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A not very hard way: Since 2^P times 5^P is 10^P, the digit must be 1 or 3; it is easy to see that 1 won't work (if both 2^P and 5^P start with 1, the product cannot be 10^P) so the answer is 3. Of course, this doesn't prove that 2^P and 5^P ever start with the same digit, but see the second solution below...
An even easier way: 2^5 and 5^5 both start with 3, so if there is a single answer, it must be "3". |
