The Schoolgirl Problem Puzzle - Solution

The Puzzle:

The Schoolgirl Problem

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)?

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!

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