fix(curriculum): rework Project Euler 74 (#42057)

* fix: rework challenge to use argument in function

* fix: add solution

* fix: use MathJax for consistent look

curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-74-digit-factorial-chains.md

@@ -10,39 +10,58 @@ dashedName: problem-74-digit-factorial-chains
 
 The number 145 is well known for the property that the sum of the factorial of its digits is equal to 145:
 
-<div style='margin-left: 4em;'>1! + 4! + 5! = 1 + 24 + 120 = 145</div>
+$$1! + 4! + 5! = 1 + 24 + 120 = 145$$
 
 Perhaps less well known is 169, in that it produces the longest chain of numbers that link back to 169; it turns out that there are only three such loops that exist:
 
-<div style='margin-left: 4em;'>
+$$\begin{align}
-  169 → 363601 → 1454 → 169<br>
+&169 → 363601 → 1454 → 169\\\\
-  871 → 45361 → 871<br>
+&871 → 45361 → 871\\\\
-  872 → 45362 → 872<br>
+&872 → 45362 → 872\\\\
-</div>
+\end{align}$$
+
 It is not difficult to prove that EVERY starting number will eventually get stuck in a loop. For example,
 
-<div style='margin-left: 4em;'>
+$$\begin{align}
-  69 → 363600 → 1454 → 169 → 363601 (→ 1454)<br>
+&69 → 363600 → 1454 → 169 → 363601\\ (→ 1454)\\\\
-  78 → 45360 → 871 → 45361 (→ 871)<br>
+&78 → 45360 → 871 → 45361\\ (→ 871)\\\\
-  540 → 145 (→ 145)<br>
+&540 → 145\\ (→ 145)\\\\
-</div>
+\end{align}$$
 
 Starting with 69 produces a chain of five non-repeating terms, but the longest non-repeating chain with a starting number below one million is sixty terms.
 
-How many chains, with a starting number below one million, contain exactly sixty non-repeating terms?
+How many chains, with a starting number below `n`, contain exactly sixty non-repeating terms?
 
 # --hints--
 
-`digitFactorialChains()` should return a number.
+`digitFactorialChains(2000)` should return a number.
 
 ```js
-assert(typeof digitFactorialChains() === 'number');
+assert(typeof digitFactorialChains(2000) === 'number');
 ```
 
-`digitFactorialChains()` should return 402.
+`digitFactorialChains(2000)` should return `6`.
 
 ```js
-assert.strictEqual(digitFactorialChains(), 402);
+assert.strictEqual(digitFactorialChains(2000), 6);
+```
+
+`digitFactorialChains(100000)` should return `42`.
+
+```js
+assert.strictEqual(digitFactorialChains(100000), 42);
+```
+
+`digitFactorialChains(500000)` should return `282`.
+
+```js
+assert.strictEqual(digitFactorialChains(500000), 282);
+```
+
+`digitFactorialChains(1000000)` should return `402`.
+
+```js
+assert.strictEqual(digitFactorialChains(1000000), 402);
 ```
 
 # --seed--
@@ -50,16 +69,63 @@ assert.strictEqual(digitFactorialChains(), 402);
 ## --seed-contents--
 
 ```js
-function digitFactorialChains() {
+function digitFactorialChains(n) {
 
   return true;
 }
 
-digitFactorialChains();
+digitFactorialChains(2000);
 ```
 
 # --solutions--
 
 ```js
-// solution required
+function digitFactorialChains(n) {
+  function sumDigitsFactorials(number) {
+    let sum = 0;
+    while (number > 0) {
+      sum += factorials[number % 10];
+      number = Math.floor(number / 10);
+    }
+    return sum;
+  }
+
+  const factorials = [1];
+  for (let i = 1; i < 10; i++) {
+    factorials.push(factorials[factorials.length - 1] * i);
+  }
+
+  const sequences = {
+    169: 3,
+    871: 2,
+    872: 2,
+    1454: 3,
+    45362: 2,
+    45461: 2,
+    3693601: 3
+  };
+  let result = 0;
+
+  for (let i = 2; i < n; i++) {
+    let curNum = i;
+    let chainLength = 0;
+    const curSequence = [];
+    while (curSequence.indexOf(curNum) === -1) {
+      curSequence.push(curNum);
+      curNum = sumDigitsFactorials(curNum);
+      chainLength++;
+      if (sequences.hasOwnProperty(curNum) > 0) {
+        chainLength += sequences[curNum];
+        break;
+      }
+    }
+    if (chainLength === 60) {
+      result++;
+    }
+    for (let j = 1; j < curSequence.length; j++) {
+      sequences[curSequence[j]] = chainLength - j;
+    }
+  }
+  return result;
+}
 ```