73 lines
1.6 KiB
Markdown
73 lines
1.6 KiB
Markdown
---
|
||
id: 5900f4b71000cf542c50ffca
|
||
challengeType: 5
|
||
title: 'Problem 331: Cross flips'
|
||
---
|
||
|
||
## Description
|
||
<section id='description'>
|
||
N×N disks are placed on a square game board. Each disk has a black side and white side.
|
||
|
||
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.
|
||
|
||
|
||
|
||
It can be proven that 3 is the minimal number of turns to finish this game.
|
||
|
||
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).
|
||
|
||
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.
|
||
|
||
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.
|
||
|
||
Find .
|
||
</section>
|
||
|
||
## Instructions
|
||
<section id='instructions'>
|
||
|
||
</section>
|
||
|
||
## Tests
|
||
<section id='tests'>
|
||
|
||
```yml
|
||
tests:
|
||
- text: <code>euler331()</code> should return 467178235146843500.
|
||
testString: assert.strictEqual(euler331(), 467178235146843500, '<code>euler331()</code> should return 467178235146843500.');
|
||
|
||
```
|
||
|
||
</section>
|
||
|
||
## Challenge Seed
|
||
<section id='challengeSeed'>
|
||
|
||
<div id='js-seed'>
|
||
|
||
```js
|
||
function euler331() {
|
||
// Good luck!
|
||
return true;
|
||
}
|
||
|
||
euler331();
|
||
```
|
||
|
||
</div>
|
||
|
||
|
||
|
||
</section>
|
||
|
||
## Solution
|
||
<section id='solution'>
|
||
|
||
```js
|
||
// solution required
|
||
```
|
||
</section>
|