# Partitioning a chessboard

You should see a standard chessboard - it is printed on paper. How many ways can you cut it up (around the squares) such that each piece has twice as many squares of one colour than of the other colour?

• Usually, puzzles like this remove a corner of the chessboard so you're dealing with 63. – corsiKa Oct 13 '14 at 0:01
• @corsiKa the idea of this particular puzzle was for one to figure out why it's impossible – d'alar'cop Oct 13 '14 at 0:02
• @rand -5 :O how pathetic ppl are. – d'alar'cop Apr 3 '15 at 9:56
• Indeed. I've gotta wonder what is wrong with this question that 6 people have downvoted it. But downvoting is a bit of a taboo subject IME... – Rand al'Thor Apr 3 '15 at 16:13

A piece that has $k$ squares of one color and $2k$ squares of the other color has $3k$ squares. It is a multiple of $3$. You cannot split $64$ squares in any number of parts that all have multiples of $3$ squares.