---
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, '<code>euler201()</code> should return 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>
