diff --git a/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-78-coin-partitions.md b/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-78-coin-partitions.md
index c5d96870e5..61f145116f 100644
--- a/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-78-coin-partitions.md
+++ b/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-78-coin-partitions.md
@@ -8,7 +8,7 @@ dashedName: problem-78-coin-partitions
# --description--
-Let p(n) represent the number of different ways in which n coins can be separated into piles. For example, five coins can be separated into piles in exactly seven different ways, so p(5)=7.
+Let ${p}(n)$ represent the number of different ways in which `n` coins can be separated into piles. For example, five coins can be separated into piles in exactly seven different ways, so ${p}(5) = 7$.
@@ -22,22 +22,40 @@ Let p(n) represent the number of different ways in which n coins can be separate
| OO O O O |
| O O O O O |
-
+
-Find the least value of `n` for which p(`n`) is divisible by one million.
+Find the least value of `n` for which ${p}(n)$ is divisible by `divisor`.
# --hints--
-`coinPartitions()` should return a number.
+`coinPartitions(7)` should return a number.
```js
-assert(typeof coinPartitions() === 'number');
+assert(typeof coinPartitions(7) === 'number');
```
-`coinPartitions()` should return 55374.
+`coinPartitions(7)` should return `5`.
```js
-assert.strictEqual(coinPartitions(), 55374);
+assert.strictEqual(coinPartitions(7), 5);
+```
+
+`coinPartitions(10000)` should return `599`.
+
+```js
+assert.strictEqual(coinPartitions(10000), 599);
+```
+
+`coinPartitions(100000)` should return `11224`.
+
+```js
+assert.strictEqual(coinPartitions(100000), 11224);
+```
+
+`coinPartitions(1000000)` should return `55374`.
+
+```js
+assert.strictEqual(coinPartitions(1000000), 55374);
```
# --seed--
@@ -45,16 +63,41 @@ assert.strictEqual(coinPartitions(), 55374);
## --seed-contents--
```js
-function coinPartitions() {
+function coinPartitions(divisor) {
return true;
}
-coinPartitions();
+coinPartitions(7);
```
# --solutions--
```js
-// solution required
+function coinPartitions(divisor) {
+ const partitions = [1];
+
+ let n = 0;
+ while (partitions[n] !== 0) {
+ n++;
+ partitions.push(0);
+
+ let i = 0;
+ let pentagonal = 1;
+ while (pentagonal <= n) {
+ const sign = i % 4 > 1 ? -1 : 1;
+ partitions[n] += sign * partitions[n - pentagonal];
+ partitions[n] = partitions[n] % divisor;
+
+ i++;
+
+ let k = Math.floor(i / 2) + 1;
+ if (i % 2 !== 0) {
+ k *= -1;
+ }
+ pentagonal = Math.floor((k * (3 * k - 1)) / 2);
+ }
+ }
+ return n;
+}
```