "5900f44e1000cf542c50ff5f", + "id": "5900f44e1000cf542c50ff5f", "challengeType": 5, "type": "bonfire", "title": "Problem 224: Almost right-angled triangles II", @@ -7580,7 +7580,7 @@ ] }, { - "_id": "5900f44e1000cf542c50ff60", + "id": "5900f44e1000cf542c50ff60", "challengeType": 5, "type": "bonfire", "title": "Problem 225: Tribonacci non-divisors", @@ -7608,7 +7608,7 @@ ] }, { - "_id": "5900f4511000cf542c50ff62", + "id": "5900f4511000cf542c50ff62", "challengeType": 5, "type": "bonfire", "title": "Problem 226: A Scoop of Blancmange", @@ -7639,7 +7639,7 @@ ] }, { - "_id": "5900f44f1000cf542c50ff61", + "id": "5900f44f1000cf542c50ff61", "challengeType": 5, "type": "bonfire", "title": "Problem 227: The Chase", @@ -7668,7 +7668,7 @@ ] }, { - "_id": "5900f4511000cf542c50ff63", + "id": "5900f4511000cf542c50ff63", "challengeType": 5, "type": "bonfire", "title": "Problem 228: Minkowski Sums", @@ -7712,7 +7712,7 @@ ] }, { - "_id": "5900f4521000cf542c50ff64", + "id": "5900f4521000cf542c50ff64", "challengeType": 5, "type": "bonfire", "title": "Problem 229: Four Representations using Squares", @@ -7752,7 +7752,7 @@ ] }, { - "_id": "5900f4531000cf542c50ff65", + "id": "5900f4531000cf542c50ff65", "challengeType": 5, "type": "bonfire", "title": "Problem 230: Fibonacci Words", @@ -7800,7 +7800,7 @@ ] }, { - "_id": "5900f4531000cf542c50ff66", + "id": "5900f4531000cf542c50ff66", "challengeType": 5, "type": "bonfire", "title": "Problem 231: The prime factorisation of binomial coefficients", @@ -7826,7 +7826,7 @@ ] }, { - "_id": "5900f4551000cf542c50ff67", + "id": "5900f4551000cf542c50ff67", "challengeType": 5, "type": "bonfire", "title": "Problem 232: The Race", @@ -7854,7 +7854,7 @@ ] }, { - "_id": "5900f4551000cf542c50ff68", + "id": "5900f4551000cf542c50ff68", "challengeType": 5, "type": "bonfire", "title": "Problem 233: Lattice points on a circle", @@ -7879,7 +7879,7 @@ ] }, { - "_id": "5900f4571000cf542c50ff69", + "id": "5900f4571000cf542c50ff69", "challengeType": 5, "type": "bonfire", "title": "Problem 234: Semidivisible numbers", @@ -7908,7 +7908,7 @@ ] }, { - "_id": "5900f4571000cf542c50ff6a", + "id": "5900f4571000cf542c50ff6a", "challengeType": 5, "type": "bonfire", "title": "Problem 235: An Arithmetic Geometric sequence", @@ -7937,7 +7937,7 @@ ] }, { - "_id": "5900f4591000cf542c50ff6b", + "id": "5900f4591000cf542c50ff6b", "challengeType": 5, "type": "bonfire", "title": "Problem 236: Luxury Hampers", @@ -7971,7 +7971,7 @@ ] }, { - "_id": "5900f4591000cf542c50ff6c", + "id": "5900f4591000cf542c50ff6c", "challengeType": 5, "type": "bonfire", "title": "Problem 237: Tours on a 4 x n playing board", @@ -8003,7 +8003,7 @@ ] }, { - "_id": "5900f45b1000cf542c50ff6d", + "id": "5900f45b1000cf542c50ff6d", "challengeType": 5, "type": "bonfire", "title": "Problem 238: Infinite string tour", @@ -8058,7 +8058,7 @@ ] }, { - "_id": "5900f45c1000cf542c50ff6e", + "id": "5900f45c1000cf542c50ff6e", "challengeType": 5, "type": "bonfire", "title": "Problem 239: Twenty-two Foolish Primes", @@ -8085,7 +8085,7 @@ ] }, { - "_id": "5900f45d1000cf542c50ff6f", + "id": "5900f45d1000cf542c50ff6f", "challengeType": 5, "type": "bonfire", "title": "Problem 240: Top Dice", @@ -8118,7 +8118,7 @@ ] }, { - "_id": "5900f45d1000cf542c50ff70", + "id": "5900f45d1000cf542c50ff70", "challengeType": 5, "type": "bonfire", "title": "Problem 241: Perfection Quotients", @@ -8148,7 +8148,7 @@ ] }, { - "_id": "5900f45f1000cf542c50ff71", + "id": "5900f45f1000cf542c50ff71", "challengeType": 5, "type": "bonfire", "title": "Problem 242: Odd Triplets", @@ -8178,7 +8178,7 @@ ] }, { - "_id": "5900f4601000cf542c50ff73", + "id": "5900f4601000cf542c50ff73", "challengeType": 5, "type": "bonfire", "title": "Problem 243: Resilience", @@ -8208,7 +8208,7 @@ ] }, { - "_id": "5900f4601000cf542c50ff72", + "id": "5900f4601000cf542c50ff72", "challengeType": 5, "type": "bonfire", "title": "Problem 244: Sliders", @@ -8255,7 +8255,7 @@ ] }, { - "_id": "5900f4621000cf542c50ff74", + "id": "5900f4621000cf542c50ff74", "challengeType": 5, "type": "bonfire", "title": "Problem 245: Coresilience", @@ -8287,7 +8287,7 @@ ] }, { - "_id": "5900f4621000cf542c50ff75", + "id": "5900f4621000cf542c50ff75", "challengeType": 5, "type": "bonfire", "title": "Problem 246: Tangents to an ellipse", @@ -8327,7 +8327,7 @@ ] }, { - "_id": "5900f4641000cf542c50ff76", + "id": "5900f4641000cf542c50ff76", "challengeType": 5, "type": "bonfire", "title": "Problem 247: Squares under a hyperbola", @@ -8364,7 +8364,7 @@ ] }, { - "_id": "5900f4651000cf542c50ff77", + "id": "5900f4651000cf542c50ff77", "challengeType": 5, "type": "bonfire", "title": "Problem 248: Numbers for which Euler’s totient function equals 13!", @@ -8387,7 +8387,7 @@ ] }, { - "_id": "5900f4671000cf542c50ff79", + "id": "5900f4671000cf542c50ff79", "challengeType": 5, "type": "bonfire", "title": "Problem 249: Prime Subset Sums", @@ -8411,7 +8411,7 @@ ] }, { - "_id": "5900f4661000cf542c50ff78", + "id": "5900f4661000cf542c50ff78", "challengeType": 5, "type": "bonfire", "title": "Problem 250: 250250", @@ -8433,7 +8433,7 @@ ] }, { - "_id": "5900f4671000cf542c50ff7a", + "id": "5900f4671000cf542c50ff7a", "challengeType": 5, "type": "bonfire", "title": "Problem 251: Cardano Triplets", @@ -8465,7 +8465,7 @@ ] }, { - "_id": "5900f4691000cf542c50ff7b", + "id": "5900f4691000cf542c50ff7b", "challengeType": 5, "type": "bonfire", "title": "Problem 252: Convex Holes", @@ -8513,7 +8513,7 @@ ] }, { - "_id": "5900f4691000cf542c50ff7c", + "id": "5900f4691000cf542c50ff7c", "challengeType": 5, "type": "bonfire", "title": "Problem 253: Tidying up", @@ -8553,7 +8553,7 @@ ] }, { - "_id": "5900f46b1000cf542c50ff7d", + "id": "5900f46b1000cf542c50ff7d", "challengeType": 5, "type": "bonfire", "title": "Problem 254: Sums of Digit Factorials", @@ -8585,7 +8585,7 @@ ] }, { - "_id": "5900f46d1000cf542c50ff7f", + "id": "5900f46d1000cf542c50ff7f", "challengeType": 5, "type": "bonfire", "title": "Problem 255: Rounded Square Roots", @@ -8630,7 +8630,7 @@ ] }, { - "_id": "5900f46c1000cf542c50ff7e", + "id": "5900f46c1000cf542c50ff7e", "challengeType": 5, "type": "bonfire", "title": "Problem 256: Tatami-Free Rooms", @@ -8677,7 +8677,7 @@ ] }, { - "_id": "5900f46e1000cf542c50ff80", + "id": "5900f46e1000cf542c50ff80", "challengeType": 5, "type": "bonfire", "title": "Problem 257: Angular Bisectors", @@ -8711,7 +8711,7 @@ ] }, { - "_id": "5900f46e1000cf542c50ff81", + "id": "5900f46e1000cf542c50ff81", "challengeType": 5, "type": "bonfire", "title": "Problem 258: A lagged Fibonacci sequence", @@ -8737,7 +8737,7 @@ ] }, { - "_id": "5900f4701000cf542c50ff82", + "id": "5900f4701000cf542c50ff82", "challengeType": 5, "type": "bonfire", "title": "Problem 259: Reachable Numbers", @@ -8769,7 +8769,7 @@ ] }, { - "_id": "5900f4701000cf542c50ff83", + "id": "5900f4701000cf542c50ff83", "challengeType": 5, "type": "bonfire", "title": "Problem 260: Stone Game", @@ -8810,7 +8810,7 @@ ] }, { - "_id": "5900f4711000cf542c50ff84", + "id": "5900f4711000cf542c50ff84", "challengeType": 5, "type": "bonfire", "title": "Problem 261: Pivotal Square Sums", @@ -8841,7 +8841,7 @@ ] }, { - "_id": "5900f4731000cf542c50ff85", + "id": "5900f4731000cf542c50ff85", "challengeType": 5, "type": "bonfire", "title": "Problem 262: Mountain Range", @@ -8878,7 +8878,7 @@ ] }, { - "_id": "5900f4741000cf542c50ff86", + "id": "5900f4741000cf542c50ff86", "challengeType": 5, "type": "bonfire", "title": "Problem 263: An engineers' dream come true", @@ -8919,7 +8919,7 @@ ] }, { - "_id": "5900f4751000cf542c50ff87", + "id": "5900f4751000cf542c50ff87", "challengeType": 5, "type": "bonfire", "title": "Problem 264: Triangle Centres", @@ -8961,7 +8961,7 @@ ] }, { - "_id": "5900f4761000cf542c50ff88", + "id": "5900f4761000cf542c50ff88", "challengeType": 5, "type": "bonfire", "title": "Problem 265: Binary Circles", @@ -8996,7 +8996,7 @@ ] }, { - "_id": "5900f4771000cf542c50ff89", + "id": "5900f4771000cf542c50ff89", "challengeType": 5, "type": "bonfire", "title": "Problem 266: Pseudo Square Root", @@ -9025,7 +9025,7 @@ ] }, { - "_id": "5900f4771000cf542c50ff8a", + "id": "5900f4771000cf542c50ff8a", "challengeType": 5, "type": "bonfire", "title": "Problem 267: Billionaire", @@ -9052,7 +9052,7 @@ ] }, { - "_id": "5900f4791000cf542c50ff8b", + "id": "5900f4791000cf542c50ff8b", "challengeType": 5, "type": "bonfire", "title": "Problem 268: Counting numbers with at least four distinct prime factors less than 100", @@ -9076,7 +9076,7 @@ ] }, { - "_id": "5900f4791000cf542c50ff8c", + "id": "5900f4791000cf542c50ff8c", "challengeType": 5, "type": "bonfire", "title": "Problem 269: Polynomials with at least one integer root", @@ -9108,7 +9108,7 @@ ] }, { - "_id": "5900f47c1000cf542c50ff8e", + "id": "5900f47c1000cf542c50ff8e", "challengeType": 5, "type": "bonfire", "title": "Problem 270: Cutting Squares", @@ -9137,7 +9137,7 @@ ] }, { - "_id": "5900f47b1000cf542c50ff8d", + "id": "5900f47b1000cf542c50ff8d", "challengeType": 5, "type": "bonfire", "title": "Problem 271: Modular Cubes, part 1", @@ -9165,7 +9165,7 @@ ] }, { - "_id": "5900f47d1000cf542c50ff8f", + "id": "5900f47d1000cf542c50ff8f", "challengeType": 5, "type": "bonfire", "title": "Problem 