Im not sure how to algebraically explain this situation, but i can explain the answer.
So you have four friends:
1 2 3 4 that want to jump on a trampoline.
They want to jump in pairs and each single friend wants to jump with the three other friends. Here is how it works
| Friends |
--------------------------------------------
| 1 | 2 | 3 | 4 |
1:2 2:3 3:4
1:3 2:4
1:4
So as you can see, if you add up all the groups there are 6 different possible combinations for the 4 friends to pair up and jump 2 at a time. So your answer is that it would take 6 turns.