Fishing. Four friends came back from fishing. Each pair of them counted the sums of their catches. Six numbers were obtained: $7,9,14,14,19,21$. Can you find out what their catches were?
## Solution

There were four friends, which means each person counted their catch three times. Therefore, if we add up all six sums, we get three times the total catch. From this, we immediately get that the total catch is 28 fish. This, in turn, means that our six sums should break down into pairs of numbers that add up to 28.

Indeed, here are these pairs: 7 and 21, 9 and 19, 14 and 14. From the first pair of numbers, it follows that the two participants (I and II) who caught the least fish, in total, caught 7 fish. This means that the one who caught the least (I) could not have caught more than 3 fish, i.e., he caught 1, 2, or 3 fish. Then the second one (II) caught 6, 5, or 4 fish, respectively. Now let's consider the last pair of sums - 14 and 14. It is clear that one of these sums is I+IV, and the other is II+III. The pairs 1-6, 2-5, and 3-4 will correspond to 13-8, 12-7, and 11-10. Let's check what the sums will be. 3+10=13 - such a sum does not exist, so the last option is ruled out. 12+5=17 - such a sum also does not exist, so this option is also ruled out. The first set - 1, 6, 8, 13 - exactly matches the condition of the problem.