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  • 272. THE NINE SCHOOLBOYS.

    From David Entwistle@qnivq.ragjvfgyr@ogvagrearg.pbz to rec.puzzles on Thu Jul 31 14:02:06 2025
    From Newsgroup: rec.puzzles

    From Amusements in Mathematics by Henry Ernest Dudeney. The book provides
    the following information and asks the following question:

    This is a new (in 1917) and interesting companion puzzle to the "Fifteen Schoolgirls" and even in the simplest possible for in which I present it
    there are unquestionable difficulties. Nine schoolboys walk out in
    triplets on the six week days so that no boy ever walks *side-by-side*
    with any other boy more than once.

    If we represent them by the first nine letters of the alphabet, they may
    be grouped on the first day as follows:-

    A B C
    D E H
    G H I

    Then A can never walk again side by side with B, nor B with C, nor D with
    E, and so on. But A can, of course, walk side by side with C. It is here
    not a question of being together in the same triplet, but of walking side
    by side in a triplet. Under these conditions they can walk out on six
    days; under the "Schoolgirls" condition they can only walk on four days.

    It isn't explicit, but I'm sure we are being asked for the six
    arrangements of schoolboys.
    --
    David Entwistle
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  • From David Entwistle@qnivq.ragjvfgyr@ogvagrearg.pbz to rec.puzzles on Thu Jul 31 14:03:36 2025
    From Newsgroup: rec.puzzles

    On Thu, 31 Jul 2025 14:02:06 -0000 (UTC), David Entwistle wrote:

    A B C D E H G H I

    Whoops.

    A B C
    D E F
    G H I
    --
    David Entwistle
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  • From James Dow Allen@user4353@newsgrouper.org.invalid to rec.puzzles on Mon Aug 4 06:13:35 2025
    From Newsgroup: rec.puzzles


    David Entwistle <qnivq.ragjvfgyr@ogvagrearg.pbz> posted:

    From Amusements in Mathematics by Henry Ernest Dudeney. The book provides the following information and asks the following question:

    This is a new (in 1917) and interesting companion puzzle to the "Fifteen Schoolgirls" and even in the simplest possible for in which I present it there are unquestionable difficulties. Nine schoolboys walk out in
    triplets on the six week days so that no boy ever walks *side-by-side*
    with any other boy more than once.

    I solved this in about 25 minutes with zero computer assistance.
    DAI / EBG / FCH
    GDC / HEA / IFB
    AGF / BHD / CIE
    BAF / EDI / HGC
    CBD / FEG / IHA
    ACE / DFH / GIB
    (On the first day A walks between D&I, B betw. E&G, C betw. F&H; etc.)

    To find this solution I first noted that it was going to be a very
    "tight squeeze" and thus that any solution needed to be very symmetric.
    The boys in the middle (ABC, DEF, GHI, ADG, BEH, CFI for the six days)
    were set in place first.

    But how did the ideas for such puzzles arise in pre-computer days?
    I dunno. I suppose Henry Dudeney was VERY clever, and that such
    constructions were his full-time job.

    James
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