272. THE NINE SCHOOLBOYS. This is a new and interesting companion puzzle to the "Fifteen Schoolgirls" (see solution of No. 269), and even in the simplest possible form 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. How would you arrange them?

If we represent them by the first nine letters of the alphabet, they (1/2)

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might be grouped on the first day as follows:--

A B C
D E F
G H I

Then A can never walk again side by side with B, or B with C, or 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" conditions they can only walk on four days. (2/2)

SOLUTION TO 272. THE NINE SCHOOLBOYS. (1/3)

SOLUTION TO 272. THE NINE SCHOOLBOYS. (2/3)

SOLUTION TO 272. THE NINE SCHOOLBOYS. (3/3)

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