# Whites capture whites and Blacks capture blacks

This is my first Chess Puzzle!

• Let suppose you start a Chess game.
• Whites' aim will be to place all their alive pieces on white squares in a minimum of moves and black will do the same, but with black squares.
• Both players can (and should) eat other pieces and all normal chess rules are maintained (check, en passant, castle and so on). except that reaching all the white (or black) squares is infinitely more important than checkmate.
• Both Whites and Blacks made peace and are in a collaborative game :) They both try to minimize the number of moves.

## What is the minimum number of moves you can make?

1. Prove this is the minimum.
2. Is this minimum the same if we permute black and white squares: Whites capture black squares and Blacks capture white squares?

I've made a very quick attempt that will give you a maximum bound of such an optimal game, with $$14$$ Whites moves:

• Is this a collaborative game? From the picture it seems so Apr 10, 2020 at 8:50
• @melfnt, thanks for your comment, I wasn't aware of what was a collaborative game. I edited accordingly :)
– JKHA
Apr 10, 2020 at 8:53

Ten moves:
1. a4 a5
2. b3 b6
3. d3 d6
4. e4 e5
5. f3 f6
6. h3 h6
7. Ra2 Ra7
8. Bxh6 Bxh3
9. Nxh3 Nxh6
10. Ke2 Ke7

• Quite elegant answer! I think just playing the game proves it to be optimal. Can you find the complement one with opposite color squares?
– JKHA
Apr 10, 2020 at 10:16
• @JKHA Compliment is mirror image. Apr 10, 2020 at 10:19
• congrats for your solution! ;)
– JKHA
Apr 10, 2020 at 10:29