Tiling Task

tiling task 1

We’ve removed two squares from this 7×8 grid, so that it numbers 54 squares. Can it be covered orthogonally with tiles like the one at right, each of which covers exactly three squares?

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No. Number the squares as shown. Now each tile, however it’s placed, must cover a 1, a 2, and a 3. But the grid contains 19 1s, 18 2s, and 17 3s. So the task is impossible. From Pierre Berloquin, The Garden of the Sphinx, 1981.

September 30, 2012February 7, 2013 | Puzzles