71 lines
1.6 KiB
Markdown
71 lines
1.6 KiB
Markdown
---
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id: 5900f4b91000cf542c50ffcc
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challengeType: 5
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title: 'Problem 333: Special partitions'
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---
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## Description
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<section id='description'>
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All positive integers can be partitioned in such a way that each and every term of the partition can be expressed as 2ix3j, where i,j ≥ 0.
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Let's consider only those such partitions where none of the terms can divide any of the other terms.
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For example, the partition of 17 = 2 + 6 + 9 = (21x30 + 21x31 + 20x32) would not be valid since 2 can divide 6. Neither would the partition 17 = 16 + 1 = (24x30 + 20x30) since 1 can divide 16. The only valid partition of 17 would be 8 + 9 = (23x30 + 20x32).
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Many integers have more than one valid partition, the first being 11 having the following two partitions.
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11 = 2 + 9 = (21x30 + 20x32)
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11 = 8 + 3 = (23x30 + 20x31)
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Let's define P(n) as the number of valid partitions of n. For example, P(11) = 2.
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Let's consider only the prime integers q which would have a single valid partition such as P(17).
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The sum of the primes q <100 such that P(q)=1 equals 233.
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Find the sum of the primes q <1000000 such that P(q)=1.
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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>euler333()</code> should return 3053105.
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testString: assert.strictEqual(euler333(), 3053105, '<code>euler333()</code> should return 3053105.');
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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 euler333() {
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// Good luck!
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return true;
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}
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euler333();
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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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