39941

1,14,6,17 used higher number than 15
2,13,7,16 used higher number than 15
3,12,8,15,1,17 used higher number than 15
4,11,9,14,2,16 used higher number than 15
5,10,10 used same number twice
6,9,11,12,4,14,7 correct solution
7,8,12,11,5,13,8 used same number twice
8,7,13,10,6,12,9 correct solution
9,6,14,9 used same number twice
10,5,15,8,8 used same number twice
11,4,16 used higher number than 15
12,3,17 used higher number than 15
13,2,18 used higher number than 15
14,1,19 used higher number than 15

The above shows all of the possible solutions using the rules of the problem.

While doing this problem we saw that with the two possible solutions it had a pattern which went +2 -2.