# The Schoolgirl Problem Puzzle - Solution

### The Puzzle:

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)?

How can it be arranged so that each schoolgirl walks in a group with two different companions every day for a week (7 days)?

### Our Solution:

Give the girls letters A to O - the schedule is then:

The famouse Schoolgirls 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!

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 famouse Schoolgirls 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!

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*Discuss this puzzle at the Math is Fun Forum*