Break up a group of 100 people into 5 so everyone gets to know each other?

Question

Algorithms

Good afternoon everyone.
Actually, I'm trying to write an algorithm to break n people into groups of 5 people, so that all n get to know each other... The first circle of fives where no one knows who did, but then how to break?

Answer 1

Just for such situations, education is needed)))) https://ru.wikipedia.org/wiki/Combinatorics
As a basis, take https://ru.wikipedia.org/wiki/Combination
-
And in the statement, a condition like "for fewer iterations", no?

Answer 2

Use the power of prime numbers as an increment of the members' numbers in the group.
5: (1,6,11,16,21), (2,7,12,17,22),..
7: (1,8,15,22,29), (2,9,..) ,..
11: (1,12,23,34,45), (2,13,..), ..
13: ...
17: ...
(plus numbering loop: 101=1, 102=2 ,..)
I won't give proof yet, just "mathematical intuition".
Lower bound: in less than 25 partitions, there is no solution, because each has to get to know 99 people, and in one split a person gets to know a maximum of 4 people, ceil(99/4)=25.