All I have to do is organise 16 dinner parties… how hard can it be?
The Rotary Club of Reading Abbey have a season of Surprise Dining, each couple signed up will host one dinner party and go to three others. The host of the dinner party does the main course, the other guests do the starter, pudding and cheese. Each couple involved will cook an entire meal but in stages.
The Rules
- Each couple will attend 4 dinner parties
- Each couple will do the Main Course once, Starter once, Pudding once, Cheese once
- Each couple should only encounter the other guests once at the dinner parties (you only have dinner with couple A once, not meeting them again)
So… is this possible?
If So… there has to be an algorithmic answer to this… I look to you stats-based people for help!
I need 16 combinations of the letters A to P where each letter is in position 1 (starter), 2 (main), 3(pudding) and 4(cheese) only once. AND there are no repeating combinations of letters – so a,b,c,d and b,a,e,f wouldn’t work as a and b have already seen each other the previous week.
Any and all ideas gratefully received!