Let's say I have 10 items, and I want to examine every combination of 5 items. Obviously, there are http://www.google.com/search?q=10+choose+5" possible combinations. But I want to actually enumerate them and iterate through them as efficiently as I can in a computer program. I'm wondering what the best way to do this might be. I don't know/remember much about combinatorics, and I'm hoping that this problem has been solved already. So far, the best thing I can think of is to iterate from the smallest 10-bit number that has 5 bits set... Code (Text): int min = (1 << 5) - 1; // 0000011111 = 31 ...to the largest 10-bit number that has 5 bits set... Code (Text): int max = min << 5; // 1111100000 = 992 ...and check every value between them to see if it has exactly 5 bits set. Can anyone think of a better way? Has this problem been solved already? How can I get the next highest integer with the same number of bits set? Thanks for any insight that you can provide.