SOLUTION: There is only one four-digit number "abcd" that is equal to a^b x c^d. The sum of its digits is a)18 b)20 c)21 d)24 e)29

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Question 1187608: There is only one four-digit number "abcd" that is equal to a^b x c^d. The sum of its digits is
a)18 b)20 c)21 d)24 e)29
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


ANSWER: a) 18

The number is 2592: (2^5)(9^2) = 32*81 = 2592

I doubt there is an algebraic way to find the answer.

Logical analysis might cut way down on the number of possibilities, making a solution by hand practical.

I found the solution using a "brute force" excel spreadsheet, looking at all 4-digit numbers not using digit 0.

If you know some computer programming, you could also write a fairly simple program that would find the answer.