Those who saw this elsewhere are invited not to spoil it for those who didn't. (And credit to Hauke R who posed the original.)
Consider partitions of the digits 0-9 into a set of decimal representations of numbers which are all exact powers of a single prime number. (As always, a leading 0 is forbidden in decimal representations, save for that of 0 itself.)
1) Prove that all such sets have at least 2 members.
2) Find all such sets.
(1) is there to encourage you to do some maths before blindly hitting brute force by reducing the search space.
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[stolen with permission from Daniel B. Cristofani]