272: Modular Cubes, part 2", @@ -9193,7 +9193,7 @@ ] }, { - "_id": "5900f47e1000cf542c50ff90", + "id": "5900f47e1000cf542c50ff90", "challengeType": 5, "type": "bonfire", "title": "Problem 273: Sum of Squares", @@ -9221,7 +9221,7 @@ ] }, { - "_id": "5900f47f1000cf542c50ff91", + "id": "5900f47f1000cf542c50ff91", "challengeType": 5, "type": "bonfire", "title": "Problem 274: Divisibility Multipliers", @@ -9255,7 +9255,7 @@ ] }, { - "_id": "5900f4801000cf542c50ff92", + "id": "5900f4801000cf542c50ff92", "challengeType": 5, "type": "bonfire", "title": "Problem 275: Balanced Sculptures", @@ -9285,7 +9285,7 @@ ] }, { - "_id": "5900f4801000cf542c50ff93", + "id": "5900f4801000cf542c50ff93", "challengeType": 5, "type": "bonfire", "title": "Problem 276: Primitive Triangles", @@ -9309,7 +9309,7 @@ ] }, { - "_id": "5900f4811000cf542c50ff94", + "id": "5900f4811000cf542c50ff94", "challengeType": 5, "type": "bonfire", "title": "Problem 277: A Modified Collatz sequence", @@ -9355,7 +9355,7 @@ ] }, { - "_id": "5900f4831000cf542c50ff95", + "id": "5900f4831000cf542c50ff95", "challengeType": 5, "type": "bonfire", "title": "Problem 278: Linear Combinations of Semiprimes", @@ -9387,7 +9387,7 @@ ] }, { - "_id": "5900f4841000cf542c50ff96", + "id": "5900f4841000cf542c50ff96", "challengeType": 5, "type": "bonfire", "title": "Problem 279: Triangles with integral sides and an integral angle", @@ -9409,7 +9409,7 @@ ] }, { - "_id": "5900f4841000cf542c50ff97", + "id": "5900f4841000cf542c50ff97", "challengeType": 5, "type": "bonfire", "title": "Problem 280: Ant and seeds", @@ -9436,7 +9436,7 @@ ] }, { - "_id": "5900f4861000cf542c50ff98", + "id": "5900f4861000cf542c50ff98", "challengeType": 5, "type": "bonfire", "title": "Problem 281: Pizza Toppings", @@ -9466,7 +9466,7 @@ ] }, { - "_id": "5900f4861000cf542c50ff99", + "id": "5900f4861000cf542c50ff99", "challengeType": 5, "type": "bonfire", "title": "Problem 282: The Ackermann function", @@ -9495,7 +9495,7 @@ ] }, { - "_id": "5900f4881000cf542c50ff9a", + "id": "5900f4881000cf542c50ff9a", "challengeType": 5, "type": "bonfire", "title": "Problem 283: Integer sided triangles for which the area/perimeter ratio is integral", @@ -9523,7 +9523,7 @@ ] }, { - "_id": "5900f4891000cf542c50ff9b", + "id": "5900f4891000cf542c50ff9b", "challengeType": 5, "type": "bonfire", "title": "Problem 284: Steady Squares", @@ -9552,7 +9552,7 @@ ] }, { - "_id": "5900f48a1000cf542c50ff9c", + "id": "5900f48a1000cf542c50ff9c", "challengeType": 5, "type": "bonfire", "title": "Problem 285: Pythagorean odds", @@ -9583,7 +9583,7 @@ ] }, { - "_id": "5900f48a1000cf542c50ff9d", + "id": "5900f48a1000cf542c50ff9d", "challengeType": 5, "type": "bonfire", "title": "Problem 286: Scoring probabilities", @@ -9609,7 +9609,7 @@ ] }, { - "_id": "5900f48b1000cf542c50ff9e", + "id": "5900f48b1000cf542c50ff9e", "challengeType": 5, "type": "bonfire", "title": "Problem 287: Quadtree encoding (a simple compression algorithm)", @@ -9646,7 +9646,7 @@ ] }, { - "_id": "5900f48d1000cf542c50ff9f", + "id": "5900f48d1000cf542c50ff9f", "challengeType": 5, "type": "bonfire", "title": "Problem 288: An enormous factorial", @@ -9683,7 +9683,7 @@ ] }, { - "_id": "5900f48d1000cf542c50ffa0", + "id": "5900f48d1000cf542c50ffa0", "challengeType": 5, "type": "bonfire", "title": "Problem 289: Eulerian Cycles", @@ -9719,7 +9719,7 @@ ] }, { - "_id": "5900f48f1000cf542c50ffa1", + "id": "5900f48f1000cf542c50ffa1", "challengeType": 5, "type": "bonfire", "title": "Problem 290: Digital Signature", @@ -9741,7 +9741,7 @@ ] }, { - "_id": "5900f48f1000cf542c50ffa2", + "id": "5900f48f1000cf542c50ffa2", "challengeType": 5, "type": "bonfire", "title": "Problem 291: Panaitopol Primes", @@ -9766,7 +9766,7 @@ ] }, { - "_id": "5900f4911000cf542c50ffa3", + "id": "5900f4911000cf542c50ffa3", "challengeType": 5, "type": "bonfire", "title": "Problem 292: Pythagorean Polygons", @@ -9795,7 +9795,7 @@ ] }, { - "_id": "5900f4931000cf542c50ffa4", + "id": "5900f4931000cf542c50ffa4", "challengeType": 5, "type": "bonfire", "title": "Problem 293: Pseudo-Fortunate Numbers", @@ -9829,7 +9829,7 @@ ] }, { - "_id": "5900f4931000cf542c50ffa5", + "id": "5900f4931000cf542c50ffa5", "challengeType": 5, "type": "bonfire", "title": "Problem 294: Sum of digits - experience #23", @@ -9862,7 +9862,7 @@ ] }, { - "_id": "5900f4931000cf542c50ffa6", + "id": "5900f4931000cf542c50ffa6", "challengeType": 5, "type": "bonfire", "title": "Problem 295: Lenticular holes", @@ -9906,7 +9906,7 @@ ] }, { - "_id": "5900f4941000cf542c50ffa7", + "id": "5900f4941000cf542c50ffa7", "challengeType": 5, "type": "bonfire", "title": "Problem 296: Angular Bisector and Tangent", @@ -9933,7 +9933,7 @@ ] }, { - "_id": "5900f4951000cf542c50ffa8", + "id": "5900f4951000cf542c50ffa8", "challengeType": 5, "type": "bonfire", "title": "Problem 297: Zeckendorf Representation", @@ -9965,7 +9965,7 @@ ] }, { - "_id": "5900f4971000cf542c50ffa9", + "id": "5900f4971000cf542c50ffa9", "challengeType": 5, "type": "bonfire", "title": "Problem 298: Selective Amnesia", @@ -10061,7 +10061,7 @@ ] }, { - "_id": "5900f4971000cf542c50ffaa", + "id": "5900f4971000cf542c50ffaa", "challengeType": 5, "type": "bonfire", "title": "Problem 299: Three similar triangles", @@ -10096,7 +10096,7 @@ ] }, { - "_id": "5900f49a1000cf542c50ffac", + "id": "5900f49a1000cf542c50ffac", "challengeType": 5, "type": "bonfire", "title": "Problem 300: Protein folding", @@ -10135,7 +10135,7 @@ ] }, { - "_id": "5900f4991000cf542c50ffab", + "id": "5900f4991000cf542c50ffab", "challengeType": 5, "type": "bonfire", "title": "Problem 301: Nim", @@ -10172,7 +10172,7 @@ ] }, { - "_id": "5900f49b1000cf542c50ffad", + "id": "5900f49b1000cf542c50ffad", "challengeType": 5, "type": "bonfire", "title": "Problem 302: Strong Achilles Numbers", @@ -10212,7 +10212,7 @@ ] }, { - "_id": "5900f49b1000cf542c50ffae", + "id": "5900f49b1000cf542c50ffae", "challengeType": 5, "type": "bonfire", "title": "Problem 303: Multiples with small digits", @@ -10238,7 +10238,7 @@ ] }, { - "_id": "5900f49d1000cf542c50ffaf", + "id": "5900f49d1000cf542c50ffaf", "challengeType": 5, "type": "bonfire", "title": "Problem 304: Primonacci", @@ -10275,7 +10275,7 @@ ] }, { - "_id": "5900f49d1000cf542c50ffb0", + "id": "5900f49d1000cf542c50ffb0", "challengeType": 5, "type": "bonfire", "title": "Problem 305: Reflexive Position", @@ -10308,7 +10308,7 @@ ] }, { - "_id": "5900f49f1000cf542c50ffb1", + "id": "5900f49f1000cf542c50ffb1", "challengeType": 5, "type": "bonfire", "title": "Problem 306: Paper-strip Game", @@ -10347,7 +10347,7 @@ ] }, { - "_id": "5900f4a01000cf542c50ffb2", + "id": "5900f4a01000cf542c50ffb2", "challengeType": 5, "type": "bonfire", "title": "Problem 307: Chip Defects", @@ -10376,7 +10376,7 @@ ] }, { - "_id": "5900f4a11000cf542c50ffb3", + "id": "5900f4a11000cf542c50ffb3", "challengeType": 5, "type": "bonfire", "title": "Problem 308: An amazing Prime-generating Automaton", @@ -10436,7 +10436,7 @@ ] }, { - "_id": "5900f4a11000cf542c50ffb4", + "id": "5900f4a11000cf542c50ffb4", "challengeType": 5, "type": "bonfire", "title": "Problem 309: Integer Ladders", @@ -10468,7 +10468,7 @@ ] }, { - "_id": "5900f4a21000cf542c50ffb5", + "id": "5900f4a21000cf542c50ffb5", "challengeType": 5, "type": "bonfire", "title": "Problem 310: Nim Square", @@ -10496,7 +10496,7 @@ ] }, { - "_id": "5900f4a31000cf542c50ffb6", + "id": "5900f4a31000cf542c50ffb6", "challengeType": 5, "type": "bonfire", "title": "Problem 311: Biclinic Integral Quadrilaterals", @@ -10532,7 +10532,7 @@ ] }, { - "_id": "5900f4a51000cf542c50ffb7", + "id": "5900f4a51000cf542c50ffb7", "challengeType": 5, "type": "bonfire", "title": "Problem 312: Cyclic paths on Sierpiński graphs", @@ -10572,7 +10572,7 @@ ] }, { - "_id": "5900f4a61000cf542c50ffb8", + "id": "5900f4a61000cf542c50ffb8", "challengeType": 5, "type": "bonfire", "title": "Problem 313: Sliding game", @@ -10604,7 +10604,7 @@ ] }, { - "_id": "5900f4a71000cf542c50ffb9", + "id": "5900f4a71000cf542c50ffb9", "challengeType": 5, "type": "bonfire", "title": "Problem 314: The Mouse on the Moon", @@ -10643,7 +10643,7 @@ ] }, { - "_id": "5900f4a71000cf542c50ffba", + "id": "5900f4a71000cf542c50ffba", "challengeType": 5, "type": "bonfire", "title": "Problem 315: Digital root clocks", @@ -10711,7 +10711,7 @@ ] }, { - "_id": "5900f4a81000cf542c50ffbb", + "id": "5900f4a81000cf542c50ffbb", "challengeType": 5, "type": "bonfire", "title": "Problem 316: Numbers in decimal expansions", @@ -10747,7 +10747,7 @@ ] }, { - "_id": "5900f4aa1000cf542c50ffbc", + "id": "5900f4aa1000cf542c50ffbc", "challengeType": 5, "type": "bonfire", "title": "Problem 317: Firecracker", @@ -10776,7 +10776,7 @@ ] }, { - "_id": "5900f4ab1000cf542c50ffbd", + "id": "5900f4ab1000cf542c50ffbd", "challengeType": 5, "type": "bonfire", "title": "Problem 318: 2011 nines", @@ -10824,7 +10824,7 @@ ] }, { - "_id": "5900f4ab1000cf542c50ffbe", + "id": "5900f4ab1000cf542c50ffbe", "challengeType": 5, "type": "bonfire", "title": "Problem 319: Bounded Sequences", @@ -10861,7 +10861,7 @@ ] }, { - "_id": "5900f4ae1000cf542c50ffbf", + "id": "5900f4ae1000cf542c50ffbf", "challengeType": 5, "type": "bonfire", "title": "Problem 320: