diff --git a/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-92-square-digit-chains.md b/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-92-square-digit-chains.md
index 7c0ecc19d0..065f0b748d 100644
--- a/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-92-square-digit-chains.md
+++ b/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-92-square-digit-chains.md
@@ -12,27 +12,45 @@ A number chain is created by continuously adding the square of the digits in a n
For example,
-
- 44 → 32 → 13 → 10 → 1 → 1
- 85 → 89 → 145 → 42 → 20 → 4 → 16 → 37 → 58 → 89
-
+$$\begin{align}
+ & 44 → 32 → 13 → 10 → \boldsymbol{1} → \boldsymbol{1}\\\\
+ & 85 → \boldsymbol{89} → 145 → 42 → 20 → 4 → 16 → 37 → 58 → \boldsymbol{89}\\\\
+\end{align}$$
Therefore any chain that arrives at 1 or 89 will become stuck in an endless loop. What is most amazing is that EVERY starting number will eventually arrive at 1 or 89.
-How many starting numbers below ten million will arrive at 89?
+How many starting numbers below `limit` will arrive at 89?
# --hints--
-`squareDigitChains()` should return a number.
+`squareDigitChains(100)` should return a number.
```js
-assert(typeof squareDigitChains() === 'number');
+assert(typeof squareDigitChains(100) === 'number');
```
-`squareDigitChains()` should return 8581146.
+`squareDigitChains(100)` should return `80`.
```js
-assert.strictEqual(squareDigitChains(), 8581146);
+assert.strictEqual(squareDigitChains(100), 80);
+```
+
+`squareDigitChains(1000)` should return `857`.
+
+```js
+assert.strictEqual(squareDigitChains(1000), 857);
+```
+
+`squareDigitChains(100000)` should return `85623`.
+
+```js
+assert.strictEqual(squareDigitChains(100000), 85623);
+```
+
+`squareDigitChains(10000000)` should return `8581146`.
+
+```js
+assert.strictEqual(squareDigitChains(10000000), 8581146);
```
# --seed--
@@ -40,16 +58,98 @@ assert.strictEqual(squareDigitChains(), 8581146);
## --seed-contents--
```js
-function squareDigitChains() {
+function squareDigitChains(limit) {
return true;
}
-squareDigitChains();
+squareDigitChains(100);
```
# --solutions--
```js
-// solution required
+function squareDigitChains(limit) {
+ // Based on https://www.xarg.org/puzzle/project-euler/problem-92/
+ function getCombinations(neededDigits, curDigits) {
+ if (neededDigits === curDigits.length) {
+ return [curDigits];
+ }
+ const combinations = [];
+ const lastDigit = curDigits.length !== 0 ? curDigits[0] : 9;
+ for (let i = 0; i <= lastDigit; i++) {
+ const results = getCombinations(neededDigits, [i].concat(curDigits));
+ combinations.push(...results);
+ }
+ return combinations;
+ }
+
+ function getPossibleSums(limit) {
+ const digitsCount = getDigits(limit).length - 1;
+ const possibleSquaredSums = [false];
+ for (let i = 1; i <= 81 * digitsCount; i++) {
+ let curVal = i;
+ while (curVal !== 1 && curVal !== 89) {
+ curVal = addSquaredDigits(curVal);
+ }
+ possibleSquaredSums[i] = curVal === 89;
+ }
+ return possibleSquaredSums;
+ }
+
+ function addSquaredDigits(num) {
+ const digits = getDigits(num);
+ let result = 0;
+ for (let i = 0; i < digits.length; i++) {
+ result += digits[i] ** 2;
+ }
+ return result;
+ }
+
+ function getDigits(number) {
+ const digits = [];
+ while (number > 0) {
+ digits.push(number % 10);
+ number = Math.floor(number / 10);
+ }
+ return digits;
+ }
+
+ function getFactorials(number) {
+ const factorials = [1];
+ for (let i = 1; i < number; i++) {
+ factorials[i] = factorials[i - 1] * i;
+ }
+ return factorials;
+ }
+
+ const neededDigits = getDigits(limit).length - 1;
+ const combinations = getCombinations(neededDigits, []);
+ const possibleSquaredDigitsSums = getPossibleSums(limit);
+ const factorials = getFactorials(neededDigits + 1);
+
+ let endingWith89 = 0;
+
+ for (let i = 0; i < combinations.length; i++) {
+ let counts = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
+ let digits = combinations[i];
+ let curSum = 0;
+ for (let j = 0; j < digits.length; j++) {
+ const curDigit = digits[j];
+ curSum += curDigit ** 2;
+ counts[curDigit]++;
+ }
+
+ if (possibleSquaredDigitsSums[curSum]) {
+ let denominator = 1;
+ for (let j = 0; j < counts.length; j++) {
+ denominator = denominator * factorials[counts[j]];
+ }
+ endingWith89 += Math.floor(
+ factorials[factorials.length - 1] / denominator
+ );
+ }
+ }
+ return endingWith89;
+}
```