I do not remember where I saw this problem.
Problem. Invent a connected shape made out of squares on the square grid that cannot be cut into dominoes (rectangles with sides 1 and 2), but if you add a domino to the shape then you can cut the new bigger shape.
This problem reminds me of another famous and beautiful domino-covering problem.
Problem. Two opposite corner squares are cut out from the 8 by 8 square board. Can you cover the remaining shape with dominoes?
The solution to the second problem is to color the shape as a chess board and check that the number of black and white squares is not the same.
What is interesting about the first problem is that it passes the color test. It made me wonder: Is there a way to characterize the shapes on a square grid that pass the color test, but still can’t be covered in dominoes?Share: