53 lines
1.2 KiB
Markdown
53 lines
1.2 KiB
Markdown
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---
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id: 5900f5371000cf542c51004a
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title: 'Problem 459: Flipping game'
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challengeType: 5
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forumTopicId: 302133
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dashedName: problem-459-flipping-game
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---
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# --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: the upper right corner of the rectangle contains a white disk the rectangle width is a perfect square (1, 4, 9, 16, ...) 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. 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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# --hints--
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`euler459()` should return 3996390106631.
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```js
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assert.strictEqual(euler459(), 3996390106631);
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```
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# --seed--
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## --seed-contents--
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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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# --solutions--
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```js
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// solution required
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```
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