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Patio

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?

Weekly Problem 32 - 2007

Stage: 3 and 4 Challenge Level: Challenge Level:1
The mean of the nine consecutive integers is the fifth number in the series, so their sum is nine times the fifth number. As nine is itself a perfect square, the sum will be a perfect square if and only if the fifth number is also a perfect square. For the options given, the fifth numbers would be 114, 124, 134, 144, 154 respectively.Of these, only 144 is a perfect square, so the answer is D.

This problem is taken from the UKMT Mathematical Challenges.

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