Weekly group assignment algorithm
algorithm, combinatorics
Solution
Round-robin algorithm will do the trick i think.
Add the remaining student to the second group and you are done.
First run
1 2 3 4 5 6 7 8 9 10 11 12
23 22 21 20 19 18 17 16 15 14 13
Second run
1 23 2 3 4 5 6 7 8 9 10 11
22 21 20 19 18 17 16 15 14 13 12
...
Problem
A friend of mine who who is a teacher has 23 students in a class. They want an algorithm that assigns students in groups of 2 and one group of 3 (handle the odd number of students) across 14 weeks such that no two pairs repeat across the 14 weeks (a pair is assigned to one week). A brute force approach would be too inefficient, so I was thinking of other approaches, matrix representation sounds appealing, and graph theory. Does anyone have any ideas? The problems that I could find deal only with 1 week and this answer I could quite figure out.