Puzzle #105: 150 Year Old Puzzle

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!

Please send your answers either directly on the blog site as comments, or to me at alokgoyal_2001@yahoo.com. If you like the puzzle, please share it with others. If you have interesting puzzles to share, please send them to me at my e-mail given above.

Happy school walks!

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