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Bob:I'm thinking of a whole number between 10 and 1300.Alice:Is it less than 500?

Bob answers her, but he lies.Alice:Is it a perfect square?

Bob answers her, but he lies.Alice:Is it a perfect cube?

Bob answers truthfully.Alice:If I knew whether the second digit from the left was a 1, I would know your number. Is it?

Bob answers her truthfully and Alice announces what she thinks is the number. But she is wrong.What is Bob's number?

Source:Puzzles for Pleasure, by E. R. Emmet, Bell Publishing, 1972.© Copyright 1997 Stan Wagon. Reproduced with permission.

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2 October 1998