Determine the probability that for a base ten positive integer x chosen at random from 1 to 9999 inclusively, this relationship is satisfied: (sod(x))² = x+2, where sod(n) denotes the sum of the digits in the base ten representation of n.

There are 7 possible integers within that range:

2, 23, 62, 119, 194, 287, 398


Probability = 7/9999 ≈0.0007000700070 . . .

Posted by hoodat on 2011-01-26 14:38:40