87 lines
1.8 KiB
Markdown
87 lines
1.8 KiB
Markdown
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---
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id: 5900f3891000cf542c50fe9c
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title: 'Problem 29: Distinct powers'
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challengeType: 5
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forumTopicId: 301941
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dashedName: problem-29-distinct-powers
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---
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# --description--
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Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:
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<div style='padding-left: 4em;'>
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2<sup>2</sup>=4, 2<sup>3</sup>=8, 2<sup>4</sup>=16, 2<sup>5</sup>=32 <br>
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3<sup>2</sup>=9, 3<sup>3</sup>=27, 3<sup>4</sup>=81, 3<sup>5</sup>=243 <br>
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4<sup>2</sup>=16, 4<sup>3</sup>=64, 4<sup>4</sup>=256, 4<sup>5</sup>=1024 <br>
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5<sup>2</sup>=25, 5<sup>3</sup>=125, 5<sup>4</sup>=625, 5<sup>5</sup>=3125 <br>
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</div>
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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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<div style='padding-left: 4em;'>
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4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125
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</div>
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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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# --hints--
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`distinctPowers(15)` should return a number.
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```js
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assert(typeof distinctPowers(15) === 'number');
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```
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`distinctPowers(15)` should return 177.
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```js
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assert.strictEqual(distinctPowers(15), 177);
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```
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`distinctPowers(20)` should return 324.
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```js
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assert.strictEqual(distinctPowers(20), 324);
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```
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`distinctPowers(25)` should return 519.
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```js
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assert.strictEqual(distinctPowers(25), 519);
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```
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`distinctPowers(30)` should return 755.
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```js
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assert.strictEqual(distinctPowers(30), 755);
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```
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# --seed--
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## --seed-contents--
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```js
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function distinctPowers(n) {
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return n;
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}
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distinctPowers(30);
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```
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# --solutions--
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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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