The Schoolgirl Problem Puzzle - Solution
The Puzzle:
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:
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!
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!