Question 874669: How do I pair 16 people for breakfast over 15 weeks?
I can do it for 4,6 and 8 people. I can't find a pattern to move to 10 people. Here is 8:
Week 1 1,2 3,4 5,6 7,8
Week 2 1,7 2,4 3,6 5,8
Week 3 1,8 2,3 4,5 6,7
Week 4 1,4 2,6 3,8 5,7
Week 5 1,3 2,5 4,7 6,8
Week 6 1,6 2,7 4,8 5,3
Week 7 1,5 2,8 3,7 6,4
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website! 16C2 = 120 ways, 120/15 = 8 , 8 pairings per week for 15 weeks
If You were to break them into 2 groups of 8
and then match between the two groups you could use
something like
(1,2) (1,3) (1,4) (1,5) (1,6) (1,7) (1,8) (2,1)
(2,3) (2,4) (2,5) (2,6) (2,7) (2,8) (3,4) (3,5)
(3,6) (3,7) (3,8) (4,5) (4,6) (4.7) (4,8) (5,6)
(5,7) (5,8) (6,7) (6,8) (5',7') (5',8') (6',7') (6',8')
remaining Other group of 8
(1'2') etc like above
(2',3') etc
(3'6') etc
Remaining 8 weeks mix the 2 groups
(1,1')(2,2') (3,3') (4,4') (5,5') (6.6') (7,7')(8,8') 1 Grouping
other seven Like Above with mixed
15 weeks - 8 groupings
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