I am organizing a dinner for 16 guests in a dining room with 4 tables of 4 seats. There are 5 courses in which the guests may change seats.
Is it possible to devise a seating arrangement such that every guest joins a table with every other guest?
There are 16*15/2 = 120 combinations required and at each course there are 4*4*3/2=24 combinations realized, so the maximum possible number of combinations that can be realized in 5 courses is 24*5 = 120, which is just enough.
My question is how to proceed and find an algorithm for this table arrangement problem if a solution exists.