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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?

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Square Routes

How many four digit square numbers are composed of even numerals? What four digit square numbers can be reversed and become the square of another number?

Square Sum

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2
See all short problems arranged by curriculum topic in the short problems collection

One of the following is the largest of nine consecutive positive integers whose sum is a perfect square. Which one is it?

A: 118, B: 128, C: 138, D:148, E:158


If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.



This problem is taken from the UKMT Mathematical Challenges.