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First I drew seven boxes on a piece of paper.I then wrote in the first box 1 in the second i wrote 14 because it adds up to 15 an so on in the next boxes, but that didn't work so i wrote 2 in the first box and carried on like the fist try.
when i got to the number 6 in the first box it seemed to work all the way to the end so i checked it and i was right.

I then carried on to see if there were any more ways but there was not so i new what i had found was right.My numbers are 6, 9, 11, 12, 4, 14 and 7.6 and 9 add to to 15, 9 and 11 adds to 20, 11 and 12 adds to 23, 12 and 4 adds to 16, 4 and 14 adds to 18 and 14 and 7 adds to 21.

There is my solution to Fifteen Cards.