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Pythagorean Triples

How many right-angled triangles are there with sides that are all integers less than 100 units?

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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?

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Time of Birth

A woman was born in a year that was a square number, lived a square number of years and died in a year that was also a square number. When was she born?

Paving the Way

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

A man completely paved a square courtyard with square tiles. He decided that it was too small, so he took up the tiles, bought 100 more and used them to pave another square courtyard. All the tiles were the same size. How many tiles did he use altogether?