Brain-Teaser 462

From The Sunday Times, 5th April 1970 [link]

A friend of mine, who is headmistress of a small school, sends her fifteen girls for a walk every day in a crocodile of threes. She told me that she had for long been trying, unsuccessfully, to arrange that no two girls ever walked together in a trio more than once during a whole week; and she added that, denoting the girls by the first fifteen letters of the alphabet, she wanted A to walk with B and C on Sunday, and with the consecutive pairs of letters for the rest of the week, finishing with N and O on Saturday.

“Well”, I replied, “if four more trios were specified, I could find a unique solution for your problem. But, if you want to work it out yourself, I shall help you by telling you B’s and C’s partners throughout the week:

Mon: BHJ, CMN
Tue: BIK, CLO
Wed: BLN, CEF
Thu: BMO, CDG
Fri: BDF, CIJ
Sat: BEG, CHK

Furthermore, F, who is a bit of a snob as regards those lower in the alphabetical order, will be relieved to find that she does not have to walk with the two available furthest from herself in that order until Saturday.

Now, you should be able to tell me with whom D walks on Sunday and on Wednesday.”

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