50 lines
1.3 KiB
Markdown
50 lines
1.3 KiB
Markdown
---
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id: 5900f3d71000cf542c50fee9
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title: 'Problem 106: Special subset sums: meta-testing'
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challengeType: 5
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forumTopicId: 301730
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dashedName: problem-106-special-subset-sums-meta-testing
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---
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# --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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1. $S(B) ≠ S(C)$; that is, sums of subsets cannot be equal.
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2. 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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# --hints--
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`subsetSumsMetaTesting()` should return `21384`.
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```js
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assert.strictEqual(subsetSumsMetaTesting(), 21384);
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```
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# --seed--
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## --seed-contents--
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```js
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function subsetSumsMetaTesting() {
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return true;
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}
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subsetSumsMetaTesting();
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```
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# --solutions--
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```js
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// solution required
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```
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