There are only three numbers that can be written as the sum of fourth powers of their digits: 1634, 8208 ,9474 (the trivial case of number 1 excluded).
The sum of these numbers is 1634 + 8208 + 9474 = 19316.

Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.

(In reply to The purpose isnt to fail the student, it's to help them succeed by Ora)

The puzzle does not ask that the valid numbers to be included should all be 5-digit numbers; the only reference to 5 is that is the power to which each of the numbers' digits should be raised. It is only happenstance that in the 4th-power case, all the non-trivial valid numbers were of 4 digits length.

The puzzle also asks that the resulting valid numbers should then themselves be summed, as was the case with the 4th-power example.

Posted by Charlie on 2012-08-31 09:59:39