How to Invite 9 friends over 12 mini dinner parties of 3 (not including you)?

You have 9 mutual friends whom you would like to invite to dinner, three at a time, over the period of 12 mini dinner parties. How can you arrange the invitations so that any pair of friends meet each other only once? Call your friends A,B,C,D,E,F,G,H, and I.

1 Answer

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  • 1 decade ago
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    Well first 3 dinner parties:

    [1] ABC

    [2] DEF

    [3] GHI

    Next 3 dinner parties:

    Invite 1 person from each of [1], [2] and [3] to each dinner party:

    [4] ADG

    [5] BEH

    [6] CFI

    Now A has not been to any dinner party with E F H or I

    But E&F, H&I, E&H, and F&I have already met. This leaves E&I and F&H

    Similarly B has not been to any dinner party with D F G or I

    D&F, G&I, D&G, F&I have already met. This leaves D&I and F&G

    Finally C has not been to any dinner party with D E G or H

    D&E, G&H, D&G, E&G have already met. This leaves D&H and E&G

    So last 6 dinner parties should have the following guests:

    [7] AEI

    [8] AFH

    [9] BDI

    [10] BFG

    [11] CDH

    [12] CEG

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