Pat has made up a list of 5-digit perfect squares (all different) which use only the digits 0 through 4, none of them starting or ending with a zero. Each of the digits 0 through 4 is used a different number of times, those numbers of times being 5 through 9.
Mike has also chosen some 5-digit perfect squares, but using only the digits from 5 through 9. Each of his digits 5 through 9 is used a different number of times in his squares, those numbers of times being 0 through 4.
What were the eligible squares for each of Pat and Mike, based on their constituent digits? Which of them did each actually use?
The eligible squares for Pat were:
10201, 10404, 12321, 22201, 23104, 32041, 33124, 40401_ of which he used only 22201
The eligible squares for Mike were:
55696, 69696, 97596, 98596, 99856, of which, he used only 55696 and 97969.
Edited on February 18, 2023, 10:20 pm
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