79d9012432
* fix(curriculum): tests quotes * fix(curriculum): fill seed-teardown * fix(curriculum): fix tests and remove unneeded seed-teardown
85 lines
2.1 KiB
Markdown
85 lines
2.1 KiB
Markdown
---
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id: 5900f5171000cf542c510029
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challengeType: 5
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title: 'Problem 426: Box-ball system'
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---
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## Description
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<section id='description'>
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Consider an infinite row of boxes. Some of the boxes contain a ball. For example, an initial configuration of 2 consecutive occupied boxes followed by 2 empty boxes, 2 occupied boxes, 1 empty box, and 2 occupied boxes can be denoted by the sequence (2, 2, 2, 1, 2), in which the number of consecutive occupied and empty boxes appear alternately.
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A turn consists of moving each ball exactly once according to the following rule: Transfer the leftmost ball which has not been moved to the nearest empty box to its right.
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After one turn the sequence (2, 2, 2, 1, 2) becomes (2, 2, 1, 2, 3) as can be seen below; note that we begin the new sequence starting at the first occupied box.
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A system like this is called a Box-Ball System or BBS for short.
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It can be shown that after a sufficient number of turns, the system evolves to a state where the consecutive numbers of occupied boxes is invariant. In the example below, the consecutive numbers of occupied boxes evolves to [1, 2, 3]; we shall call this the final state.
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We define the sequence {ti}:s0 = 290797
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sk+1 = sk2 mod 50515093
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tk = (sk mod 64) + 1
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Starting from the initial configuration (t0, t1, …, t10), the final state becomes [1, 3, 10, 24, 51, 75].
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Starting from the initial configuration (t0, t1, …, t10 000 000), find the final state.
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Give as your answer the sum of the squares of the elements of the final state. For example, if the final state is [1, 2, 3] then 14 ( = 12 + 22 + 32) is your answer.
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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>euler426()</code> should return 31591886008.
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testString: assert.strictEqual(euler426(), 31591886008, '<code>euler426()</code> should return 31591886008.');
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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 euler426() {
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// Good luck!
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return true;
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}
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euler426();
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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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