39781

For this problem I used "Guess and Check." I started by drawing seven cards and then I wrote down the numbers from 1-15, then I used elimination by crossing out all the numbers that I used so I don't use the same one twice. I started from the first I started with the low numbers but none worked, but as I got higher I found 2 solutions altogether. To make sure I had found all the solutions, I made a list of all the numbers that =15 then I did a list that =20 and so on. After that I made solutions from joining up the numbers for example the bottom of the first list is 8 + 7 so I searched for a seven in the next list and found it with 13 so I wrote 13 and so on... My answers were;

1)
8, 7, 13, 10, 6, 12, 9

2)
6, 9, 11, 12, 4, 14, 7