Surprise Dining Algorithm Problem

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.

Paris
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!

7 thoughts on “Surprise Dining Algorithm Problem

  1. 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

  2. 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 🙂

  3. 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

  4. … 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!

  5. 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!

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