2010 UNCO Math Contest II Problems/Problem 1
Find a -digit integer less than where each digit is odd and the sum of the cubes of the digits is the original number.
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.
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