Puzzles
Fifteen schoolgirls, seven days, no repeated walking partners
Fifteen schoolgirls walk to school each day in five groups of three. Can you schedule the groups across seven days so that no two girls ever end up in the same group more than once?
Reveal the answer
Yes — seven genuinely distinct arrangements exist, once rotations and relabelling of the girls are discounted, and finding them helped found combinatorial design theory. Thomas Penyngton Kirkman posed the puzzle as a reader's query in The Lady's and Gentleman's Diary in 1850.
— Thomas Penyngton Kirkman, Query VI, The Lady's and Gentleman's Diary — 1850