55 lines
1.3 KiB
Markdown
55 lines
1.3 KiB
Markdown
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---
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id: 5900f4231000cf542c50ff36
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title: 'Problem 183: Maximum product of parts'
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challengeType: 5
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forumTopicId: 301819
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dashedName: problem-183-maximum-product-of-parts
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---
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# --description--
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Let N be a positive integer and let N be split into k equal parts, r = N/k, so that N = r + r + ... + r.
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Let P be the product of these parts, P = r × r × ... × r = rk.
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For example, if 11 is split into five equal parts, 11 = 2.2 + 2.2 + 2.2 + 2.2 + 2.2, then P = 2.25 = 51.53632.
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Let M(N) = Pmax for a given value of N.
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It turns out that the maximum for N = 11 is found by splitting eleven into four equal parts which leads to Pmax = (11/4)4; that is, M(11) = 14641/256 = 57.19140625, which is a terminating decimal.
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However, for N = 8 the maximum is achieved by splitting it into three equal parts, so M(8) = 512/27, which is a non-terminating decimal.
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Let D(N) = N if M(N) is a non-terminating decimal and D(N) = -N if M(N) is a terminating decimal.
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For example, ΣD(N) for 5 ≤ N ≤ 100 is 2438.
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Find ΣD(N) for 5 ≤ N ≤ 10000.
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# --hints--
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`euler183()` should return 48861552.
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```js
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assert.strictEqual(euler183(), 48861552);
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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 euler183() {
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return true;
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}
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euler183();
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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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