The solutions for the fifteen cards question are 8,7,13,10,6,2,9 and 6,9,11,12,4,14,7.
Explanation:
You could just guess, check and estimate the answer for all the cards, but it won't exactly get you all the solutions, so let's first take a look at how you do it logically.
First you make a list of possibilities for all the clues like the first clue 15, you list all of them so you should get all the numbers in the picture. Next, get rid of some equations that can't even be possible to be added together like 1+17 for clue 5 because 17 is bigger than clue 4 which is 16 so you can't possibly add 17 to become 16. Thirdly, you mix and match them together but only match the ones with the same number in each equations because of the clues, like you can match 6+9 and 9+11 together because they have both got the number 9. After this process, you should get the two solutions I listed before by mix and matching, a good thing is to join them with lines!