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!

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my head hurts!

but try this first matrix set the pattern

First letter starter

ABCD

EFGH

IJKL

MNOP

then you go diagonally down

1st letter Main

AFKP

EJOD

INCH

MBGL

then you go diagonally down again

1st letter Pud

AJCL

ENGP

IBKD

MFOH

then you go diagonally down again

1st letter cheese

ANKH

EBOL

IFCP

MJGD

nope just re read it and M is meeting G twice so there are probably other repeats

darn!

Very interesting little puzzle, it can actually be solved very easily with a magic square, then using the permeations of that magic square to shift people between groups

ill send you a spreadsheet on MSN with my solution when I see you online next 🙂

Here is your solution 4 letters per party, each letter is in place of what course it is providing

AEIM (A providing Starter, E providing Main, I providing Dessert….)

BFJN

CGKO

DHLP

PAFK

OBEL

NCHI

MDGJ

JOAH

IPBG

LMCF

KNDE

GLNA

HKMB

EJPC

FIOD

… on first glance I think that works!

I haven’t done magic squares since secondary school! Is this a classic case of over complicating things?! Would love to get my hands on your spreadsheet!

its kinda counter intuitive that A never meets B, C or D! but it works! lol, ill have to psudo code it once i figure out quite how i did it :S damn logic puzzles, it all starts fitting into place and you get a little carried away with yourself over it :S oh well!