Solution to: Chessboard Chunks
No, it is not possible to cut the chessboard paper into pieces such that each piece has twice as much squares of one color than of the other color.
If it would be possible, then every piece would have a number of squares divisible by 3 (because if a piece has n squares of one color and 2×n squares of the other color, it has 3×n squares in total). The total number of squares of all pieces would then also be divisible by 3. This is, however, impossible since the total number of squares on the chessboard is 64, which is not divisible by 3.