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Same unused digits

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?

WIN £15 will be awarded to the sender of the first correct answer opened on Wednesday 14 October. The Editor’s decision is final. Please send entries to Enigma 1562, ¿ìè¶ÌÊÓƵ, Lacon House, 84 Theobald’s Road, London WC1X 8NS, or to enigma@newscientist.com (please include your postal address).

Answer to 1556 Card trick: 19 centimetres

The winner Josie Huddleston of Durham, UK