24432

My solution is: 6 on the first card 9 on the second 11 on the third 12 on the fourth 4 on the fifth 14 on the sixth and finally 7 on the seventh.
Because the first two cards had to add up to 15 I added 6 and 9 then 9 plus something had to equal 20 so i took 9 away from 20 which gave me the answer of 11. Then 11 plus something had to equal 23 so I took away 11 from 23 which gave me 12 and so on until I had my first 7 cards.

Then I made sure it was right so I added them up step by step and it worked the first time for me. So my seven cards 6 9 11 12 4 14 7.