How many right-angled triangles are there with sides that are all
integers less than 100 units?
A man paved a square courtyard and then decided that it was too
small. He took up the tiles, bought 100 more and used them to pave
another square courtyard. How many tiles did he use altogether?
A square patio was tiled with square tiles all the same size. Some
of the tiles were removed from the middle of the patio in order to
make a square flower bed, but the number of the remaining tiles was
still a square number. What were the dimensions of the patio and
the flower bed?
Published February 2011.