Enigma 1746: Square in common
24 April 2013
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From New Scientist #2914, 27th April 2013 [link]
Harry and Tom each chose two four-digit perfect squares (with no leading zero) which used eight different digits. Each of them told me which two digits were not used in his squares, and that information enabled me to deduce with certainty which two squares each of them had chosen. They had not made the same choice of squares, but their choices did have one square in common.
What was the square that both of them chose?