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I have a group of 16 people that are working together on a committee. We want to get to know each other better by splitting into smaller groups of 4 for icebreakers.

I believe if we did this 5 times, every member would be able to meet every other member, with nobody meeting the same person twice. I can't figure out the formula for this. Can you help?

Alethea
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1 Answers1

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Here is a solution. Arrange the $16$ people in a square. First break them up by rows, then by columns, and then as follows:

Round 3:      Round 4:      Round 5:
A B C D       A C D B       A D B C
B A D C       B D C A       B C A D
C D A B       C A B D       C B D A
D C B A       D B A C       D A C B
Mike Earnest
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