There are 2 solutions.The first solution is 6,9,11,12,4,14,7 and the second solution is 8,7,13,10,6,12,9.This was found out by first finding the combinations of 15,20,23,16,18 and 21 through addition. Then,we tried joining the combinations. Next,we looked through the final results and found out that there are only 2 solutions which are listed above.
This is an example on how we worked it out.
15 20 23
1+14 5+15 8+15
2+13 6+14 9+14
3+12 7+13 10+13
4+11 8+12 11+12
5+10 9+11 12+11
6+9 10+10 13+10
7+8 11+9 14+9
8+7 12+8 15+8
9+6 13+7
10+5 14+6
11+4 15+5
12+3
13+2
14+1
6+9 11 12 This is the beginning of one of the solutions.