fix(challenges): Edit Description and Add Solution for Project Euler …

…44 (#17127)

Updated the problem description with <sup> and <var> tags, and centered
some text. Also, added a solution that user @elliotjz contributed to the
fCC Arcade Mode.

BREAKING CHANGE: None

seed/challenges/08-coding-interview-questions-and-take-home-assignments/project-euler-problems.json

@@ -1579,23 +1579,23 @@
       "type": "bonfire",
       "title": "Problem 44: Pentagon numbers",
       "tests": [
-        "assert.strictEqual(euler44(), 5482660, 'message: <code>euler44()</code> should return 5482660.');"
+        "assert.strictEqual(pentagonNumbers(), 5482660, 'message: <code>pentagonNumbers()</code> should return 5482660.');"
       ],
-      "solutions": [],
+      "solutions": ["function pentagonNumbers() {\n  function isPentagonal(num) {\n  // Formula found by solving pentagonal number\n  // equation for n.\n  const n = (Math.sqrt((24 * num) + 1) + 1) / 6;\n  return n % 1 === 0;\n  }\n\n  function pentagonal(num) {\n    return (num * ((3 * num) - 1)) / 2;\n  }\n  let result;\n  let i = 1;\n  while (!result) {\n  i++;\n  const num1 = (i * ((3 * i) - 1)) / 2; // Pentagonal num formula\n  const minDiff = num1 - (((i - 1) * ((3 * (i - 1)) - 1)) / 2);\n  let j = i - 1;\n  while (j > 0 && !result) {\n  const num2 = (j * ((3 * j) - 1)) / 2;\n  if (isPentagonal(num1 - num2) && isPentagonal(num1 + num2)) {\n        result = num1 - num2;\n      }\n      j--;\n    }\n  }\n  return result;\n  }"],
       "translations": {},
       "challengeSeed": [
-        "function euler44() {",
+        "function pentagonNumbers() {",
         "  // Good luck!",
         "  return true;",
         "}",
         "",
-        "euler44();"
+        "pentagonNumbers();"
       ],
       "description": [
-        "Pentagonal numbers are generated by the formula, Pn=n(3n−1)/2. The first ten pentagonal numbers are:",
-        "1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ...",
-        "It can be seen that P4 + P7 = 22 + 70 = 92 = P8. However, their difference, 70 − 22 = 48, is not pentagonal.",
-        "Find the pair of pentagonal numbers, Pj and Pk, for which their sum and difference are pentagonal and D = |Pk − Pj| is minimised; what is the value of D?"
+        "Pentagonal numbers are generated by the formula, P<sub>n</sub>=<var>n</var>(3<var>n</var>−1)/2. The first ten pentagonal numbers are:",
+        "<span style='display: block; text-align: center;'>1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ...</span>",
+        "It can be seen that P<sub>4</sub> + P<sub>7</sub> = 22 + 70 = 92 = P<sub>8</sub>. However, their difference, 70 − 22 = 48, is not pentagonal.",
+        "Find the pair of pentagonal numbers, P<sub>j</sub> and P<sub>k</sub>, for which their sum and difference are pentagonal and D = |P<sub>k</sub> − P<sub>j</sub>| is minimised; what is the value of D?"
       ]
     },
     {