81 lines
1.7 KiB
Markdown
81 lines
1.7 KiB
Markdown
---
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id: 5900f3891000cf542c50fe9c
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challengeType: 5
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title: 'Problem 29: Distinct powers'
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forumTopicId: 301941
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---
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## Description
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<section id='description'>
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Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:
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22=4, 23=8, 24=16, 25=32
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32=9, 33=27, 34=81, 35=243
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42=16, 43=64, 44=256, 45=1024
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52=25, 53=125, 54=625, 55=3125
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If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:
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4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125
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How many distinct terms are in the sequence generated by ab for 2 ≤ a ≤ n and 2 ≤ b ≤ n?
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>distinctPowers(15)</code> should return 177.
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testString: assert.strictEqual(distinctPowers(15), 177);
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- text: <code>distinctPowers(20)</code> should return 324.
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testString: assert.strictEqual(distinctPowers(20), 324);
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- text: <code>distinctPowers(25)</code> should return 519.
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testString: assert.strictEqual(distinctPowers(25), 519);
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- text: <code>distinctPowers(30)</code> should return 755.
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testString: assert.strictEqual(distinctPowers(30), 755);
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function distinctPowers(n) {
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// Good luck!
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return n;
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}
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distinctPowers(30);
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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const distinctPowers = (n) => {
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let list = [];
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for (let a=2; a<=n; a++) {
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for (let b=2; b<=n; b++) {
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let term = Math.pow(a, b);
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if (list.indexOf(term)===-1) list.push(term);
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}
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}
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return list.length;
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};
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```
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</section>
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