fix(curriculum): rework Project Euler 73 (#42300)

* fix: rework challenge to use argument in function

* fix: add solution

* fix: use MathJax to improve math notation look

curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-73-counting-fractions-in-a-range.md

@@ -8,28 +8,46 @@ dashedName: problem-73-counting-fractions-in-a-range
 
 # --description--
 
-Consider the fraction, `n`/`d`, where n and d are positive integers. If `n`<`d` and HCF(`n`,`d`)=1, it is called a reduced proper fraction.
+Consider the fraction, $\frac{n}{d}$, where `n` and `d` are positive integers. If `n` < `d` and highest common factor, ${HCF}(n, d) = 1$, it is called a reduced proper fraction.
 
 If we list the set of reduced proper fractions for `d` ≤ 8 in ascending order of size, we get:
 
-<div style='text-align: center;'>1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, <strong>3/8</strong>, <strong>2/5</strong>, <strong>3/7</strong>, 1/2, 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8</div>
+$$\frac{1}{8}, \frac{1}{7}, \frac{1}{6}, \frac{1}{5}, \frac{1}{4}, \frac{2}{7}, \frac{1}{3}, \mathbf{\frac{3}{8}, \frac{2}{5}, \frac{3}{7}}, \frac{1}{2}, \frac{4}{7}, \frac{3}{5}, \frac{5}{8}, \frac{2}{3}, \frac{5}{7}, \frac{3}{4}, \frac{4}{5}, \frac{5}{6}, \frac{6}{7}, \frac{7}{8}$$
 
-It can be seen that there are 3 fractions between 1/3 and 1/2.
+It can be seen that there are `3` fractions between $\frac{1}{3}$ and $\frac{1}{2}$.
 
-How many fractions lie between 1/3 and 1/2 in the sorted set of reduced proper fractions for `d` ≤ 12,000?
+How many fractions lie between $\frac{1}{3}$ and $\frac{1}{2}$ in the sorted set of reduced proper fractions for `d` ≤ `limit`?
 
 # --hints--
 
-`countingFractionsInARange()` should return a number.
+`countingFractionsInARange(8)` should return a number.
 
 ```js
-assert(typeof countingFractionsInARange() === 'number');
+assert(typeof countingFractionsInARange(8) === 'number');
 ```
 
-`countingFractionsInARange()` should return 7295372.
+`countingFractionsInARange(8)` should return `3`.
 
 ```js
-assert.strictEqual(countingFractionsInARange(), 7295372);
+assert.strictEqual(countingFractionsInARange(8), 3);
+```
+
+`countingFractionsInARange(1000)` should return `50695`.
+
+```js
+assert.strictEqual(countingFractionsInARange(1000), 50695);
+```
+
+`countingFractionsInARange(6000)` should return `1823861`.
+
+```js
+assert.strictEqual(countingFractionsInARange(6000), 1823861);
+```
+
+`countingFractionsInARange(12000)` should return `7295372`.
+
+```js
+assert.strictEqual(countingFractionsInARange(12000), 7295372);
 ```
 
 # --seed--
@@ -37,16 +55,29 @@ assert.strictEqual(countingFractionsInARange(), 7295372);
 ## --seed-contents--
 
 ```js
-function countingFractionsInARange() {
+function countingFractionsInARange(limit) {
 
   return true;
 }
 
-countingFractionsInARange();
+countingFractionsInARange(8);
 ```
 
 # --solutions--
 
 ```js
-// solution required
+function countingFractionsInARange(limit) {
+  let result = 0;
+  const stack = [[3, 2]];
+  while (stack.length > 0) {
+    const [startDenominator, endDenominator] = stack.pop();
+    const curDenominator = startDenominator + endDenominator;
+    if (curDenominator <= limit) {
+      result++;
+      stack.push([startDenominator, curDenominator]);
+      stack.push([curDenominator, endDenominator]);
+    }
+  }
+  return result;
+}
 ```