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 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 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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