78 lines
1.4 KiB
Markdown
78 lines
1.4 KiB
Markdown
---
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id: 5900f5371000cf542c51004a
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challengeType: 5
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title: 'Problem 459: Flipping game'
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forumTopicId: 302133
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---
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## Description
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<section id='description'>
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The flipping game is a two player game played on a N by N square board.
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Each square contains a disk with one side white and one side black.
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The game starts with all disks showing their white side.
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A turn consists of flipping all disks in a rectangle with the following properties:
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the upper right corner of the rectangle contains a white disk
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the rectangle width is a perfect square (1, 4, 9, 16, ...)
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the rectangle height is a triangular number (1, 3, 6, 10, ...)
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Players alternate turns. A player wins by turning the grid all black.
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Let W(N) be the number of winning moves for the first player on a N by N board with all disks white, assuming perfect play.
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W(1) = 1, W(2) = 0, W(5) = 8 and W(102) = 31395.
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For N=5, the first player's eight winning first moves are:
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Find W(106).
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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>euler459()</code> should return 3996390106631.
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testString: assert.strictEqual(euler459(), 3996390106631);
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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 euler459() {
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return true;
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}
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euler459();
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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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