Here is a set of numbers: {93, 4, 2} . Each number is less than 100, and there is no way that you can add any of the numbers up to get exactly 100. Find the largest set like this. That is, find the set with the most numbers so that they’re all less than 100 and you can’t add up any combination of them to get exactly 100.
Make the sums too big: pick { 50, 51, 52, . . . , 99} .