2010 UNCO Math Contest II Problems/Problem 1
Problem
Find a 
-digit integer less than 
where each digit is odd and the sum of the cubes of the digits is
the original number.
Solution
We have a three digit number that can be represented as 
. We know that 
and 
are odd, and that 
. This means that both and are within the set 
. We also notice that since 
and 
are both far greater than , they can not be our digits, so the remaining set is 
. Looking at only the last digits of 
, we see that only when 
and 
are together can we get a last digit of 
or , which we see is 
. Upon checking, 
is a working solution.
See also
| 2010 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
| Preceded by First Question |
Followed by Problem 2 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
| All UNCO Math Contest Problems and Solutions | ||
