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curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-29-distinct-powers.md

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+---
+id: 5900f3891000cf542c50fe9c
+challengeType: 5
+title: 'Problem 29: Distinct powers'
+forumTopicId: 301941
+---
+
+## Description
+<section id='description'>
+
+Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:
+
+<div style='padding-left: 4em;'>
+  2<sup>2</sup>=4, 2<sup>3</sup>=8, 2<sup>4</sup>=16, 2<sup>5</sup>=32 <br>
+  3<sup>2</sup>=9, 3<sup>3</sup>=27, 3<sup>4</sup>=81, 3<sup>5</sup>=243 <br>
+  4<sup>2</sup>=16, 4<sup>3</sup>=64, 4<sup>4</sup>=256, 4<sup>5</sup>=1024 <br>
+  5<sup>2</sup>=25, 5<sup>3</sup>=125, 5<sup>4</sup>=625, 5<sup>5</sup>=3125 <br>
+</div>
+
+If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:
+
+<div style='padding-left: 4em;'>
+  4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125
+</div>
+
+How many distinct terms are in the sequence generated by <var>a<sup>b</sup></var> for 2 ≤ <var>a</var> ≤ <var>`n`</var> and 2 ≤ <var>b</var> ≤ <var>`n`</var>?
+
+</section>
+
+## Instructions
+<section id='instructions'>
+
+</section>
+
+## Tests
+<section id='tests'>
+
+```yml
+tests:
+  - text: <code>distinctPowers(15)</code> should return a number.
+    testString: assert(typeof distinctPowers(15) === 'number');
+  - text: <code>distinctPowers(15)</code> should return 177.
+    testString: assert.strictEqual(distinctPowers(15), 177);
+  - text: <code>distinctPowers(20)</code> should return 324.
+    testString: assert.strictEqual(distinctPowers(20), 324);
+  - text: <code>distinctPowers(25)</code> should return 519.
+    testString: assert.strictEqual(distinctPowers(25), 519);
+  - text: <code>distinctPowers(30)</code> should return 755.
+    testString: assert.strictEqual(distinctPowers(30), 755);
+
+```
+
+</section>
+
+## Challenge Seed
+<section id='challengeSeed'>
+
+<div id='js-seed'>
+
+```js
+function distinctPowers(n) {
+
+  return n;
+}
+
+distinctPowers(30);
+```
+
+</div>
+
+
+
+</section>
+
+## Solution
+<section id='solution'>
+
+
+```js
+const distinctPowers = (n) => {
+  let list = [];
+  for (let a=2; a<=n; a++) {
+    for (let b=2; b<=n; b++) {
+      let term = Math.pow(a, b);
+      if (list.indexOf(term)===-1) list.push(term);
+    }
+  }
+  return list.length;
+};
+```
+
+</section>