---
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>