Sally and Sue have a strong desire to date Sam. They all live on the same street yet neither Sally or Sue knows where Sam lives. The houses on this street are numbered 1 to 99.

Sally asks Sam, "Is your house number a perfect square?". He answers. Then Sally asks "Is it greater than 50?". He answers again. Sally thinks she now knows the address of Sam's house and decides to visit. When she gets there, she finds out she is wrong. This is not surprising, considering Sam answered only the second question truthfully.

Sue, unaware of Sally's conversation, asks Sam two questions. Sue asks "Is your house number a perfect cube?". He answers. She then asks "Is it greater than 25?". He answers again. Sue thinks she knows where Sam lives and decides to pay him a visit. She too is mistaken as Sam once again answered only the second question truthfully.

If Sam's house number is less than the numbers of the houses where Sue and Sally live, and that the sum of all three of their numbers is a perfect square multiplied by two, what are Sally's, Sue's, and Sam's house numbers?

(In reply to re2: re: Solution by Nick Reed)

They say "Great minds think alike," apparently they do it at the same time, too. :)

Posted by TomM on 2002-06-14 07:55:48