A board with two corners cut off, and a box of dominoes. Sometimes they cover it exactly and sometimes two squares are always left stranded — and a chessboard coloring tells the two apart at a glance.
The answer key prints on a separate page.
Every domino covers two squares that share an edge, and on a chessboard those are always one dark and one light. So a covering needs equal numbers of each color — and when two opposite corners are removed, they are the SAME color, leaving one color two short. No arrangement can ever fix that, and no amount of trying to lay the dominoes shows it. Only the coloring does.
The trap this sheet sets is that half the boards CAN be covered: two corners are removed from those too, but the two at the same end of an edge, which on an even board are opposite colors. The counts stay equal and the board tiles. A child who has decided "corners removed means no" gets those wrong — the only way to tell the halves apart is to color, which is exactly the move the sheet is teaching.