47 lines
1.2 KiB
Markdown
47 lines
1.2 KiB
Markdown
---
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id: 5900f4041000cf542c50ff17
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title: 'Problem 152: Writing one half as a sum of inverse squares'
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challengeType: 5
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forumTopicId: 301783
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dashedName: problem-152-writing-one-half-as-a-sum-of-inverse-squares
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---
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# --description--
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There are several ways to write the number $\frac{1}{2}$ as a sum of inverse squares using distinct integers.
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For instance, the numbers {2,3,4,5,7,12,15,20,28,35} can be used:
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$$\frac{1}{2} = \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \frac{1}{5^2} + \frac{1}{7^2} + \frac{1}{{12}^2} + \frac{1}{{15}^2} + \frac{1}{{20}^2} + \frac{1}{{28}^2} + \frac{1}{{35}^2}$$
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In fact, only using integers between 2 and 45 inclusive, there are exactly three ways to do it, the remaining two being: {2,3,4,6,7,9,10,20,28,35,36,45} and {2,3,4,6,7,9,12,15,28,30,35,36,45}.
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How many ways are there to write the number $\frac{1}{2}$ as a sum of inverse squares using distinct integers between 2 and 80 inclusive?
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# --hints--
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`sumInverseSquares()` should return `301`.
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```js
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assert.strictEqual(sumInverseSquares(), 301);
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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 sumInverseSquares() {
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return true;
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}
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sumInverseSquares();
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```
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# --solutions--
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```js
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// solution required
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```
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