43 lines
726 B
Markdown
43 lines
726 B
Markdown
|
---
|
||
|
id: 5900f42b1000cf542c50ff3d
|
||
|
title: 'Problem 190: Maximising a weighted product'
|
||
|
challengeType: 5
|
||
|
forumTopicId: 301828
|
||
|
dashedName: problem-190-maximising-a-weighted-product
|
||
|
---
|
||
|
|
||
|
# --description--
|
||
|
|
||
|
Let Sm = (x1, x2, ... , xm) be the m-tuple of positive real numbers with x1 + x2 + ... + xm = m for which Pm = x1 \* x22 \* ... \* xmm is maximised.
|
||
|
|
||
|
For example, it can be verified that \[P10] = 4112 (\[ ] is the integer part function).
|
||
|
|
||
|
Find Σ\[Pm] for 2 ≤ m ≤ 15.
|
||
|
|
||
|
# --hints--
|
||
|
|
||
|
`euler190()` should return 371048281.
|
||
|
|
||
|
```js
|
||
|
assert.strictEqual(euler190(), 371048281);
|
||
|
```
|
||
|
|
||
|
# --seed--
|
||
|
|
||
|
## --seed-contents--
|
||
|
|
||
|
```js
|
||
|
function euler190() {
|
||
|
|
||
|
return true;
|
||
|
}
|
||
|
|
||
|
euler190();
|
||
|
```
|
||
|
|
||
|
# --solutions--
|
||
|
|
||
|
```js
|
||
|
// solution required
|
||
|
```
|