1.6 KiB
id | challengeType | title |
---|---|---|
5900f4b71000cf542c50ffca | 5 | Problem 331: Cross flips |
Description
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 .
Instructions
Tests
tests:
- text: <code>euler331()</code> should return 467178235146843500.
testString: assert.strictEqual(euler331(), 467178235146843500, '<code>euler331()</code> should return 467178235146843500.');
Challenge Seed
function euler331() {
// Good luck!
return true;
}
euler331();
Solution
// solution required