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This Python program runs in 42ms. We could prune the candidate lists of numbers by noting that they cannot contain repeated digits.

Solution:FOUR=1024, FIVE=1597, SIX=358.Harry and Tom’s numbers are (FOUR=2601, FIVE=2584, SIX=753) and (FOUR=2916, FIVE=2584, SIX=753) – which have the same values for FIVE and SIX – but we don’t know who found which set.