Logic Puzzles

## The Bus Number

Difficulty: While visiting a small town in the United States, I lost my overcoat in a bus. When I reported the matter to the bus company I was asked the number of the bus. Though I did not remember the exact number I did remember that the bus number bad a certain peculiarity about it. The number plate showed the bus number as a perfect square and also if the plate was turned upside down? the number would still be a perfect square — of course it was not?

I came to know from the bus company they had only five hundred buses numbered from 1 to 500.

From this I was able to deduce the bus number. Can you tell what was the other number?

By experiment'we find that the only numbers that can be turned upside down and still read as a number are 0, 1, 6, 8 and 9. The numbers 0, 1 and 8 remain 0, 1 and 8 when turned over, but 6 becomes 9 and 9 becomes 6. Therefore the possible numbers on the bus were 9, 16, 81, 100, 169 or 196. However, the number 196 is the only number which becomes a perfect square when turned over because 961 is the perfect square of 31. Therefore 196 is the correct answer.