Kirkman's Schoolgirls-Whataguy

[AuSmith]

This problem posed by Thomas Kirkman in 1847 came up again. It's one that has particularly interested me and is fairly significant in combinatorics, so give it a whirl. Give up if you want to.

A school mistress has fifteen girl pupils and she wishes to take them on a daily walk. The girls are to walk in five rows of three girls each. It is required that no two girls should walk in the same row more than once per week. Can this be done?

I found a very nicely worked solution here:

http://home.wlu.edu/~mcraea/Finite_Geom ... lem31.html

-Aaron

[AuSmith]

Oh, I think it's better if the girls walk at 5 different times. Then, it makes more sense to make sure every pair of girls has had their walk for the week.