I decided to work backwards. If the far right card is 15 no, 14 no, 13 no, 12 no, 11 no, 10 no,
9,8, and 7 are yes!
6 and down will not work because the numbers are 1-15
Laying out each row
14 1 19 4 12 6 15 (can't use 19)
13 2 18 5 11 7 14 (can't use 18)
12 3 17 6 10 8 13 (can't use 17)
11 4 16 7 9 9 12 (can't use 16 or 2 9s)
10 5 15 8 8 10 11 (can't use 8 twice)
9 6 14 9 7 11 10(can't use 2 9s)
8 7 13 10 6 12 9 YES
7 8 12 11 5 13 8 YES
6 9 11 12 4 14 7 YES
5 10 10 13 3 15 6 (can't use 2 10s)
4 11 9 14 2 16 5 (can't use 16)
3 12 8 15 1 17 4 (can't use 18)
2 13 7 16 -------- undefined
1 14 6 17 -------- undefined