Find a set of numbers, all less than 100, such that none of them add up to 100. For example, here is such a set: . All these numbers are less than 100 and no combination of them sums to 100. Find the largest such set.
Solution
There is a trick here. Make all the sums too big, i.e., bigger than 100. The answer is This set has 50 numbers in it. Any set with more than 50 numbers will have to include two numbers that add up to 100.