fix: speed up tests

Either improved the algorithm or reduced the difficulty for the slowest
tests. All these pass with testProtectTimeout = 500, so should be safe
on most machines with the current timeout of 2500.

curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-12-highly-divisible-triangular-number.english.md

@@ -62,44 +62,67 @@ divisibleTriangleNumber(500);
 
 </div>
 
-
-
 </section>
 
 ## Solution
 <section id='solution'>
 
-
 ```js
 function divisibleTriangleNumber(n) {
+  if (n === 1) return 3;
   let counter = 1;
   let triangleNumber = counter++;
 
-  function getFactors(num) {
-    let factors = [];
 
-    let possibleFactor = 1;
-    let sqrt = Math.sqrt(num);
+ while (noOfFactors(triangleNumber) < n) {
+   triangleNumber += counter++;
+ }
+return triangleNumber;
+}
 
-    while (possibleFactor <= sqrt) {
-      if (num % possibleFactor == 0) {
-        factors.push(possibleFactor);
-        var otherPossibleFactor = num / possibleFactor;
-        if (otherPossibleFactor > possibleFactor) {
-          factors.push(otherPossibleFactor);
-        }
+function noOfFactors(num) {
+  const primeFactors = getPrimeFactors(num);
+  let prod = 1;
+  for(let p in primeFactors) {
+    prod *= (primeFactors[p] + 1)
+  }
+  return prod;
+}
+
+function getPrimeFactors(num) {
+  let n = num;
+  let primes = {};
+
+  let p = 2;
+  let sqrt = Math.sqrt(num);
+
+  function checkAndUpdate(inc) {
+    if (n % p === 0) {
+      const curr = primes[p];
+      if (curr) {
+        primes[p]++
+      } else {
+        primes[p] = 1;
       }
-      possibleFactor++;
+      n /= p;
+    } else {
+      p += inc;
     }
-
-    return factors;
   }
 
-  while (getFactors(triangleNumber).length < n) {
-    triangleNumber += counter++;
+  while(p === 2 && p <= n) {
+    checkAndUpdate(1);
   }
-  console.log(triangleNumber)
-  return triangleNumber;
+
+  while (p <= n && p <= sqrt) {
+    checkAndUpdate(2);
+  }
+  if(Object.keys(primes).length === 0) {
+    primes[num] = 1;
+  } else if(n !== 1) {
+    primes[n] = 1;
+  }
+  return primes;
 }
 ```
 

curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-14-longest-collatz-sequence.english.md

@@ -35,8 +35,8 @@ tests:
     testString: assert.strictEqual(longestCollatzSequence(46500), 35655);
   - text: <code>longestCollatzSequence(54512)</code> should return 52527.
     testString: assert.strictEqual(longestCollatzSequence(54512), 52527);
-  - text: <code>longestCollatzSequence(1000000)</code> should return 837799.
-    testString: assert.strictEqual(longestCollatzSequence(1000000), 837799);
+  - text: <code>longestCollatzSequence(100000)</code> should return 77031.
+    testString: assert.strictEqual(longestCollatzSequence(100000), 77031);
 
 ```
 

curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-7-10001st-prime.english.md

@@ -61,21 +61,22 @@ nthPrime(10001);
 
 
 ```js
-const nthPrime = (number)=>{
- let pN = 2;
- let step = 0;
- while (step<number) {
-   let isPrime = true;
-   for(let i = 2;i<pN;i++){
-      if(!(pN%i)){
+const nthPrime = n => {
+  let pN = 2;
+  let step = 0;
+  while (step < n) {
+    let isPrime = true;
+    let rootN = Math.sqrt(pN);
+    for (let i = 2; i <= rootN; i++) {
+      if (!(pN % i)) {
         isPrime = false;
         break;
       }
-   }
-   isPrime ? step++ : '';
+    }
+    isPrime ? step++ : '';
     pN++;
- }
- return pN-1;
+  }
+  return pN - 1;
 }
 ```