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How to organize 16 people to have breakfast in unique pairs over 15 weeks?

GROUPS:
During each week, each person meets once. I can do this for 4, 6, 8 people and can't find a pattern! Help!

For 8 people:
              Pair 1  Pair 2  Pair 3  Pair 4Week 1 ---1 2 ----3 4 ----5 6 ----7 8Week 2 ---1 7 ----2 4 ----3 6 ----5 8Week 3 ---1 8 ----2 3 ----4 5 ----6 7Week 4 ---1 4 ----2 6 ----3 8 ----5 7Week 5 ---1 3 ----2 5 ----4 7 ----6 8Week 6 ---1 6 ----2 7 ----4 8 ----5 3Week 7 ---1 5 ----2 8 ----3 7 ----6 4

I tried connecting points arond a circle (hexagram, octagon) - funny patterns.
POSTED BY: Mark Good
Answer
2 months ago
One way to do this is with BitXor, e.g., label your people 0,1,2,...15 and then at week n the ith person is paired with

BitXor[i,n]

This is symmetric for each week n, i.e. when the formula assigns x to y it also assigns y to x, because Xor[a,b]==c means that Xor[c,b]==a.  Also, each person gets a different assignment each week because BitXor[i,n]==BitXor[j,n] only when i==j,
POSTED BY: Todd Rowland
Answer
2 months ago
Thank you Todd.
I used Wolfram alpha and this function worked like a charm! I have my pairs. The group will be delighted!
Respectfully and in a bit of awe,
Mark Good, PhD
POSTED BY: Mark Good
Answer
2 months ago