### 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?

### 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?

### 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:
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.