Question

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 it exactly, I did remember that the bus number had a certain peculiarity about it. The number plate showed the bus number was 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 the number was?

Pls give explaination.​

Answer 1

Answer:

By experiment we find that the onlynumbers 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, 1and 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.

Answer 2

Answer:

only 0,1,8 gives same number when return in upside down

6,9 shows 9,6 when kept upside down

therefore we need perfect square on number plate below 500 196 is perfects square and gives same numbers when kept upside down

961 -31^2 So , And is 196