Consider a set containing the integers between 1 and 10 (inclusive). How many unique subsets exist such that the sum of the elements of the subset is 10?
I know this is easily done by hand, but I was wondering if there is a general formula that exists to solve such a problem.
Edit: I was given the answer below, but, writing out the sets, I appear to get the answer to be 9. The unique sets I get are {7,1,2}, {6,1,3}, {5,1,4}, {5,2,3}, {9,1}, {8,2}, {7,3}, {6,4}, {1,2,3,4}. Also, could someone please explain how ones gets that q(10) = 10 in the Answer?
Thank You
An equivalent question is the number of integer partitions of 10 into distinct parts. This is sometimes denoted as $q(n)$. Quite a bit is known about this function, e.g. $q(10)=10$, but there is no nice closed-form formula.