While visiting a small town in some country, 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 of the bus, I did remember that the bus number had 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.

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 number.

Can you find out the bus number and the other one, too ?

On the basis that 1,2,5,6,8,9,0 all remain numbers when inverted, then there are several possible solutions depending on the numbering convention used:

1 = 1^2, 1 inverted is 1 = 1^2
001 = 1 = 1^2, 001 inverted is 100 = 10^2
100 = 10^2, 100 inverted is 001 = 1 = 1^2
121 = 11^2, 121 inverted is 121 = 11^2
196 = 14^2, 196 inverted is 961 = 31^2

At least this narrows it down from searching through 500 buses!

Posted by fwaff on 2003-03-04 21:46:54