17 19 5
The only way that three of the listed numbers can be made to "add" to 31 is
17 + 19 - 5 = 31
If only positive signs are allowed, only these sums can be made from 3 of the numbers.
{10, 22, 24, 24, 25, 26, 27, 38, 39, 41}
If positive or negative signs are allowed, any of these sums can be made.
{1, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 31, 33, 34, 38, 39, 41}
17 + 19 - 5 = 31
If only positive signs are allowed, only these sums can be made from 3 of the numbers.
{10, 22, 24, 24, 25, 26, 27, 38, 39, 41}
If positive or negative signs are allowed, any of these sums can be made.
{1, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 31, 33, 34, 38, 39, 41}