Expert: Richard J. Raridon - 3/30/2004

Question
Find all integers between 100 and 1000 such that each digit is a different odd number and the sum of the cubes of the digits is the original three-digit number.

Answer
You have quite a few possibilities to check out.  For example, if two of the digits are 8, and 9, the other digit can be any from 1 through 7. Of course, 891 will give you the same sum of cubes as 189.  
If two of the digits are 9 and 7, the other digit can be any from 1 through 6.  
you can also have 965 and 876 combinations.