88 lines
1.6 KiB
Markdown
88 lines
1.6 KiB
Markdown
---
|
|
id: 5900f4361000cf542c50ff48
|
|
challengeType: 5
|
|
title: 'Problem 201: Subsets with a unique sum'
|
|
---
|
|
|
|
## Description
|
|
<section id='description'>
|
|
For any set A of numbers, let sum(A) be the sum of the elements of A.
|
|
Consider the set B = {1,3,6,8,10,11}. There are 20 subsets of B containing three elements, and their sums are:
|
|
|
|
|
|
sum({1,3,6}) = 10,
|
|
sum({1,3,8}) = 12,
|
|
sum({1,3,10}) = 14,
|
|
sum({1,3,11}) = 15,
|
|
sum({1,6,8}) = 15,
|
|
sum({1,6,10}) = 17,
|
|
sum({1,6,11}) = 18,
|
|
sum({1,8,10}) = 19,
|
|
sum({1,8,11}) = 20,
|
|
sum({1,10,11}) = 22,
|
|
sum({3,6,8}) = 17,
|
|
sum({3,6,10}) = 19,
|
|
sum({3,6,11}) = 20,
|
|
sum({3,8,10}) = 21,
|
|
sum({3,8,11}) = 22,
|
|
sum({3,10,11}) = 24,
|
|
sum({6,8,10}) = 24,
|
|
sum({6,8,11}) = 25,
|
|
sum({6,10,11}) = 27,
|
|
sum({8,10,11}) = 29.
|
|
|
|
Some of these sums occur more than once, others are unique.
|
|
For a set A, let U(A,k) be the set of unique sums of k-element subsets of A, in our example we find U(B,3) = {10,12,14,18,21,25,27,29} and sum(U(B,3)) = 156.
|
|
|
|
Now consider the 100-element set S = {12, 22, ... , 1002}.
|
|
S has 100891344545564193334812497256 50-element subsets.
|
|
|
|
Determine the sum of all integers which are the sum of exactly one of the 50-element subsets of S, i.e. find sum(U(S,50)).
|
|
</section>
|
|
|
|
## Instructions
|
|
<section id='instructions'>
|
|
|
|
</section>
|
|
|
|
## Tests
|
|
<section id='tests'>
|
|
|
|
```yml
|
|
tests:
|
|
- text: <code>euler201()</code> should return 115039000.
|
|
testString: assert.strictEqual(euler201(), 115039000);
|
|
|
|
```
|
|
|
|
</section>
|
|
|
|
## Challenge Seed
|
|
<section id='challengeSeed'>
|
|
|
|
<div id='js-seed'>
|
|
|
|
```js
|
|
function euler201() {
|
|
// Good luck!
|
|
return true;
|
|
}
|
|
|
|
euler201();
|
|
```
|
|
|
|
</div>
|
|
|
|
|
|
|
|
</section>
|
|
|
|
## Solution
|
|
<section id='solution'>
|
|
|
|
```js
|
|
// solution required
|
|
```
|
|
|
|
</section>
|