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.

DEFDBL A-Z

FOR n = 1 TO 354294
  s$ = LTRIM$(STR$(n))
  tot = 0
  FOR i = 1 TO LEN(s$)
    d = VAL(MID$(s$, i, 1))
    tot = tot + d * d * d * d * d
  NEXT
  IF tot = n THEN PRINT n
NEXT

finds

1
4150
4151
54748
92727
93084
194979

The sum of these numbers is 443,840, and is in fact what is asked for. However, if we're to follow the 4th power example, we should subtract the trivial 1 to get 443,839, though the final, instructional, paragraph does not tell us explicitly to do this.

BTW, the 354294 in the program is 6*9^5 as the largest sum of fifth powers of six digits could be this. All sets of digits with more than six digits add up to a number with fewer than whatever number the fifth power total comes to.

Posted by Charlie on 2012-08-30 14:31:37