**From New Scientist #2725, 12th September 2009** [link]

I chose two four-digit perfect squares (with no leading zero) that contained eight different digits. So did Harry, and so did Tom.

Our six chosen squares were all different, but the two digits that were unused were the same for all three of us. If you knew what those two digits were you would be able to deduce with certainty what the six squares that we chose were.

What were the largest and smallest of our six squares?

[enigma1562]

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The following Python program runs in 40ms.

Solution:The largest square is 8649. The smallest square is 2809.