Factorials divisible by a huge integer", @@ -10891,7 +10891,7 @@ ] }, { - "_id": "5900f4ae1000cf542c50ffc0", + "id": "5900f4ae1000cf542c50ffc0", "challengeType": 5, "type": "bonfire", "title": "Problem 321: Swapping Counters", @@ -10927,7 +10927,7 @@ ] }, { - "_id": "5900f4af1000cf542c50ffc1", + "id": "5900f4af1000cf542c50ffc1", "challengeType": 5, "type": "bonfire", "title": "Problem 322: Binomial coefficients divisible by 10", @@ -10953,7 +10953,7 @@ ] }, { - "_id": "5900f4b01000cf542c50ffc2", + "id": "5900f4b01000cf542c50ffc2", "challengeType": 5, "type": "bonfire", "title": "Problem 323: Bitwise-OR operations on random integers", @@ -10982,7 +10982,7 @@ ] }, { - "_id": "5900f4b11000cf542c50ffc3", + "id": "5900f4b11000cf542c50ffc3", "challengeType": 5, "type": "bonfire", "title": "Problem 324: Building a tower", @@ -11007,7 +11007,7 @@ ] }, { - "_id": "5900f4b11000cf542c50ffc4", + "id": "5900f4b11000cf542c50ffc4", "challengeType": 5, "type": "bonfire", "title": "Problem 325: Stone Game II", @@ -11053,7 +11053,7 @@ ] }, { - "_id": "5900f4b21000cf542c50ffc5", + "id": "5900f4b21000cf542c50ffc5", "challengeType": 5, "type": "bonfire", "title": "Problem 326: Modulo Summations", @@ -11088,7 +11088,7 @@ ] }, { - "_id": "5900f4b31000cf542c50ffc6", + "id": "5900f4b31000cf542c50ffc6", "challengeType": 5, "type": "bonfire", "title": "Problem 327: Rooms of Doom", @@ -11131,7 +11131,7 @@ ] }, { - "_id": "5900f4b41000cf542c50ffc7", + "id": "5900f4b41000cf542c50ffc7", "challengeType": 5, "type": "bonfire", "title": "Problem 328: Lowest-cost Search", @@ -11175,7 +11175,7 @@ ] }, { - "_id": "5900f4b51000cf542c50ffc8", + "id": "5900f4b51000cf542c50ffc8", "challengeType": 5, "type": "bonfire", "title": "Problem 329: Prime Frog", @@ -11208,7 +11208,7 @@ ] }, { - "_id": "5900f4b71000cf542c50ffc9", + "id": "5900f4b71000cf542c50ffc9", "challengeType": 5, "type": "bonfire", "title": "Problem 330: Euler's Number", @@ -11270,7 +11270,7 @@ ] }, { - "_id": "5900f4b71000cf542c50ffca", + "id": "5900f4b71000cf542c50ffca", "challengeType": 5, "type": "bonfire", "title": "Problem 331: Cross flips", @@ -11309,7 +11309,7 @@ ] }, { - "_id": "5900f4b91000cf542c50ffcb", + "id": "5900f4b91000cf542c50ffcb", "challengeType": 5, "type": "bonfire", "title": "Problem 332: Spherical triangles", @@ -11344,7 +11344,7 @@ ] }, { - "_id": "5900f4b91000cf542c50ffcc", + "id": "5900f4b91000cf542c50ffcc", "challengeType": 5, "type": "bonfire", "title": "Problem 333: Special partitions", @@ -11381,7 +11381,7 @@ ] }, { - "_id": "5900f4ba1000cf542c50ffcd", + "id": "5900f4ba1000cf542c50ffcd", "challengeType": 5, "type": "bonfire", "title": "Problem 334: Spilling the beans", @@ -11457,7 +11457,7 @@ ] }, { - "_id": "5900f4bd1000cf542c50ffce", + "id": "5900f4bd1000cf542c50ffce", "challengeType": 5, "type": "bonfire", "title": "Problem 335: Gathering the beans", @@ -11487,7 +11487,7 @@ ] }, { - "_id": "5900f4bd1000cf542c50ffcf", + "id": "5900f4bd1000cf542c50ffcf", "challengeType": 5, "type": "bonfire", "title": "Problem 336: Maximix Arrangements", @@ -11522,7 +11522,7 @@ ] }, { - "_id": "5900f4be1000cf542c50ffd0", + "id": "5900f4be1000cf542c50ffd0", "challengeType": 5, "type": "bonfire", "title": "Problem 337: Totient Stairstep Sequences", @@ -11553,7 +11553,7 @@ ] }, { - "_id": "5900f4be1000cf542c50ffd1", + "id": "5900f4be1000cf542c50ffd1", "challengeType": 5, "type": "bonfire", "title": "Problem 338: Cutting Rectangular Grid Paper", @@ -11592,7 +11592,7 @@ ] }, { - "_id": "5900f4c01000cf542c50ffd2", + "id": "5900f4c01000cf542c50ffd2", "challengeType": 5, "type": "bonfire", "title": "Problem 339: Peredur fab Efrawg", @@ -11623,7 +11623,7 @@ ] }, { - "_id": "5900f4c21000cf542c50ffd4", + "id": "5900f4c21000cf542c50ffd4", "challengeType": 5, "type": "bonfire", "title": "Problem 340: Crazy Function", @@ -11657,7 +11657,7 @@ ] }, { - "_id": "5900f4c11000cf542c50ffd3", + "id": "5900f4c11000cf542c50ffd3", "challengeType": 5, "type": "bonfire", "title": "Problem 341: Golomb's self-describing sequence", @@ -11687,7 +11687,7 @@ ] }, { - "_id": "5900f4c31000cf542c50ffd5", + "id": "5900f4c31000cf542c50ffd5", "challengeType": 5, "type": "bonfire", "title": "Problem 342: The totient of a square is a cube", @@ -11717,7 +11717,7 @@ ] }, { - "_id": "5900f4c41000cf542c50ffd6", + "id": "5900f4c41000cf542c50ffd6", "challengeType": 5, "type": "bonfire", "title": "Problem 343: Fractional Sequences", @@ -11760,7 +11760,7 @@ ] }, { - "_id": "5900f4c51000cf542c50ffd7", + "id": "5900f4c51000cf542c50ffd7", "challengeType": 5, "type": "bonfire", "title": "Problem 344: Silver dollar game", @@ -11802,7 +11802,7 @@ ] }, { - "_id": "5900f4c81000cf542c50ffda", + "id": "5900f4c81000cf542c50ffda", "challengeType": 5, "type": "bonfire", "title": "Problem 345: Matrix Sum", @@ -11849,7 +11849,7 @@ ] }, { - "_id": "5900f4c71000cf542c50ffd8", + "id": "5900f4c71000cf542c50ffd8", "challengeType": 5, "type": "bonfire", "title": "Problem 346: Strong Repunits", @@ -11876,7 +11876,7 @@ ] }, { - "_id": "5900f4c81000cf542c50ffd9", + "id": "5900f4c81000cf542c50ffd9", "challengeType": 5, "type": "bonfire", "title": "Problem 347: Largest integer divisible by two primes", @@ -11912,7 +11912,7 @@ ] }, { - "_id": "5900f4c81000cf542c50ffdb", + "id": "5900f4c81000cf542c50ffdb", "challengeType": 5, "type": "bonfire", "title": "Problem 348: Sum of a square and a cube", @@ -11943,7 +11943,7 @@ ] }, { - "_id": "5900f4ca1000cf542c50ffdc", + "id": "5900f4ca1000cf542c50ffdc", "challengeType": 5, "type": "bonfire", "title": "Problem 349: Langton's ant", @@ -11970,7 +11970,7 @@ ] }, { - "_id": "5900f4cb1000cf542c50ffdd", + "id": "5900f4cb1000cf542c50ffdd", "challengeType": 5, "type": "bonfire", "title": "Problem 350: Constraining the least greatest and the greatest least", @@ -12005,7 +12005,7 @@ ] }, { - "_id": "5900f4cb1000cf542c50ffde", + "id": "5900f4cb1000cf542c50ffde", "challengeType": 5, "type": "bonfire", "title": "Problem 351: Hexagonal orchards", @@ -12046,7 +12046,7 @@ ] }, { - "_id": "5900f4cd1000cf542c50ffdf", + "id": "5900f4cd1000cf542c50ffdf", "challengeType": 5, "type": "bonfire", "title": "Problem 352: Blood tests", @@ -12105,7 +12105,7 @@ ] }, { - "_id": "5900f4cd1000cf542c50ffe0", + "id": "5900f4cd1000cf542c50ffe0", "challengeType": 5, "type": "bonfire", "title": "Problem 353: Risky moon", @@ -12155,7 +12155,7 @@ ] }, { - "_id": "5900f4cf1000cf542c50ffe1", + "id": "5900f4cf1000cf542c50ffe1", "challengeType": 5, "type": "bonfire", "title": "Problem 354: Distances in a bee's honeycomb", @@ -12188,7 +12188,7 @@ ] }, { - "_id": "5900f4d01000cf542c50ffe2", + "id": "5900f4d01000cf542c50ffe2", "challengeType": 5, "type": "bonfire", "title": "Problem 355: Maximal coprime subset", @@ -12217,7 +12217,7 @@ ] }, { - "_id": "5900f4d01000cf542c50ffe3", + "id": "5900f4d01000cf542c50ffe3", "challengeType": 5, "type": "bonfire", "title": "Problem 356: Largest roots of cubic polynomials", @@ -12246,7 +12246,7 @@ ] }, { - "_id": "5900f4d11000cf542c50ffe4", + "id": "5900f4d11000cf542c50ffe4", "challengeType": 5, "type": "bonfire", "title": "Problem 357: Prime generating integers", @@ -12273,7 +12273,7 @@ ] }, { - "_id": "5900f4d21000cf542c50ffe5", + "id": "5900f4d21000cf542c50ffe5", "challengeType": 5, "type": "bonfire", "title": "Problem 358: Cyclic numbers", @@ -12323,7 +12323,7 @@ ] }, { - "_id": "5900f4d31000cf542c50ffe6", + "id": "5900f4d31000cf542c50ffe6", "challengeType": 5, "type": "bonfire", "title": "Problem 359: Hilbert's New Hotel", @@ -12374,7 +12374,7 @@ ] }, { - "_id": "5900f4d41000cf542c50ffe7", + "id": "5900f4d41000cf542c50ffe7", "challengeType": 5, "type": "bonfire", "title": "Problem 360: Scary Sphere", @@ -12407,7 +12407,7 @@ ] }, { - "_id": "5900f4d51000cf542c50ffe8", + "id": "5900f4d51000cf542c50ffe8", "challengeType": 5, "type": "bonfire", "title": "Problem 361: Subsequence of Thue-Morse sequence", @@ -12454,7 +12454,7 @@ ] }, { - "_id": "5900f4d61000cf542c50ffe9", + "id": "5900f4d61000cf542c50ffe9", "challengeType": 5, "type": "bonfire", "title": "Problem 362: Squarefree factors", @@ -12492,7 +12492,7 @@ ] }, { - "_id": "5900f4d91000cf542c50ffeb", + "id": "5900f4d91000cf542c50ffeb", "challengeType": 5, "type": "bonfire", "title": "Problem 363: Bézier Curves", @@ -12535,7 +12535,7 @@ ] }, { - "_id": "5900f4d91000cf542c50ffea", + "id": "5900f4d91000cf542c50ffea", "challengeType": 5, "type": "bonfire", "title": "Problem 364: Comfortable distance", @@ -12569,7 +12569,7 @@ ] }, { - "_id": "5900f4da1000cf542c50ffec", + "id": "5900f4da1000cf542c50ffec", "challengeType": 5, "type": "bonfire", "title": "Problem 365: A huge binomial coefficient", @@ -12597,7 +12597,7 @@ ] }, { - "_id": "5900f4da1000cf542c50ffed", + "id": "5900f4da1000cf542c50ffed", "challengeType": 5, "type": "bonfire", "title": "Problem 366: Stone Game III", @@ -12642,7 +12642,7 @@ ] }, { - "_id": "5900f4db1000cf542c50ffee", + "id": "5900f4db1000cf542c50ffee", "challengeType": 5, "type": "bonfire", "title": "Problem 367: Bozo sort", @@ -12680,7 +12680,7 @@ ] }, { - "_id": "5900f4dd1000cf542c50ffef", + "id": "5900f4dd1000cf542c50ffef", "challengeType": 5, "type": "bonfire", "title": "Problem 368: A