The Schoolgirl Problem

 
The Schoolgirl Problem

Problem statement:

In a boarding school there are fifteen schoolgirls who always take their daily walks in groups of three.
 
How can it be arranged so that each schoolgirl walks in a group with two different companions every day for a week (7 days)?

Done thinking? Click here to view the solution.

Give the girls letters A to O – the schedule is then:
 
Sun Mon Tue Wed Thu Fri Sat
ABC ADE AFG AHI AJK ALM ANO
DHL BIK BHJ BEG CDF BEF BDG
EJN CMO CLN CMN BLO CIJ CHK
FIO FHN DIM DJO EHM DKN EIL
GKM GJL EKO FKL GIN GHO FJM 
 
The famous Schoolgirl Problem was first posed by Reverend Thomas Kirkman in 1857. It led to a new branch of mathematics called Combinatorics. The problem has since been described as a specific example of a Steiner Triple System. Numerous methods of solution exist, but Trial and Error still (just!) works, but you must be patient!