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Solution:(1) Your squares are 9025, 361 and 784; (2) Harry and Tom’s solutions have 3025 and 784 in common.I observed the output of this program.

Then I deleted the same results to reduce the number of the solutions to 5.

If the number of the intersection with 3 solutions is one number, it will be 784

That is, my solution is 361,784,9025

Harry’s and Tom’s solutions are:

169, 784, 3025 and 196, 784, 3025

That’s a solution, but we can’t actually deduce the “non-common” squares for Harry and Tom. The three squares 169, 196 and 961 use the same digits and Harry and Tom must have picked two of them, but we don’t know which two.