Kempner-like series", @@ -12715,7 +12715,7 @@ ] }, { - "_id": "5900f4de1000cf542c50fff0", + "id": "5900f4de1000cf542c50fff0", "challengeType": 5, "type": "bonfire", "title": "Problem 369: Badugi", @@ -12741,7 +12741,7 @@ ] }, { - "_id": "5900f4de1000cf542c50fff1", + "id": "5900f4de1000cf542c50fff1", "challengeType": 5, "type": "bonfire", "title": "Problem 370: Geometric triangles", @@ -12769,7 +12769,7 @@ ] }, { - "_id": "5900f4e01000cf542c50fff2", + "id": "5900f4e01000cf542c50fff2", "challengeType": 5, "type": "bonfire", "title": "Problem 371: Licence plates", @@ -12803,7 +12803,7 @@ ] }, { - "_id": "5900f4e11000cf542c50fff3", + "id": "5900f4e11000cf542c50fff3", "challengeType": 5, "type": "bonfire", "title": "Problem 372: Pencils of rays", @@ -12831,7 +12831,7 @@ ] }, { - "_id": "5900f4e11000cf542c50fff4", + "id": "5900f4e11000cf542c50fff4", "challengeType": 5, "type": "bonfire", "title": "Problem 373: Circumscribed Circles", @@ -12862,7 +12862,7 @@ ] }, { - "_id": "5900f4e51000cf542c50fff6", + "id": "5900f4e51000cf542c50fff6", "challengeType": 5, "type": "bonfire", "title": "Problem 374: Maximum Integer Partition Product", @@ -12903,7 +12903,7 @@ ] }, { - "_id": "5900f4e41000cf542c50fff5", + "id": "5900f4e41000cf542c50fff5", "challengeType": 5, "type": "bonfire", "title": "Problem 375: Minimum of subsequences", @@ -12940,7 +12940,7 @@ ] }, { - "_id": "5900f4e51000cf542c50fff7", + "id": "5900f4e51000cf542c50fff7", "challengeType": 5, "type": "bonfire", "title": "Problem 376: Nontransitive sets of dice", @@ -12998,7 +12998,7 @@ ] }, { - "_id": "5900f4e51000cf542c50fff8", + "id": "5900f4e51000cf542c50fff8", "challengeType": 5, "type": "bonfire", "title": "Problem 377: Sum of digits, experience 13", @@ -13029,7 +13029,7 @@ ] }, { - "_id": "5900f4e61000cf542c50fff9", + "id": "5900f4e61000cf542c50fff9", "challengeType": 5, "type": "bonfire", "title": "Problem 378: Triangle Triples", @@ -13069,7 +13069,7 @@ ] }, { - "_id": "5900f4e81000cf542c50fffa", + "id": "5900f4e81000cf542c50fffa", "challengeType": 5, "type": "bonfire", "title": "Problem 379: Least common multiple count", @@ -13101,7 +13101,7 @@ ] }, { - "_id": "5900f4e81000cf542c50fffb", + "id": "5900f4e81000cf542c50fffb", "challengeType": 5, "type": "bonfire", "title": "Problem 380: Amazing Mazes!", @@ -13136,7 +13136,7 @@ ] }, { - "_id": "5900f4ea1000cf542c50fffc", + "id": "5900f4ea1000cf542c50fffc", "challengeType": 5, "type": "bonfire", "title": "Problem 381: (prime-k) factorial", @@ -13169,7 +13169,7 @@ ] }, { - "_id": "5900f4eb1000cf542c50fffd", + "id": "5900f4eb1000cf542c50fffd", "challengeType": 5, "type": "bonfire", "title": "Problem 382: Generating polygons", @@ -13214,7 +13214,7 @@ ] }, { - "_id": "5900f4ed1000cf542c50ffff", + "id": "5900f4ed1000cf542c50ffff", "challengeType": 5, "type": "bonfire", "title": "Problem 383: Divisibility comparison between factorials", @@ -13246,7 +13246,7 @@ ] }, { - "_id": "5900f4ed1000cf542c50fffe", + "id": "5900f4ed1000cf542c50fffe", "challengeType": 5, "type": "bonfire", "title": "Problem 384: Rudin-Shapiro sequence", @@ -13292,7 +13292,7 @@ ] }, { - "_id": "5900f4ee1000cf542c510000", + "id": "5900f4ee1000cf542c510000", "challengeType": 5, "type": "bonfire", "title": "Problem 385: Ellipses inside triangles", @@ -13334,7 +13334,7 @@ ] }, { - "_id": "5900f4ef1000cf542c510001", + "id": "5900f4ef1000cf542c510001", "challengeType": 5, "type": "bonfire", "title": "Problem 386: Maximum length of an antichain", @@ -13366,7 +13366,7 @@ ] }, { - "_id": "5900f4f11000cf542c510003", + "id": "5900f4f11000cf542c510003", "challengeType": 5, "type": "bonfire", "title": "Problem 387: Harshad Numbers", @@ -13404,7 +13404,7 @@ ] }, { - "_id": "5900f4f11000cf542c510002", + "id": "5900f4f11000cf542c510002", "challengeType": 5, "type": "bonfire", "title": "Problem 388: Distinct Lines", @@ -13435,7 +13435,7 @@ ] }, { - "_id": "5900f4f21000cf542c510004", + "id": "5900f4f21000cf542c510004", "challengeType": 5, "type": "bonfire", "title": "Problem 389: Platonic Dice", @@ -13458,7 +13458,7 @@ ] }, { - "_id": "5900f4f21000cf542c510005", + "id": "5900f4f21000cf542c510005", "challengeType": 5, "type": "bonfire", "title": "Problem 390: Triangles with non rational sides and integral area", @@ -13489,7 +13489,7 @@ ] }, { - "_id": "5900f4f31000cf542c510006", + "id": "5900f4f31000cf542c510006", "challengeType": 5, "type": "bonfire", "title": "Problem 391: Hopping Game", @@ -13538,7 +13538,7 @@ ] }, { - "_id": "5900f4f41000cf542c510007", + "id": "5900f4f41000cf542c510007", "challengeType": 5, "type": "bonfire", "title": "Problem 392: Enmeshed unit circle", @@ -13576,7 +13576,7 @@ ] }, { - "_id": "5900f4f61000cf542c510008", + "id": "5900f4f61000cf542c510008", "challengeType": 5, "type": "bonfire", "title": "Problem 393: Migrating ants", @@ -13604,7 +13604,7 @@ ] }, { - "_id": "5900f4f71000cf542c510009", + "id": "5900f4f71000cf542c510009", "challengeType": 5, "type": "bonfire", "title": "Problem 394: Eating pie", @@ -13642,7 +13642,7 @@ ] }, { - "_id": "5900f4f71000cf542c51000a", + "id": "5900f4f71000cf542c51000a", "challengeType": 5, "type": "bonfire", "title": "Problem 395: Pythagorean tree", @@ -13682,7 +13682,7 @@ ] }, { - "_id": "5900f4f81000cf542c51000b", + "id": "5900f4f81000cf542c51000b", "challengeType": 5, "type": "bonfire", "title": "Problem 396: Weak Goodstein sequence", @@ -13728,7 +13728,7 @@ ] }, { - "_id": "5900f4f91000cf542c51000c", + "id": "5900f4f91000cf542c51000c", "challengeType": 5, "type": "bonfire", "title": "Problem 397: Triangle on parabola", @@ -13757,7 +13757,7 @@ ] }, { - "_id": "5900f4fa1000cf542c51000d", + "id": "5900f4fa1000cf542c51000d", "challengeType": 5, "type": "bonfire", "title": "Problem 398: Cutting rope", @@ -13788,7 +13788,7 @@ ] }, { - "_id": "5900f4fc1000cf542c51000e", + "id": "5900f4fc1000cf542c51000e", "challengeType": 5, "type": "bonfire", "title": "Problem 399: Squarefree Fibonacci Numbers", @@ -13831,7 +13831,7 @@ ] }, { - "_id": "5900f4fe1000cf542c510010", + "id": "5900f4fe1000cf542c510010", "challengeType": 5, "type": "bonfire", "title": "Problem 400: Fibonacci tree game", @@ -13874,7 +13874,7 @@ ] }, { - "_id": "5900f4fd1000cf542c51000f", + "id": "5900f4fd1000cf542c51000f", "challengeType": 5, "type": "bonfire", "title": "Problem 401: Sum of squares of divisors", @@ -13907,7 +13907,7 @@ ] }, { - "_id": "5900f4ff1000cf542c510011", + "id": "5900f4ff1000cf542c510011", "challengeType": 5, "type": "bonfire", "title": "Problem 402: Integer-valued polynomials", @@ -13946,7 +13946,7 @@ ] }, { - "_id": "5900f5001000cf542c510013", + "id": "5900f5001000cf542c510013", "challengeType": 5, "type": "bonfire", "title": "Problem 403: Lattice points enclosed by parabola and line", @@ -13979,7 +13979,7 @@ ] }, { - "_id": "5900f5001000cf542c510012", + "id": "5900f5001000cf542c510012", "challengeType": 5, "type": "bonfire", "title": "Problem 404: Crisscross Ellipses", @@ -14020,7 +14020,7 @@ ] }, { - "_id": "5900f5021000cf542c510014", + "id": "5900f5021000cf542c510014", "challengeType": 5, "type": "bonfire", "title": "Problem 405: A rectangular tiling", @@ -14063,7 +14063,7 @@ ] }, { - "_id": "5900f5021000cf542c510015", + "id": "5900f5021000cf542c510015", "challengeType": 5, "type": "bonfire", "title": "Problem 406: Guessing Game", @@ -14108,7 +14108,7 @@ ] }, { - "_id": "5900f5041000cf542c510016", + "id": "5900f5041000cf542c510016", "challengeType": 5, "type": "bonfire", "title": "Problem 407: Idempotents", @@ -14138,7 +14138,7 @@ ] }, { - "_id": "5900f5091000cf542c51001b", + "id": "5900f5091000cf542c51001b", "challengeType": 5, "type": "bonfire", "title": "Problem 408: Admissible paths through a grid", @@ -14169,7 +14169,7 @@ ] }, { - "_id": "5900f5061000cf542c510017", + "id": "5900f5061000cf542c510017", "challengeType": 5, "type": "bonfire", "title": "Problem 409: Nim Extreme", @@ -14197,7 +14197,7 @@ ] }, { - "_id": "5900f5071000cf542c510018", + "id": "5900f5071000cf542c510018", "challengeType": 5, "type": "bonfire", "title": "Problem 410: Circle and tangent line", @@ -14226,7 +14226,7 @@ ] }, { - "_id": "5900f5081000cf542c510019", + "id": "5900f5081000cf542c510019", "challengeType": 5, "type": "bonfire", "title": "Problem 411: Uphill paths", @@ -14260,7 +14260,7 @@ ] }, { - "_id": "5900f5081000cf542c51001a", + "id": "5900f5081000cf542c51001a", "challengeType": 5, "type": "bonfire", "title": "Problem 412: Gnomon numbering", @@ -14296,7 +14296,7 @@ ] }, { - "_id": "5900f50a1000cf542c51001c", + "id": "5900f50a1000cf542c51001c", "challengeType": 5, "type": "bonfire", "title": "Problem 413: One-child Numbers", @@ -14327,7 +14327,7 @@ ] }, { - "_id": "5900f50b1000cf542c51001d", + "id": "5900f50b1000cf542c51001d", "challengeType": 5, "type": "bonfire", "title": "Problem 414: Kaprekar constant", @@ -14380,7 +14380,7 @@ ] }, { - "_id": "5900f50c1000cf542c51001e", + "id": "5900f50c1000cf542c51001e", "challengeType": 5, "type": "bonfire", "title": "Problem 415: Titanic sets", @@ -14411,7 +14411,7 @@ ] }, { - "_id": "5900f50e1000cf542c510020", + "id": "5900f50e1000cf542c510020", "challengeType": 5, "type": "bonfire", "title": "Problem 416: A frog's trip", @@ -14438,7 +14438,7 @@ ] }, { - "_id": "5900f50d1000cf542c51001f", + "id": "5900f50d1000cf542c51001f", "challengeType": 5, "type": "bonfire", "title": "Problem 417: Reciprocal cycles II", @@ -14482,7 +14482,7 @@ ] }, { - "_id": "5900f50f1000cf542c510021", + "id": "5900f50f1000cf542c510021", "challengeType": 5, "type": "bonfire", "title": "Problem 418: Factorisation triples", @@ -14513,7 +14513,7 @@ ] }, { - "_id": "5900f5101000cf542c510022", + "id": "5900f5101000cf542c510022", "challengeType": 5, "type": "bonfire", "title": "Problem 419: Look and say sequence", @@ -14552,7 +14552,7 @@ ] }, { - "_id": "5900f5111000cf542c510023", + "id": "5900f5111000cf542c510023", "challengeType": 5, "type": "bonfire", "title": "Problem 420: 2x2 positive integer matrix", @@ -14586,7 +14586,7 @@ ] }, { - "_id": "5900f5131000cf542c510024", + "id": "5900f5131000cf542c510024", "challengeType": 5, "type": "bonfire", "title": "Problem 421: Prime factors of n15+1", @@ -14616,7 +14616,7 @@ ] }, { - "_id": "5900f5131000cf542c510025", + "id": "5900f5131000cf542c510025", "challengeType": 5, "type": "bonfire", "title": "Problem 422: Sequence of points on a hyperbola", @@ -14650,7 +14650,7 @@ ] }, { - "_id": "5900f5141000cf542c510027", + "id": "5900f5141000cf542c510027", "challengeType": 5, "type": "bonfire", "title": "Problem 423: Consecutive die throws", @@ -14689,7 +14689,7 @@ ] }, { - "_id": "5900f5141000cf542c510026", + "id": "5900f5141000cf542c510026", "challengeType": 5, "type": "bonfire", "title": "Problem 424: Kakuro", @@ -14731,7 +14731,7 @@ ] }, { - "_id": "5900f5151000cf542c510028", + "id": "5900f5151000cf542c510028", "challengeType": 5, "type": "bonfire", "title": "Problem 425: Prime connection", @@ -14770,7 +14770,7 @@ ] }, { - "_id": "5900f5171000cf542c510029", + "id": "5900f5171000cf542c510029", "challengeType": 5, "type": "bonfire", "title": "Problem 426: Box-ball system", @@ -14821,7 +14821,7 @@ ] }, { - "_id": "5900f5181000cf542c51002a", + "id": "5900f5181000cf542c51002a", "challengeType": 5, "type": "bonfire", "title": "Problem 427: n-sequences", @@ -14853,7 +14853,7 @@ ] }, { - "_id": "5900f5191000cf542c51002b", + "id": "5900f5191000cf542c51002b", "challengeType": 5, "type": "bonfire", "title": "Problem 428: About Project Euler", @@ -14875,7 +14875,7 @@ ] }, { - "_id": "5900f5191000cf542c51002c", + "id": "5900f5191000cf542c51002c", "challengeType": 5, "type": "bonfire", "title": "Problem 429: Sum of squares of unitary divisors", @@ -14905,7 +14905,7 @@ ] }, { - "_id": "5900f51a1000cf542c51002d", + "id": "5900f51a1000cf542c51002d", "challengeType": 5, "type": "bonfire", "title": "Problem 430: Range flips", @@ -14941,7 +14941,7 @@ ] }, { - "_id": "5900f51b1000cf542c51002e", + "id": "5900f51b1000cf542c51002e", "challengeType": 5, "type": "bonfire", "title": "Problem 431: Square Space Silo", @@ -14974,7 +14974,7 @@ ] }, { - "_id": "5900f51e1000cf542c510030", + "id": "5900f51e1000cf542c510030", "challengeType": 5, "type": "bonfire", "title": "Problem 432: Totient sum", @@ -15001,7 +15001,7 @@ ] }, { - "_id": "5900f51d1000cf542c51002f", + "id": "5900f51d1000cf542c51002f", "challengeType": 5, "type": "bonfire", "title": "Problem 433: Steps in Euclid's algorithm", @@ -15034,7 +15034,7 @@ ] }, { - "_id": "5900f51f1000cf542c510031", + "id": "5900f51f1000cf542c510031", "challengeType": 5, "type": "bonfire", "title": "Problem 434: Rigid graphs", @@ -15071,7 +15071,7 @@ ] }, { - "_id": "5900f5201000cf542c510032", + "id": "5900f5201000cf542c510032", "challengeType": 5, "type": "bonfire", "title": "Problem 435: Polynomials of Fibonacci numbers", @@ -15096,7 +15096,7 @@ ] }, { - "_id": "5900f5221000cf542c510033", + "id": "5900f5221000cf542c510033", "challengeType": 5, "type": "bonfire", "title": "Problem 436: Unfair wager", @@ -15132,7 +15132,7 @@ ] }, { - "_id": "5900f5241000cf542c510036", + "id": "5900f5241000cf542c510036", "challengeType": 5, "type": "bonfire", "title": "Problem 437: Fibonacci primitive roots", @@ -15172,7 +15172,7 @@ ] }, { - "_id": "5900f5231000cf542c510034", + "id": "5900f5231000cf542c510034", "challengeType": 5, "type": "bonfire", "title": "Problem 438: Integer part of polynomial equation's solutions", @@ -15206,7 +15206,7 @@ ] }, { - "_id": "5900f5231000cf542c510035", + "id": "5900f5231000cf542c510035", "challengeType": 5, "type": "bonfire", "title": "Problem 439: Sum of sum of divisors", @@ -15233,7 +15233,7 @@ ] }, { - "_id": "5900f5241000cf542c510037", + "id": "5900f5241000cf542c510037", "challengeType": 5, "type": "bonfire", "title": "Problem 440: GCD and Tiling", @@ -15269,7 +15269,7 @@ ] }, { - "_id": "5900f5261000cf542c510038", + "id": "5900f5261000cf542c510038", "challengeType": 5, "type": "bonfire", "title": "Problem 441: The inverse summation of coprime couples", @@ -15301,7 +15301,7 @@ ] }, { - "_id": "5900f5271000cf542c510039", + "id": "5900f5271000cf542c510039", "challengeType": 5, "type": "bonfire", "title": "Problem 442: Eleven-free integers", @@ -15329,7 +15329,7 @@ ] }, { - "_id": "5900f5271000cf542c51003a", + "id": "5900f5271000cf542c51003a", "challengeType": 5, "type": "bonfire", "title": "Problem 443: GCD sequence", @@ -15363,7 +15363,7 @@ ] }, { - "_id": "5900f52a1000cf542c51003b", + "id": "5900f52a1000cf542c51003b", "challengeType": 5, "type": "bonfire", "title": "Problem 444: The Roundtable Lottery", @@ -15401,7 +15401,7 @@ ] }, { - "_id": "5900f52a1000cf542c51003c", + "id": "5900f52a1000cf542c51003c", "challengeType": 5, "type": "bonfire", "title": "Problem 445: Retractions A", @@ -15434,7 +15434,7 @@ ] }, { - "_id": "5900f52c1000cf542c51003d", + "id": "5900f52c1000cf542c51003d", "challengeType": 5, "type": "bonfire", "title": "Problem 446: Retractions B", @@ -15465,7 +15465,7 @@ ] }, { - "_id": "5900f52c1000cf542c51003e", + "id": "5900f52c1000cf542c51003e", "challengeType": 5, "type": "bonfire", "title": "Problem 447: Retractions C", @@ -15497,7 +15497,7 @@ ] }, { - "_id": "5900f52c1000cf542c51003f", + "id": "5900f52c1000cf542c51003f", "challengeType": 5, "type": "bonfire", "title": "Problem 448: Average least common multiple", @@ -15527,7 +15527,7 @@ ] }, { - "_id": "5900f52d1000cf542c510040", + "id": "5900f52d1000cf542c510040", "challengeType": 5, "type": "bonfire", "title": "Problem 449: Chocolate covered candy", @@ -15561,7 +15561,7 @@ ] }, { - "_id": "5900f52e1000cf542c510041", + "id": "5900f52e1000cf542c510041", "challengeType": 5, "type": "bonfire", "title": "Problem 450: Hypocycloid and Lattice points", @@ -15611,7 +15611,7 @@ ] }, { - "_id": "5900f5311000cf542c510042", + "id": "5900f5311000cf542c510042", "challengeType": 5, "type": "bonfire", "title": "Problem 451: Modular inverses", @@ -15648,7 +15648,7 @@ ] }, { - "_id": "5900f5311000cf542c510043", + "id": "5900f5311000cf542c510043", "challengeType": 5, "type": "bonfire", "title": "Problem 452: Long Products", @@ -15673,7 +15673,7 @@ ] }, { - "_id": "5900f5311000cf542c510044", + "id": "5900f5311000cf542c510044", "challengeType": 5, "type": "bonfire", "title": "Problem 453: Lattice Quadrilaterals", @@ -15703,7 +15703,7 @@ ] }, { - "_id": "5900f5331000cf542c510045", + "id": "5900f5331000cf542c510045", "challengeType": 5, "type": "bonfire", "title": "Problem 454: Diophantine reciprocals III", @@ -15736,7 +15736,7 @@ ] }, { - "_id": "5900f5331000cf542c510046", + "id": "5900f5331000cf542c510046", "challengeType": 5, "type": "bonfire", "title": "Problem 455: Powers With Trailing Digits", @@ -15766,7 +15766,7 @@ ] }, { - "_id": "5900f5351000cf542c510047", + "id": "5900f5351000cf542c510047", "challengeType": 5, "type": "bonfire", "title": "Problem 456: Triangles containing the origin II", @@ -15803,7 +15803,7 @@ ] }, { - "_id": "5900f5361000cf542c510048", + "id": "5900f5361000cf542c510048", "challengeType": 5, "type": "bonfire", "title": "Problem 457: A polynomial modulo the square of a prime", @@ -15833,7 +15833,7 @@ ] }, { - "_id": "5900f5361000cf542c510049", + "id": "5900f5361000cf542c510049", "challengeType": 5, "type": "bonfire", "title": "Problem 458: Permutations of Project", @@ -15861,7 +15861,7 @@ ] }, { - "_id": "5900f5371000cf542c51004a", + "id": "5900f5371000cf542c51004a", "challengeType": 5, "type": "bonfire", "title": "Problem 459: Flipping game", @@ -15903,7 +15903,7 @@ ] }, { - "_id": "5900f5381000cf542c51004b", + "id": "5900f5381000cf542c51004b", "challengeType": 5, "type": "bonfire", "title": "Problem 460: An ant on the move", @@ -15945,7 +15945,7 @@ ] }, { - "_id": "5900f53a1000cf542c51004c", + "id": "5900f53a1000cf542c51004c", "challengeType": 5, "type": "bonfire", "title": "Problem 461: Almost Pi", @@ -15973,7 +15973,7 @@ ] }, { - "_id": "5900f53b1000cf542c51004d", + "id": "5900f53b1000cf542c51004d", "challengeType": 5, "type": "bonfire", "title": "Problem 462: Permutation of 3-smooth numbers", @@ -16009,7 +16009,7 @@ ] }, { - "_id": "5900f53c1000cf542c51004e", + "id": "5900f53c1000cf542c51004e", "challengeType": 5, "type": "bonfire", "title": "Problem 463: A weird recurrence relation", @@ -16040,7 +16040,7 @@ ] }, { - "_id": "5900f53d1000cf542c51004f", + "id": "5900f53d1000cf542c51004f", "challengeType": 5, "type": "bonfire", "title": "Problem 464: Möbius function and