+1694 How many unique sums can be formed by adding any three different numbers from the set {4,6,8,10,12,...,154}?
+104 Since all of he numbers in the set are divisible by 2, we can divide them all by 2 and we would still have the same number of unique sums (I can easily prove this if you need me to). So now our set is {2, 3, 4, 5, 6,...,77}. The smallest possible sum in this set is 2 + 3 + 4 = 9, and the largest sum is 75 + 76 + 77 = 228. Because all other numbers in the set are one more then the one before it, we can easily add one to any sum by just increasing a number by one. This means that you can only make the sums of all the numbers from 9 to 228. There are 220 numbers in that range, so there are 220 unique sums that you can make.
