40004

I thought about my number bonds to 15. I started with the 1st card being 1, so the 2nd card had to be 14. This didn't work because it meant that card no.4 had to be too high in order to make 23. The same thing would have happened if I'd tried 2 or 3 1st. The same thing happened with the bigger numbers (11,12,13,14)as the first card.

I found two solutions. The first one was 6,9,11,12,4,14,7. The second one was 8,7,13,10,6,12,9.

I knew that there were no other solutions because I had already tried all the ways of making 15 with the first two cards.