In a boarding school there are fifteen schoolgirls who always take their daily walks in rows of threes. How can it be arranged so that each schoolgirl walks in the same row with every other schoolgirl exactly once a week? Solution of this problem is equivalent to constructing a Kirkman triple system of order n=2. The following table gives one of the 7 distinct (up to permutations of letters) solutions to the problem. A visualization is shown above. Sun ABC DEF GHI JKL MNO Mon ADH BEK CIO FLN GJM Tue AEM BHN CGK DIL FJO Wed AFI BLO CHJ DKM EGN Thu AGL BDJ CFM EHO IKN Fri AJN BIM CEL DOG FHK Sat AKO BFG CDN EIJ HLM
(The table of Dörrie 1965 contains four omissions in which the a_1=B and a_2=C entries for Wednesday and Thursday are written simply as a.) Thanks & Regrads Shashank -- You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