intervals", @@ -16081,7 +16081,7 @@ ] }, { - "_id": "5900f53d1000cf542c510050", + "id": "5900f53d1000cf542c510050", "challengeType": 5, "type": "bonfire", "title": "Problem 465: Polar polygons", @@ -16119,7 +16119,7 @@ ] }, { - "_id": "5900f53e1000cf542c510051", + "id": "5900f53e1000cf542c510051", "challengeType": 5, "type": "bonfire", "title": "Problem 466: Distinct terms in a multiplication table", @@ -16156,7 +16156,7 @@ ] }, { - "_id": "5900f5411000cf542c510052", + "id": "5900f5411000cf542c510052", "challengeType": 5, "type": "bonfire", "title": "Problem 467: Superinteger", @@ -16196,7 +16196,7 @@ ] }, { - "_id": "5900f5411000cf542c510054", + "id": "5900f5411000cf542c510054", "challengeType": 5, "type": "bonfire", "title": "Problem 468: Smooth divisors of binomial coefficients", @@ -16232,7 +16232,7 @@ ] }, { - "_id": "5900f5411000cf542c510053", + "id": "5900f5411000cf542c510053", "challengeType": 5, "type": "bonfire", "title": "Problem 469: Empty chairs", @@ -16264,7 +16264,7 @@ ] }, { - "_id": "5900f5431000cf542c510055", + "id": "5900f5431000cf542c510055", "challengeType": 5, "type": "bonfire", "title": "Problem 470: Super Ramvok", @@ -16298,7 +16298,7 @@ ] }, { - "_id": "5900f5431000cf542c510056", + "id": "5900f5431000cf542c510056", "challengeType": 5, "type": "bonfire", "title": "Problem 471: Triangle inscribed in ellipse", @@ -16329,7 +16329,7 @@ ] }, { - "_id": "5900f5451000cf542c510057", + "id": "5900f5451000cf542c510057", "challengeType": 5, "type": "bonfire", "title": "Problem 472: Comfortable Distance II", @@ -16368,7 +16368,7 @@ ] }, { - "_id": "5900f5461000cf542c510058", + "id": "5900f5461000cf542c510058", "challengeType": 5, "type": "bonfire", "title": "Problem 473: Phigital number base", @@ -16407,7 +16407,7 @@ ] }, { - "_id": "5900f5471000cf542c510059", + "id": "5900f5471000cf542c510059", "challengeType": 5, "type": "bonfire", "title": "Problem 474: Last digits of divisors", @@ -16436,7 +16436,7 @@ ] }, { - "_id": "5900f5481000cf542c51005a", + "id": "5900f5481000cf542c51005a", "challengeType": 5, "type": "bonfire", "title": "Problem 475: Music festival", @@ -16465,7 +16465,7 @@ ] }, { - "_id": "5900f5481000cf542c51005b", + "id": "5900f5481000cf542c51005b", "challengeType": 5, "type": "bonfire", "title": "Problem 476: Circle Packing II", @@ -16490,7 +16490,7 @@ ] }, { - "_id": "5900f54a1000cf542c51005c", + "id": "5900f54a1000cf542c51005c", "challengeType": 5, "type": "bonfire", "title": "Problem 477: Number Sequence Game", @@ -16526,7 +16526,7 @@ ] }, { - "_id": "5900f54c1000cf542c51005e", + "id": "5900f54c1000cf542c51005e", "challengeType": 5, "type": "bonfire", "title": "Problem 478: Mixtures", @@ -16568,7 +16568,7 @@ ] }, { - "_id": "5900f54b1000cf542c51005d", + "id": "5900f54b1000cf542c51005d", "challengeType": 5, "type": "bonfire", "title": "Problem 479: Roots on the Rise", @@ -16598,7 +16598,7 @@ ] }, { - "_id": "5900f54c1000cf542c51005f", + "id": "5900f54c1000cf542c51005f", "challengeType": 5, "type": "bonfire", "title": "Problem 480: The Last Question", @@ -16658,7 +16658,7 @@ ] }, { - "_id": "5900f54d1000cf542c510060", + "id": "5900f54d1000cf542c510060", "challengeType": 5, "type": "bonfire", "title": "Problem 481: Chef Showdown", @@ -16690,7 +16690,7 @@ ] }, { - "_id": "5900f54f1000cf542c510061", + "id": "5900f54f1000cf542c510061", "challengeType": 5, "type": "bonfire", "title": "Problem 482: The incenter of a triangle", @@ -16722,7 +16722,7 @@ ] }, { - "_id": "5900f54f1000cf542c510062", + "id": "5900f54f1000cf542c510062", "challengeType": 5, "type": "bonfire", "title": "Problem 483: Repeated permutation", @@ -16761,7 +16761,7 @@ ] }, { - "_id": "5900f5501000cf542c510063", + "id": "5900f5501000cf542c510063", "challengeType": 5, "type": "bonfire", "title": "Problem 484: Arithmetic Derivative", @@ -16790,7 +16790,7 @@ ] }, { - "_id": "5900f5511000cf542c510064", + "id": "5900f5511000cf542c510064", "challengeType": 5, "type": "bonfire", "title": "Problem 485: Maximum number of divisors", @@ -16820,7 +16820,7 @@ ] }, { - "_id": "5900f5531000cf542c510065", + "id": "5900f5531000cf542c510065", "challengeType": 5, "type": "bonfire", "title": "Problem 486: Palindrome-containing strings", @@ -16854,7 +16854,7 @@ ] }, { - "_id": "5900f5531000cf542c510066", + "id": "5900f5531000cf542c510066", "challengeType": 5, "type": "bonfire", "title": "Problem 487: Sums of power sums", @@ -16882,7 +16882,7 @@ ] }, { - "_id": "5900f5541000cf542c510067", + "id": "5900f5541000cf542c510067", "challengeType": 5, "type": "bonfire", "title": "Problem 488: Unbalanced Nim", @@ -16925,7 +16925,7 @@ ] }, { - "_id": "5900f5561000cf542c510068", + "id": "5900f5561000cf542c510068", "challengeType": 5, "type": "bonfire", "title": "Problem 489: Common factors between two sequences", @@ -16951,7 +16951,7 @@ ] }, { - "_id": "5900f5561000cf542c510069", + "id": "5900f5561000cf542c510069", "challengeType": 5, "type": "bonfire", "title": "Problem 490: Jumping frog", @@ -17002,7 +17002,7 @@ ] }, { - "_id": "5900f5591000cf542c51006b", + "id": "5900f5591000cf542c51006b", "challengeType": 5, "type": "bonfire", "title": "Problem 491: Double pandigital number divisible by 11", @@ -17026,7 +17026,7 @@ ] }, { - "_id": "5900f5581000cf542c51006a", + "id": "5900f5581000cf542c51006a", "challengeType": 5, "type": "bonfire", "title": "Problem 492: Exploding sequence", @@ -17069,7 +17069,7 @@ ] }, { - "_id": "5900f55a1000cf542c51006c", + "id": "5900f55a1000cf542c51006c", "challengeType": 5, "type": "bonfire", "title": "Problem 493: Under The Rainbow", @@ -17093,7 +17093,7 @@ ] }, { - "_id": "5900f55a1000cf542c51006d", + "id": "5900f55a1000cf542c51006d", "challengeType": 5, "type": "bonfire", "title": "Problem 494: Collatz prefix families", @@ -17132,7 +17132,7 @@ ] }, { - "_id": "5900f55b1000cf542c51006e", + "id": "5900f55b1000cf542c51006e", "challengeType": 5, "type": "bonfire", "title": "Problem 495: Writing n as the product of k distinct positive integers", @@ -17165,7 +17165,7 @@ ] }, { - "_id": "5900f55d1000cf542c51006f", + "id": "5900f55d1000cf542c51006f", "challengeType": 5, "type": "bonfire", "title": "Problem 496: Incenter and circumcenter of triangle", @@ -17195,7 +17195,7 @@ ] }, { - "_id": "5900f55f1000cf542c510070", + "id": "5900f55f1000cf542c510070", "challengeType": 5, "type": "bonfire", "title": "Problem 497: Drunken Tower of Hanoi", @@ -17236,7 +17236,7 @@ ] }, { - "_id": "5900f55f1000cf542c510071", + "id": "5900f55f1000cf542c510071", "challengeType": 5, "type": "bonfire", "title": "Problem 498: Remainder of polynomial division", @@ -17265,7 +17265,7 @@ ] }, { - "_id": "5900f5611000cf542c510072", + "id": "5900f5611000cf542c510072", "challengeType": 5, "type": "bonfire", "title": "Problem 499: St. Petersburg Lottery", @@ -17294,7 +17294,7 @@ ] }, { - "_id": "5900f5611000cf542c510073", + "id": "5900f5611000cf542c510073", "challengeType": 5, "type": "bonfire", "title": "Problem 500: Problem 500!!!", @@ -17321,7 +17321,7 @@ ] }, { - "_id": "5900f5621000cf542c510074", + "id": "5900f5621000cf542c510074", "challengeType": 5, "type": "bonfire", "title": "Problem 501: Eight Divisors", @@ -17347,7 +17347,7 @@ ] }, { - "_id": "5900f5621000cf542c510075", + "id": "5900f5621000cf542c510075", "challengeType": 5, "type": "bonfire", "title": "Problem 502: Counting Castles", @@ -17388,7 +17388,7 @@ ] }, { - "_id": "5900f5631000cf542c510076", + "id": "5900f5631000cf542c510076", "challengeType": 5, "type": "bonfire", "title": "Problem 503: Compromise or persist", @@ -17423,7 +17423,7 @@ ] }, { - "_id": "5900f5641000cf542c510077", + "id": "5900f5641000cf542c510077", "challengeType": 5, "type": "bonfire", "title": "Problem 504: Square on the Inside", @@ -17451,7 +17451,7 @@ ] }, { - "_id": "5900f5661000cf542c510078", + "id": "5900f5661000cf542c510078", "challengeType": 5, "type": "bonfire", "title": "Problem 505: Bidirectional Recurrence", @@ -17477,7 +17477,7 @@ ] }, { - "_id": "5900f5671000cf542c510079", + "id": "5900f5671000cf542c510079", "challengeType": 5, "type": "bonfire", "title": "Problem 506: Clock sequence", @@ -17506,7 +17506,7 @@ ] }, { - "_id": "5900f5671000cf542c51007a", + "id": "5900f5671000cf542c51007a", "challengeType": 5, "type": "bonfire", "title": "Problem 507: Shortest Lattice Vector", @@ -17545,7 +17545,7 @@ ] }, { - "_id": "5900f5691000cf542c51007c", + "id": "5900f5691000cf542c51007c", "challengeType": 5, "type": "bonfire", "title": "Problem 508: Integers in base i-1", @@ -17585,7 +17585,7 @@ ] }, { - "_id": "5900f5691000cf542c51007b", + "id": "5900f5691000cf542c51007b", "challengeType": 5, "type": "bonfire", "title": "Problem 509: Divisor Nim", @@ -17617,7 +17617,7 @@ ] }, { - "_id": "5900f56b1000cf542c51007d", + "id": "5900f56b1000cf542c51007d", "challengeType": 5, "type": "bonfire", "title": "Problem 510: Tangent Circles", @@ -17645,7 +17645,7 @@ ] }, { - "_id": "5900f56b1000cf542c51007e", + "id": "5900f56b1000cf542c51007e", "challengeType": 5, "type": "bonfire", "title": "Problem 511: Sequences with nice divisibility properties", @@ -17686,7 +17686,7 @@ ] }, { - "_id": "5900f56d1000cf542c51007f", + "id": "5900f56d1000cf542c51007f", "challengeType": 5, "type": "bonfire", "title": "Problem 