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Organizing a "speedback" in a functional way

Speedback is the merging of speed-dating with feedback: a 2 min. 1-on-1 talk with all members of a group of people.

I'm in a team and I want to plan the ideal speedback setup: all team members have to give feedback to eachother. I want to group people in a way that maximizes the concurrency of simultaneous pairs so we reduce the total time of the sessions.

Consider the input: "alexandre", "sergiu", "joana", "tiago", "susana", "david"

combinations(6,2) = 15 possible pairs

1st session:

"alexandre" with "sergiu"
"joana" with "tiago"
"susana" with "david"

2nd session:

"alexandre" with "joana"
"sergiu" with "tiago"
"joana" with "david"

3rd session:

...

you get the ideia.. until everyone "dates" everyone.

I need all the possible pairs to be matched in the end.

Do you how to get this output? (or can you hint about the solution)?