A walking group has fifteen members and meets for a walk seven days a week. The group always splits into five groups of three, and these groups are changed daily, so everyone meets different people.
How is it possible to organise the groups so that each person walks with two different companions every day for the week?
Labelling the fifteen members a to O a possible solution is:
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
This is a branch of mathematics called Combinatorics.