512: Sums of totients of powers", @@ -17714,7 +17714,7 @@ ] }, { - "_id": "5900f56e1000cf542c510080", + "id": "5900f56e1000cf542c510080", "challengeType": 5, "type": "bonfire", "title": "Problem 513: Integral median", @@ -17741,7 +17741,7 @@ ] }, { - "_id": "5900f56f1000cf542c510081", + "id": "5900f56f1000cf542c510081", "challengeType": 5, "type": "bonfire", "title": "Problem 514: Geoboard Shapes", @@ -17775,7 +17775,7 @@ ] }, { - "_id": "5900f5711000cf542c510083", + "id": "5900f5711000cf542c510083", "challengeType": 5, "type": "bonfire", "title": "Problem 515: Dissonant Numbers", @@ -17803,7 +17803,7 @@ ] }, { - "_id": "5900f5701000cf542c510082", + "id": "5900f5701000cf542c510082", "challengeType": 5, "type": "bonfire", "title": "Problem 516: 5-smooth totients", @@ -17831,7 +17831,7 @@ ] }, { - "_id": "5900f5721000cf542c510084", + "id": "5900f5721000cf542c510084", "challengeType": 5, "type": "bonfire", "title": "Problem 517: A real recursion", @@ -17861,7 +17861,7 @@ ] }, { - "_id": "5900f5721000cf542c510085", + "id": "5900f5721000cf542c510085", "challengeType": 5, "type": "bonfire", "title": "Problem 518: Prime triples and geometric sequences", @@ -17892,7 +17892,7 @@ ] }, { - "_id": "5900f5741000cf542c510086", + "id": "5900f5741000cf542c510086", "challengeType": 5, "type": "bonfire", "title": "Problem 519: Tricolored Coin Fountains", @@ -17920,7 +17920,7 @@ ] }, { - "_id": "5900f5751000cf542c510087", + "id": "5900f5751000cf542c510087", "challengeType": 5, "type": "bonfire", "title": "Problem 520: Simbers", @@ -17950,7 +17950,7 @@ ] }, { - "_id": "5900f5751000cf542c510088", + "id": "5900f5751000cf542c510088", "challengeType": 5, "type": "bonfire", "title": "Problem 521: Smallest prime factor", @@ -17979,7 +17979,7 @@ ] }, { - "_id": "5900f5761000cf542c510089", + "id": "5900f5761000cf542c510089", "challengeType": 5, "type": "bonfire", "title": "Problem 522: Hilbert's Blackout", @@ -18017,7 +18017,7 @@ ] }, { - "_id": "5900fe885726495c153991c8", + "id": "5900fe885726495c153991c8", "challengeType": 5, "type": "bonfire", "title": "Problem 523: First Sort I", @@ -18055,7 +18055,7 @@ ] }, { - "_id": "5900fece58d9425c70af4f5e", + "id": "5900fece58d9425c70af4f5e", "challengeType": 5, "type": "bonfire", "title": "Problem 524: First Sort II", @@ -18098,7 +18098,7 @@ ] }, { - "_id": "5900fecf58d9425c70af4f5f", + "id": "5900fecf58d9425c70af4f5f", "challengeType": 5, "type": "bonfire", "title": "Problem 525: Rolling Ellipse", @@ -18134,7 +18134,7 @@ ] }, { - "_id": "5900fed058d9425c70af4f60", + "id": "5900fed058d9425c70af4f60", "challengeType": 5, "type": "bonfire", "title": "Problem 526: Largest prime factors of consecutive numbers", @@ -18164,7 +18164,7 @@ ] }, { - "_id": "5900fed158d9425c70af4f61", + "id": "5900fed158d9425c70af4f61", "challengeType": 5, "type": "bonfire", "title": "Problem 527: Randomized Binary Search", @@ -18196,7 +18196,7 @@ ] }, { - "_id": "5900fed258d9425c70af4f62", + "id": "5900fed258d9425c70af4f62", "challengeType": 5, "type": "bonfire", "title": "Problem 528: Constrained Sums", @@ -18222,7 +18222,7 @@ ] }, { - "_id": "5900fed358d9425c70af4f63", + "id": "5900fed358d9425c70af4f63", "challengeType": 5, "type": "bonfire", "title": "Problem 529: 10-substrings", @@ -18251,7 +18251,7 @@ ] }, { - "_id": "5900fed458d9425c70af4f64", + "id": "5900fed458d9425c70af4f64", "challengeType": 5, "type": "bonfire", "title": "Problem 530: GCD of Divisors", @@ -18283,7 +18283,7 @@ ] }, { - "_id": "5900fed558d9425c70af4f65", + "id": "5900fed558d9425c70af4f65", "challengeType": 5, "type": "bonfire", "title": "Problem 531: Chinese leftovers", @@ -18318,7 +18318,7 @@ ] }, { - "_id": "5900fed658d9425c70af4f66", + "id": "5900fed658d9425c70af4f66", "challengeType": 5, "type": "bonfire", "title": "Problem 532: Nanobots on Geodesics", @@ -18350,7 +18350,7 @@ ] }, { - "_id": "5900fed758d9425c70af4f67", + "id": "5900fed758d9425c70af4f67", "challengeType": 5, "type": "bonfire", "title": "Problem 533: Minimum values of the Carmichael function", @@ -18378,7 +18378,7 @@ ] }, { - "_id": "5900fed858d9425c70af4f68", + "id": "5900fed858d9425c70af4f68", "challengeType": 5, "type": "bonfire", "title": "Problem 534: Weak Queens", @@ -18410,7 +18410,7 @@ ] }, { - "_id": "5900fed958d9425c70af4f69", + "id": "5900fed958d9425c70af4f69", "challengeType": 5, "type": "bonfire", "title": "Problem 535: Fractal Sequence", @@ -18442,7 +18442,7 @@ ] }, { - "_id": "5900feda58d9425c70af4f6a", + "id": "5900feda58d9425c70af4f6a", "challengeType": 5, "type": "bonfire", "title": "Problem 536: Modulo power identity", @@ -18471,7 +18471,7 @@ ] }, { - "_id": "5900fedb58d9425c70af4f6b", + "id": "5900fedb58d9425c70af4f6b", "challengeType": 5, "type": "bonfire", "title": "Problem 537: Counting tuples", @@ -18508,7 +18508,7 @@ ] }, { - "_id": "5900fedc58d9425c70af4f6c", + "id": "5900fedc58d9425c70af4f6c", "challengeType": 5, "type": "bonfire", "title": "Problem 538: Maximum quadrilaterals", @@ -18544,7 +18544,7 @@ ] }, { - "_id": "5900fedd58d9425c70af4f6d", + "id": "5900fedd58d9425c70af4f6d", "challengeType": 5, "type": "bonfire", "title": "Problem 539: Odd elimination", @@ -18579,7 +18579,7 @@ ] }, { - "_id": "5900fede58d9425c70af4f6e", + "id": "5900fede58d9425c70af4f6e", "challengeType": 5, "type": "bonfire", "title": "Problem 540: Counting primitive Pythagorean triples", @@ -18608,7 +18608,7 @@ ] }, { - "_id": "5900fedf58d9425c70af4f6f", + "id": "5900fedf58d9425c70af4f6f", "challengeType": 5, "type": "bonfire", "title": "Problem 541: Divisibility of Harmonic Number Denominators", @@ -18639,7 +18639,7 @@ ] }, { - "_id": "5900fee058d9425c70af4f70", + "id": "5900fee058d9425c70af4f70", "challengeType": 5, "type": "bonfire", "title": "Problem 542: Geometric Progression with Maximum Sum", @@ -18668,7 +18668,7 @@ ] }, { - "_id": "5900fee158d9425c70af4f71", + "id": "5900fee158d9425c70af4f71", "challengeType": 5, "type": "bonfire", "title": "Problem 543: Prime-Sum Numbers", @@ -18700,7 +18700,7 @@ ] }, { - "_id": "5900fee258d9425c70af4f72", + "id": "5900fee258d9425c70af4f72", "challengeType": 5, "type": "bonfire", "title": "Problem 544: Chromatic Conundrum", @@ -18730,7 +18730,7 @@ ] }, { - "_id": "5900fee358d9425c70af4f73", + "id": "5900fee358d9425c70af4f73", "challengeType": 5, "type": "bonfire", "title": "Problem 545: Faulhaber's Formulas", @@ -18762,7 +18762,7 @@ ] }, { - "_id": "5900fee458d9425c70af4f74", + "id": "5900fee458d9425c70af4f74", "challengeType": 5, "type": "bonfire", "title": "Problem 546: The Floor's Revenge", @@ -18788,7 +18788,7 @@ ] }, { - "_id": "5900fee558d9425c70af4f75", + "id": "5900fee558d9425c70af4f75", "challengeType": 5, "type": "bonfire", "title": "Problem 547: Distance of random points within hollow square laminae", @@ -18828,7 +18828,7 @@ ] }, { - "_id": "5900fee658d9425c70af4f76", + "id": "5900fee658d9425c70af4f76", "challengeType": 5, "type": "bonfire", "title": "Problem 548: Gozinta Chains", @@ -18857,7 +18857,7 @@ ] }, { - "_id": "5900fee758d9425c70af4f77", + "id": "5900fee758d9425c70af4f77", "challengeType": 5, "type": "bonfire", "title": "Problem 549: Divisibility of factorials", @@ -18888,7 +18888,7 @@ ] }, { - "_id": "5900fee858d9425c70af4f78", + "id": "5900fee858d9425c70af4f78", "challengeType": 5, "type": "bonfire", "title": "Problem 550: Divisor game", @@ -18921,7 +18921,7 @@ ] }, { - "_id": "5900fee958d9425c70af4f79", + "id": "5900fee958d9425c70af4f79", "challengeType": 5, "type": "bonfire", "title": "Problem 551: Sum of digits sequence", @@ -18948,7 +18948,7 @@ ] }, { - "_id": "5900feea58d9425c70af4f7a", + "id": "5900feea58d9425c70af4f7a", "challengeType": 5, "type": "bonfire", "title": "Problem 552: Chinese leftovers II", @@ -18986,7 +18986,7 @@ ] }, { - "_id": "5900feeb58d9425c70af4f7b", + "id": "5900feeb58d9425c70af4f7b", "challengeType": 5, "type": "bonfire", "title": "Problem 553: Power sets of power sets", @@ -19026,7 +19026,7 @@ ] }, { - "_id": "5900feec58d9425c70af4f7c", + "id": "5900feec58d9425c70af4f7c", "challengeType": 5, "type": "bonfire", "title": "Problem 554: Centaurs on a chess board", @@ -19058,7 +19058,7 @@ ] }, { - "_id": "5900feed58d9425c70af4f7d", + "id": "5900feed58d9425c70af4f7d", "challengeType": 5, "type": "bonfire", "title": "Problem 555: McCarthy 91 function", @@ -19118,7 +19118,7 @@ ] }, { - "_id": "5900feee58d9425c70af4f7e", + "id": "5900feee58d9425c70af4f7e", "challengeType": 5, "type": "bonfire", "title": "Problem 556: Squarefree Gaussian Integers", @@ -19165,7 +19165,7 @@ ] }, { - "_id": "5900feef58d9425c70af4f7f", + "id": "5900feef58d9425c70af4f7f", "challengeType": 5, "type": "bonfire", "title": "Problem 557: Cutting triangles", @@ -19199,7 +19199,7 @@ ] }, { - "_id": "5900fef058d9425c70af4f80", + "id": "5900fef058d9425c70af4f80", "challengeType": 5, "type": "bonfire", "title": "Problem 558: Irrational base", @@ -19235,7 +19235,7 @@ ] }, { - "_id": "5900fef158d9425c70af4f81", + "id": "5900fef158d9425c70af4f81", "challengeType": 5, "type": "bonfire", "title": "Problem 559: Permuted Matrices", @@ -19269,7 +19269,7 @@ ] }, { - "_id": "5900fef258d9425c70af4f82", + "id": "5900fef258d9425c70af4f82", "challengeType": 