There are 184,430 sets of such numbers. If you disallow sets with repeated numbers in them, there are 105,690 different sets of such numbers. Among them are these {38, 35, 24, 19, 13, 9}, {37, 32, 29, 21, 10, 9}, {37, 32, 27, 19, 13, 10}
You can choose 3 pairs, each of which adds to 46, or you can choose two sets that add to 69 each (as in the above cases). This can tend to simplify the problem a little bit. Example Pick 3 "random" numbers between 1 and 22 (inclusive). Subtract each from 46. You now have 6 numbers that add to 138. If we choose 5, 10, 15, the other numbers are 41, 36, 31 and our set is {5, 10, 15, 31, 36, 41}. {40, 30, 30, 20, 17, 1} is an example of a set with repeated numbers.
You can choose 3 pairs, each of which adds to 46, or you can choose two sets that add to 69 each (as in the above cases). This can tend to simplify the problem a little bit. Example Pick 3 "random" numbers between 1 and 22 (inclusive). Subtract each from 46. You now have 6 numbers that add to 138. If we choose 5, 10, 15, the other numbers are 41, 36, 31 and our set is {5, 10, 15, 31, 36, 41}. {40, 30, 30, 20, 17, 1} is an example of a set with repeated numbers.
