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id	title	challengeType	forumTopicId	dashedName
5900f3d71000cf542c50fee9	Problem 106: Special subset sums: meta-testing	5	301730	problem-106-special-subset-sums-meta-testing

--description--

Let S(A) represent the sum of elements in set A of size n. We shall call it a special sum set if for any two non-empty disjoint subsets, B and C, the following properties are true:

S(B) ≠ S(C); that is, sums of subsets cannot be equal.
If B contains more elements than C then S(B) > S(C).

For this problem we shall assume that a given set contains n strictly increasing elements and it already satisfies the second rule.

Surprisingly, out of the 25 possible subset pairs that can be obtained from a set for which n = 4, only 1 of these pairs need to be tested for equality (first rule). Similarly, when n = 7, only 70 out of the 966 subset pairs need to be tested.

For n = 12, how many of the 261625 subset pairs that can be obtained need to be tested for equality?

Note: This problem is related to Problem 103 and Problem 105.

--hints--

subsetSumsMetaTesting() should return 21384.

assert.strictEqual(subsetSumsMetaTesting(), 21384);

--seed--

--seed-contents--

function subsetSumsMetaTesting() {

  return true;
}

subsetSumsMetaTesting();

--solutions--

// solution required

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