110 lines
1.8 KiB
Markdown
110 lines
1.8 KiB
Markdown
---
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id: 5900f4ba1000cf542c50ffcd
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challengeType: 5
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title: 'Problem 334: Spilling the beans'
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---
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## Description
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<section id='description'>
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In Plato's heaven, there exist an infinite number of bowls in a straight line.
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Each bowl either contains some or none of a finite number of beans.
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A child plays a game, which allows only one kind of move: removing two beans from any bowl, and putting one in each of the two adjacent bowls. The game ends when each bowl contains either one or no beans.
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For example, consider two adjacent bowls containing 2 and 3 beans respectively, all other bowls being empty. The following eight moves will finish the game:
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You are given the following sequences:
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t0 = 123456.
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ti =
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ti-12
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,
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if ti-1 is even
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ti-12
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926252,
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if ti-1 is odd
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where ⌊x⌋ is the floor function
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and is the bitwise XOR operator.
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bi = ( ti mod 211) + 1.
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The first two terms of the last sequence are b1 = 289 and b2 = 145.
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If we start with b1 and b2 beans in two adjacent bowls, 3419100 moves would be required to finish the game.
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Consider now 1500 adjacent bowls containing b1, b2,..., b1500 beans respectively, all other bowls being empty. Find how many moves it takes before the game ends.
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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>euler334()</code> should return 150320021261690850.
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testString: 'assert.strictEqual(euler334(), 150320021261690850, ''<code>euler334()</code> should return 150320021261690850.'');'
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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 euler334() {
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// Good luck!
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return true;
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}
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euler334();
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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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