79d9012432
* fix(curriculum): tests quotes * fix(curriculum): fill seed-teardown * fix(curriculum): fix tests and remove unneeded seed-teardown
89 lines
2.0 KiB
Markdown
89 lines
2.0 KiB
Markdown
---
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id: 5900f45b1000cf542c50ff6d
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challengeType: 5
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title: 'Problem 238: Infinite string tour'
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---
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## Description
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<section id='description'>
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Create a sequence of numbers using the "Blum Blum Shub" pseudo-random number generator:
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s0
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=
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14025256
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sn+1
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=
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sn2 mod 20300713
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Concatenate these numbers s0s1s2… to create a string w of infinite length.
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Then, w = 14025256741014958470038053646…
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For a positive integer k, if no substring of w exists with a sum of digits equal to k, p(k) is defined to be zero. If at least one substring of w exists with a sum of digits equal to k, we define p(k) = z, where z is the starting position of the earliest such substring.
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For instance:
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The substrings 1, 14, 1402, …
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with respective sums of digits equal to 1, 5, 7, …
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start at position 1, hence p(1) = p(5) = p(7) = … = 1.
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The substrings 4, 402, 4025, …
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with respective sums of digits equal to 4, 6, 11, …
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start at position 2, hence p(4) = p(6) = p(11) = … = 2.
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The substrings 02, 0252, …
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with respective sums of digits equal to 2, 9, …
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start at position 3, hence p(2) = p(9) = … = 3.
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Note that substring 025 starting at position 3, has a sum of digits equal to 7, but there was an earlier substring (starting at position 1) with a sum of digits equal to 7, so p(7) = 1, not 3.
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We can verify that, for 0 < k ≤ 103, ∑ p(k) = 4742.
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Find ∑ p(k), for 0 < k ≤ 2·1015.
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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>euler238()</code> should return 9922545104535660.
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testString: assert.strictEqual(euler238(), 9922545104535660, '<code>euler238()</code> should return 9922545104535660.');
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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 euler238() {
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// Good luck!
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return true;
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}
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euler238();
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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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