64 lines
1.5 KiB
Markdown
64 lines
1.5 KiB
Markdown
---
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id: 5900f3d71000cf542c50fee9
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challengeType: 5
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title: 'Problem 106: Special subset sums: meta-testing'
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forumTopicId: 301730
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---
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## Description
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<section id='description'>
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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:
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S(B) ≠ S(C); that is, sums of subsets cannot be equal.
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If B contains more elements than C then S(B) > S(C).
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For this problem we shall assume that a given set contains n strictly increasing elements and it already satisfies the second rule.
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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.
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For n = 12, how many of the 261625 subset pairs that can be obtained need to be tested for equality?
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NOTE: This problem is related to Problem 103 and Problem 105.
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>euler106()</code> should return 21384.
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testString: assert.strictEqual(euler106(), 21384);
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function euler106() {
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// Good luck!
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return true;
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}
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euler106();
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// solution required
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```
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</section>
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