freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-201-subsets-with-a-unique-sum.md

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5900f4361000cf542c50ff48	Problem 201: Subsets with a unique sum	5	301841	problem-201-subsets-with-a-unique-sum

--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:

$$\begin{align} & sum(\{1,3,6\}) = 10 \\ & sum(\{1,3,8\}) = 12 \\ & sum(\{1,3,10\}) = 14 \\ & sum(\{1,3,11\}) = 15 \\ & sum(\{1,6,8\}) = 15 \\ & sum(\{1,6,10\}) = 17 \\ & sum(\{1,6,11\}) = 18 \\ & sum(\{1,8,10\}) = 19 \\ & sum(\{1,8,11\}) = 20 \\ & sum(\{1,10,11\}) = 22 \\ & sum(\{3,6,8\}) = 17 \\ & sum(\{3,6,10\}) = 19 \\ & sum(\{3,6,11\}) = 20 \\ & sum(\{3,8,10\}) = 21 \\ & sum(\{3,8,11\}) = 22 \\ & sum(\{3,10,11\}) = 24 \\ & sum(\{6,8,10\}) = 24 \\ & sum(\{6,8,11\}) = 25 \\ & sum(\{6,10,11\}) = 27 \\ & sum(\{8,10,11\}) = 29 \end{align}$$

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 = \\{1^2, 2^2, \ldots , {100}^2\\}. S has 100\\,891\\,344\\,545\\,564\\,193\\,334\\,812\\,497\\,256\\; $50$-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)).

--hints--

uniqueSubsetsSum() should return 115039000.

assert.strictEqual(uniqueSubsetsSum(), 115039000);

--seed--

--seed-contents--

function uniqueSubsetsSum() {

  return true;
}

uniqueSubsetsSum();

--solutions--

// solution required