How can I create 14 unique team rosters from 24 students in groups of 2?

Question

I have a class of 24 students, and they have 14 labs in which I have students partner up. I am trying to find a way to create a roster automatically such that none of my students has a repeat partner for the duration of the semester. Is there a simple way to do this?

Answer 1

This is part of what's called "combinatorial design theory". In your case you can think of this as designing a round-robin tournament - the sort of tournament where everybody plays everybody - except you can cut it off after 14 rounds. If you look at the section "scheduling algorithm" you can find out how to do this. Basically, number your students from 1 to 24. Then for the first lab you pair them up as

01 02 03 04 05 06 07 08 09 10 11 12
24 23 22 21 20 19 18 17 16 15 14 13

(The 0s in numbers like 01 don't mean anything; they're just there to make things line up nicely.) So 1 is paired with 24, 2 with 23, and so on.

Now fix the number 01, and rotate the other 23 numbers clockwise, so you get

01 24 02 03 04 05 06 07 08 09 10 11
23 22 21 20 19 18 17 16 15 14 13 12

and so 1 is paired with 23, 24 with 22, and so on. Repeat this twelve more times to get the pairings for the twelve remaining labs.