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 |