1. The problem statement, all variables and given/known data Consider an 8x8 checkerboard with two squares from each of two opposite corners deleted so that 60 squares are left (i.e the top row has 6 squares with the 2 far right squares missing, and the bottom row has 6 squares left with the 2 far left missing). Prove that the remaining squares cannot be covered exactly by T-shaped dominos consisting of four squares and their rotations. I figured that if the domino is centered on a white piece, then its must cover 3 black pieces surrounding it, and vice versa. this would mean that centering the domino on 10 white pieces automatically covers the 30 black pieces, and thus there is no way to cover the remaining 20 white pieces. Unfortunately, I don't know how to formalize this proof and show that this must be the case.