51 lines
1.4 KiB
Markdown
51 lines
1.4 KiB
Markdown
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---
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id: 5900f4b71000cf542c50ffca
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title: 'Problem 331: Cross flips'
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challengeType: 5
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forumTopicId: 301989
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dashedName: problem-331-cross-flips
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---
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# --description--
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N×N disks are placed on a square game board. Each disk has a black side and white side.
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At each turn, you may choose a disk and flip all the disks in the same row and the same column as this disk: thus 2×N-1 disks are flipped. The game ends when all disks show their white side. The following example shows a game on a 5×5 board.
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It can be proven that 3 is the minimal number of turns to finish this game.
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The bottom left disk on the N×N board has coordinates (0,0); the bottom right disk has coordinates (N-1,0) and the top left disk has coordinates (0,N-1).
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Let CN be the following configuration of a board with N×N disks: A disk at (x,y) satisfying , shows its black side; otherwise, it shows its white side. C5 is shown above.
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Let T(N) be the minimal number of turns to finish a game starting from configuration CN or 0 if configuration CN is unsolvable. We have shown that T(5)=3. You are also given that T(10)=29 and T(1 000)=395253.
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Find .
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# --hints--
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`euler331()` should return 467178235146843500.
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```js
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assert.strictEqual(euler331(), 467178235146843500);
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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 euler331() {
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return true;
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}
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euler331();
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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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