Well over 150 years ago, the Reverend Thomas Kirkman posed an interesting problem in The Ladies' and Gentlemen's Diary for 1850. The curiously-named publication was in fact a mathematical journal and, as such, Kirkman's problem was mathematical in nature.

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.

It's a common scenario that happens at just about every school. Given any group of schoolgirls — say, Ashley, Beth, Celeste, Daisy, Edna, Flo, Gwen, Harriet, Ingrid, Jane, Kate, Lisa, Mary, Nadia, and Odessa — they will instinctually find a way to gossip with as many smaller groups of girls as possible, and will thereby end up with an daily ordering like follows.

Sun Mon Tue Wed Thu Fri Sat
A, F, K A, B, E B, C, F E, F, I C, E, K E, G, M K, M, D
B, G, L C, D, G D, E, H G, H, K D, F, L F, H, N L, N, E
C, H, M H, I, L I, J, M L, M, A G, I, O I, K, B O, B, H
D, I, N J, K, N K, L, O N, O, C H, J, A J, L, C A, C, I
E, J, O M, O, F N, A, G B, D, J M, N, B O, A, D F, G, J

With 15 girls, there are 455 different ways to group them in three, and we need to pick 35 (5 daily groups * 7 days) of those 455 combinations.