Let's find the least possibilities:
First number: 6
Second number: 8
Third number: 10
6 + 8 + 10 = 24
Now we can see that we are still missing 31 - 24 = 7.
7 can be gained by adding 3 and 4, so:
First number: 6 + 3 = 9
Second number: 8 + 4 = 12
Third number: 10
9 + 12 + 10 = 31