This is truly an old puzzle. I was sent this one by Salik Shah (thank you Salik). It appeared in the WIRED magazine. I am reproducing the puzzle verbatim as I saw it in WIRED:
IN 1850, THE Reverend Thomas Kirkman, rector of the parish of Croft-with-Southworth in Lancashire, England, posed an innocent-looking puzzle in the Lady’s and Gentleman’s Diary, a recreational mathematics journal:
“Fifteen young ladies in a school walk out three abreast for seven days in succession: it is required to arrange them daily, so that no two shall walk twice abreast.” (By “abreast,” Kirkman meant “in a group,” so the girls are walking out in groups of three, and each pair of girls should be in the same group just once.)
Caution: The problem is more difficult than it seems!
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Happy school walks!