Same Five Digits

April 19, 2011

[Today's exercise was written by guest author Bob Miller. Bob has been writing system software for Unix since the VAX was new and shiny, and his current hobby is writing Scheme interpreters. Suggestions for exercises are always welcome, or you may wish to contribute your own exercise; feel free to contact me if you are interested.]

Enigma is a weekly column in New Scientist. Every week it has a new puzzle. Some of the Enigma puzzles could be solved using a computer.

A recent puzzle, Enigma Number 1638, is in that category:

I have written down three different 5-digit perfect squares, which between them use five different digits. Each of the five digits is used a different number of times, the five numbers of times being the same as the five digits of the perfect squares. No digit is used its own number of times. If you knew which digit I have used just once you could deduce my three squares with certainty.

What are my three perfect squares?

Your task is to write a program that finds and prints the three perfect squares. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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