Enigma 1638: Same five digits
11 December 2011
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From New Scientist #2804, 19th March 2011 [link]
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?