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Math Help - repetition

  1. #1
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    repetition

    Sorry, I do not know what to call this type of query.

    A class of nine kindergarten children is to be taken for a
    walk each afternoon. The teacher decides that they will
    'walk in sets of three, and any pair of children will walk
    together on one day only. For how many days can this
    system be maintained without repetition?
    (A) 1 (B) 2 (C) 3 (D) 4 (E) 5

    I have worked it out by hand and get 4 days
    I would like advice on how to approach this question please?

    thank you
    Cody, Perth


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  2. #2
    MHF Contributor ebaines's Avatar
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    :Let's call the nine students A, B, C, ...., I. On the first day student A can walk with B & C, on the second day he can walk with D & E, on the third day F & G , and on the fourth day H & I. Hence after 4 days student A can't be matched with anyone he hasn't already walked with. Therefore 4 days is the maximum number of days this will work. This doesn't prove that it will actually work for 4 days; only that the answer can't be more than 4 days.
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  3. #3
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    Thank you very much enaines,
    for spending time on my problem.
    It is good to know I had it correct,
    after I realised to just focus on the first child
    the rest seemed easier.
    Thank you again, Cody in Perth
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