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 - one possible schedule is then:
Sun Mon Tues Wed Thu Fri Sat
AFK ABE BCF EFI CEK EGM KMD
BGL CDG DEH GHK DFL FHN LNE
CHM HIL IJM LMA GIO IKB OBH
DIN JKN KLO NOC HJA JLC ACI
EJO MOF NAG BDJ MNB OAD FGJ
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 Tues Wed Thu Fri Sat AFK ABE BCF EFI CEK EGM KMD BGL CDG DEH GHK DFL FHN LNE CHM HIL IJM LMA GIO IKB OBH DIN JKN KLO NOC HJA JLC ACI EJO MOF NAG BDJ MNB OAD FGJ
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!