Free lab

Grid Board Lab

A resizable grid: color it, cut out cells, tile it with dominoes, place pieces — the counters update as you go.

Things to try

1. Use “Cut out” to remove two opposite corner cells, then try to cover the remaining 62 cells with 1×2 dominoes. Stuck? Switch on “Checkerboard” and look at how many black and white cells are left in “Uncovered cells”.
2. Now remove one black and one white cell instead. Can the board be covered? Try several positions.
3. Clear the board and tile the 8×8 board with 1×3 strips: 64 is not a multiple of 3, so it cannot be done. What if you cut out one cell first? Switch on “3-color diagonals” to see which cell gives you a chance.
4. Use “Pieces” to place pieces on the 8×8 board so that no two share a row, a column or a diagonal. What is the largest number you can place?
5. Use “Paint” to design your own coloring so that every 1×3 strip, wherever it lies, covers exactly one A, one B and one C.