Sample Problem

N is an even number with a digital sum (sum of all its digits) of 50. What is the smallest, possible N?



In order to make N as small as possible, we want it to have the fewest number of digits, since a larger number of digits would occupy higher place values. To minimize the number of digits, we need to make each digit as large as possible, so that we achieve the digital sum of 50 using the fewest amount of digits. The best way to approach this problem is to work backwards, starting from the unit’s digit and moving towards the highest place value.

Because N is an even number, the largest units digit we can have is 8. For the next 4 digits we place a 9 since that is highest number we can put. This forces the 6th number to be 6, since 8 + 9 + 9 + 9 + 9 + 6 = 50. The smallest, possible N is therefore N = 699998.