## Sunday, June 21, 2015

### "The Nine Schoolgirls Challenge"

From Quanta (the Marilyn & Jim--yes that Jim--Simons Foundation):

A Design Dilemma Solved, Minus Designs
A 150-year-old conundrum about how to group people has been solved, but many puzzles remain.
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.)

### The Nine Schoolgirls Challenge:

Solve a variation of Thomas Kirkman’s puzzle by arranging nine girls in walking groups. And think fast — the clock is ticking.
Pull out a pencil and paper, and you’ll quickly find that the problem is harder than it looks: After arranging the schoolgirls for the first two or three days, you’ll almost inevitably have painted yourself into a corner, and have to undo your work.
The puzzle tantalized readers with its simplicity, and in the years following its publication it went viral, in a slow, modestly Victorian sort of way. It generated solutions from amateurs (here’s one of seven solutions) and papers by distinguished mathematicians, and was even turned into a verse by “a lady,” that begins:

A governess of great renown,