Say I have an eleven by eleven chessboard, so there's 121 squares total. I remove the centermost piece so there's 120 pieces. I want to tile the chessboard with 1x4 or 4x1 pieces in a way that none of the pieces I place hang off of the board or overlap with one another. I also want the entire chessboard to be covered. Can it be done? I heard this problem from a friend and looked up a lot of domino tiling theory but can't figure it out still.
Any answers? Even incomplete answers or thoughts would be useful.