5, "type": "bonfire", "title": "Problem 560: Coprime Nim", @@ -19298,7 +19298,7 @@ ] }, { - "_id": "5900fef358d9425c70af4f83", + "id": "5900fef358d9425c70af4f83", "challengeType": 5, "type": "bonfire", "title": "Problem 561: Divisor Pairs", @@ -19329,7 +19329,7 @@ ] }, { - "_id": "5900fef458d9425c70af4f84", + "id": "5900fef458d9425c70af4f84", "challengeType": 5, "type": "bonfire", "title": "Problem 562: Maximal perimeter", @@ -19358,7 +19358,7 @@ ] }, { - "_id": "5900fef558d9425c70af4f85", + "id": "5900fef558d9425c70af4f85", "challengeType": 5, "type": "bonfire", "title": "Problem 563: Robot Welders", @@ -19388,7 +19388,7 @@ ] }, { - "_id": "5900fef658d9425c70af4f86", + "id": "5900fef658d9425c70af4f86", "challengeType": 5, "type": "bonfire", "title": "Problem 564: Maximal polygons", @@ -19419,7 +19419,7 @@ ] }, { - "_id": "5900fef758d9425c70af4f87", + "id": "5900fef758d9425c70af4f87", "challengeType": 5, "type": "bonfire", "title": "Problem 565: Divisibility of sum of divisors", @@ -19456,7 +19456,7 @@ ] }, { - "_id": "5900fef858d9425c70af4f88", + "id": "5900fef858d9425c70af4f88", "challengeType": 5, "type": "bonfire", "title": "Problem 566: Cake Icing Puzzle", @@ -19496,7 +19496,7 @@ ] }, { - "_id": "5900fef958d9425c70af4f89", + "id": "5900fef958d9425c70af4f89", "challengeType": 5, "type": "bonfire", "title": "Problem 567: Reciprocal games I", @@ -19529,7 +19529,7 @@ ] }, { - "_id": "5900fefa58d9425c70af4f8a", + "id": "5900fefa58d9425c70af4f8a", "challengeType": 5, "type": "bonfire", "title": "Problem 568: Reciprocal games II", @@ -19563,7 +19563,7 @@ ] }, { - "_id": "5900fefb58d9425c70af4f8b", + "id": "5900fefb58d9425c70af4f8b", "challengeType": 5, "type": "bonfire", "title": "Problem 569: Prime Mountain Range", @@ -19595,7 +19595,7 @@ ] }, { - "_id": "5900fefc58d9425c70af4f8c", + "id": "5900fefc58d9425c70af4f8c", "challengeType": 5, "type": "bonfire", "title": "Problem 570: Snowflakes", @@ -19633,7 +19633,7 @@ ] }, { - "_id": "5900fefd58d9425c70af4f8d", + "id": "5900fefd58d9425c70af4f8d", "challengeType": 5, "type": "bonfire", "title": "Problem 571: Super Pandigital Numbers", @@ -19662,7 +19662,7 @@ ] }, { - "_id": "5900fefe58d9425c70af4f8e", + "id": "5900fefe58d9425c70af4f8e", "challengeType": 5, "type": "bonfire", "title": "Problem 572: Idempotent matrices", @@ -19697,7 +19697,7 @@ ] }, { - "_id": "5900feff58d9425c70af4f8f", + "id": "5900feff58d9425c70af4f8f", "challengeType": 5, "type": "bonfire", "title": "Problem 573: Unfair race", @@ -19728,7 +19728,7 @@ ] }, { - "_id": "5900ff0058d9425c70af4f90", + "id": "5900ff0058d9425c70af4f90", "challengeType": 5, "type": "bonfire", "title": "Problem 574: Verifying Primes", @@ -19763,7 +19763,7 @@ ] }, { - "_id": "5900ff0158d9425c70af4f91", + "id": "5900ff0158d9425c70af4f91", "challengeType": 5, "type": "bonfire", "title": "Problem 575: Wandering Robots", @@ -19808,7 +19808,7 @@ ] }, { - "_id": "5900ff0258d9425c70af4f92", + "id": "5900ff0258d9425c70af4f92", "challengeType": 5, "type": "bonfire", "title": "Problem 576: Irrational jumps", @@ -19841,7 +19841,7 @@ ] }, { - "_id": "5900ff0358d9425c70af4f93", + "id": "5900ff0358d9425c70af4f93", "challengeType": 5, "type": "bonfire", "title": "Problem 577: Counting hexagons", @@ -19872,7 +19872,7 @@ ] }, { - "_id": "5900ff0458d9425c70af4f94", + "id": "5900ff0458d9425c70af4f94", "challengeType": 5, "type": "bonfire", "title": "Problem 578: Integers with decreasing prime powers", @@ -19904,7 +19904,7 @@ ] }, { - "_id": "5900ff0558d9425c70af4f95", + "id": "5900ff0558d9425c70af4f95", "challengeType": 5, "type": "bonfire", "title": "Problem 579: Lattice points in lattice cubes", @@ -19941,7 +19941,7 @@ ] }, { - "_id": "5900ff0658d9425c70af4f96", + "id": "5900ff0658d9425c70af4f96", "challengeType": 5, "type": "bonfire", "title": "Problem 580: Squarefree Hilbert numbers", @@ -19967,7 +19967,7 @@ ] }, { - "_id": "5900ff0758d9425c70af4f97", + "id": "5900ff0758d9425c70af4f97", "challengeType": 5, "type": "bonfire", "title": "Problem 581: 47-smooth triangular numbers", @@ -19991,7 +19991,7 @@ ] }, { - "_id": "5900ff0858d9425c70af4f98", + "id": "5900ff0858d9425c70af4f98", "challengeType": 5, "type": "bonfire", "title": "Problem 582: Nearly isosceles 120 degree triangles", @@ -20016,7 +20016,7 @@ ] }, { - "_id": "5900ff0958d9425c70af4f99", + "id": "5900ff0958d9425c70af4f99", "challengeType": 5, "type": "bonfire", "title": "Problem 583: Heron Envelopes", @@ -20052,7 +20052,7 @@ ] }, { - "_id": "5900ff0a58d9425c70af4f9a", + "id": "5900ff0a58d9425c70af4f9a", "challengeType": 5, "type": "bonfire", "title": "Problem 584: Birthday Problem Revisited", @@ -20092,7 +20092,7 @@ ] }, { - "_id": "5900ff0b58d9425c70af4f9b", + "id": "5900ff0b58d9425c70af4f9b", "challengeType": 5, "type": "bonfire", "title": "Problem 585: Nested square roots", @@ -20130,7 +20130,7 @@ ] }, { - "_id": "5900ff0c58d9425c70af4f9c", + "id": "5900ff0c58d9425c70af4f9c", "challengeType": 5, "type": "bonfire", "title": "Problem 586: Binary Quadratic Form", @@ -20165,7 +20165,7 @@ ] }, { - "_id": "5900ff0d58d9425c70af4f9d", + "id": "5900ff0d58d9425c70af4f9d", "challengeType": 5, "type": "bonfire", "title": "Problem 587: Concave triangle", @@ -20210,7 +20210,7 @@ ] }, { - "_id": "5900ff0e58d9425c70af4f9e", + "id": "5900ff0e58d9425c70af4f9e", "challengeType": 5, "type": "bonfire", "title": "Problem 588: Quintinomial coefficients", @@ -20247,7 +20247,7 @@ ] }, { - "_id": "5900ff0f58d9425c70af4f9f", + "id": "5900ff0f58d9425c70af4f9f", "challengeType": 5, "type": "bonfire", "title": "Problem 589: Poohsticks Marathon", @@ -20284,7 +20284,7 @@ ] }, { - "_id": "5900ff1058d9425c70af4fa0", + "id": "5900ff1058d9425c70af4fa0", "challengeType": 5, "type": "bonfire", "title": "Problem 590: Sets with a given Least Common Multiple", @@ -20321,7 +20321,7 @@ ] }, { - "_id": "5900ff1158d9425c70af4fa1", + "id": "5900ff1158d9425c70af4fa1", "challengeType": 5, "type": "bonfire", "title": "Problem 591: Best Approximations by Quadratic Integers", @@ -20351,7 +20351,7 @@ ] }, { - "_id": "5900ff1258d9425c70af4fa2", + "id": "5900ff1258d9425c70af4fa2", "challengeType": 5, "type": "bonfire", "title": "Problem 592: Factorial trailing digits 2", @@ -20378,7 +20378,7 @@ ] }, { - "_id": "5900ff1358d9425c70af4fa3", + "id": "5900ff1358d9425c70af4fa3", "challengeType": 5, "type": "bonfire", "title": "Problem 593: Fleeting Medians", @@ -20410,7 +20410,7 @@ ] }, { - "_id": "5900ff1458d9425c70af4fa4", + "id": "5900ff1458d9425c70af4fa4", "challengeType": 5, "type": "bonfire", "title": "Problem 594: Rhombus Tilings", @@ -20451,7 +20451,7 @@ ] }, { - "_id": "5900ff1558d9425c70af4fa5", + "id": "5900ff1558d9425c70af4fa5", "challengeType": 5, "type": "bonfire", "title": "Problem 595: Incremental Random Sort", @@ -20484,7 +20484,7 @@ ] }, { - "_id": "5900ff1658d9425c70af4fa6", + "id": "5900ff1658d9425c70af4fa6", "challengeType": 5, "type": "bonfire", "title": "Problem 596: Number of lattice points in a hyperball", @@ -20510,7 +20510,7 @@ ] }, { - "_id": "5900ff1758d9425c70af4fa7", + "id": "5900ff1758d9425c70af4fa7", "challengeType": 5, "type": "bonfire", "title": "Problem 597: Torpids", @@ -20593,7 +20593,7 @@ ] }, { - "_id": "5900ff1858d9425c70af4fa8", + "id": "5900ff1858d9425c70af4fa8", "challengeType": 5, "type": "bonfire", "title": "Problem 598: Split Divisibilities", @@ -20625,7 +20625,7 @@ ] }, { - "_id": "5900ff1958d9425c70af4fa9", + "id": "5900ff1958d9425c70af4fa9", "challengeType": 5, "type": "bonfire", "title": "Problem 599: Distinct Colourings of a Rubik's Cube", @@ -20659,7 +20659,7 @@ ] }, { - "_id": "5900ff1a58d9425c70af4faa", + "id": "5900ff1a58d9425c70af4faa", "challengeType": 5, "type": "bonfire", "title": "Problem 600: Integer sided equiangular hexagons", diff --git a/test-challenges.js b/test-challenges.js index b645f0a71c..10e10b1107 100644 --- a/test-challenges.js +++ b/test-challenges.js @@ -2,8 +2,30 @@ import _ from 'lodash'; import { Observable } from 'rx'; import tape from 'tape'; +import { isMongoId } from 'validator'; + import getChallenges from './getChallenges'; +const notMongoId = id => !isMongoId(id); + +let existingIds = []; + +function validateObjectId(id, title) { + if (notMongoId(id)) { + throw new Error(`Expected a vaild ObjectId for ${title}, got ${id}`); + } + const idIndex = _.findIndex(existingIds, existing => id === existing); + if (idIndex !== -1) { + throw new Error(` + All challenges must have a unique id. + + The id for ${title} is already assigned + `); + } + existingIds = [ ...existingIds, id ]; + return; +} + function createIsAssert(t, isThing) { const { assert } = t; return function() { @@ -52,6 +74,7 @@ function fillAssert(t) { function createTest({ title, + id = '', tests = [], solutions = [], head = [], @@ -60,6 +83,7 @@ function createTest({ redux = false, reactRedux = false }) { + validateObjectId(id, title); solutions = solutions.filter(solution => !!solution); tests = tests.filter(test => !!test); @@ -215,7 +239,7 @@ Observable.from(getChallenges()) .toArray() .subscribe( (noSolutions) => { - if(noSolutions){ + if (noSolutions) { console.log( '# These challenges have no solutions\n- [ ] ' + noSolutions.join('\n- [ ] ')