I tried doing the first one by writing all the possibilities down in my book, like 2x3, 2x4, 4x5 etc. Then i added the other numbers: if I was trying 2x3, i'd add 1, 4 and 5 together. The answers to both of those weren't the same, so I tried the rest. none of those worked either so that meant that one is the part that would sink.
Now i did the same with the second and third parts, and there were answers.
I think this puzzle was really fun and it took me while to actually understand what I was supposed to do. It took me ages to find the answers to the problem, and I was really confused when the first one didn't have a possibility because I forgot there was one that didn't work.