freeCodeCamp/problem-408-admissible-paths-through-a-grid.english.md at 81a0c0c8e07a6c3a4f99228a8af10967fa0c53d9

Valeriy 79d9012432 fix(curriculum): quotes in tests (#18828 )

* fix(curriculum): tests quotes

* fix(curriculum): fill seed-teardown

* fix(curriculum): fix tests and remove unneeded seed-teardown

2018-10-20 23:32:47 +05:30

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Raw Blame History

id, challengeType, title

id	challengeType	title
5900f5091000cf542c51001b	5	Problem 408: Admissible paths through a grid

Description

Let's call a lattice point (x, y) inadmissible if x, y and x + y are all positive perfect squares. For example, (9, 16) is inadmissible, while (0, 4), (3, 1) and (9, 4) are not.

Consider a path from point (x1, y1) to point (x2, y2) using only unit steps north or east. Let's call such a path admissible if none of its intermediate points are inadmissible.

Let P(n) be the number of admissible paths from (0, 0) to (n, n). It can be verified that P(5) = 252, P(16) = 596994440 and P(1000) mod 1 000 000 007 = 341920854.

Find P(10 000 000) mod 1 000 000 007.

Instructions

Tests

tests:
  - text: <code>euler408()</code> should return 299742733.
    testString: assert.strictEqual(euler408(), 299742733, '<code>euler408()</code> should return 299742733.');

Challenge Seed

function euler408() {
  // Good luck!
  return true;
}

euler408();

Solution

// solution required

1.2 KiB Raw Blame History