There are 10 tables in the Conversing Club and 15 members. Each day, 3 people sit together around each of 5 of 10 possible tables in the club talking to each other.

Every week (7 days) everyone is at the same table with everyone else exactly once. Also, nobody is at the same table twice in the course of a week to provide a change of scenery each time. The first day is as following:

ABC DEF GHI JKL MNO

(The second day A couldn't sit with B, or C; B couldn't sit with C; D couldn't sit with E or F, but could sit with A, B, or C.)

How could their schedule be configured?

(Based on Fifteen Schoolgirls)

The number in parentheses after each group of 3 Schoolgirls signifies the room they're in.

Day 1: ABC(1), DEF(2); GHI(3); JKL(4); MNO(5);
Day 2: ADG(6); BEH(7); CLO(8); JNI(9); MKF(10);
Day 3: DHO(1); AJM(2); BNK(3); CFI(4); GEL(5);
Day 4: AEN(4); DKI(5); BFO(6); CGJ(7); MHL(9);
Day 5: GNF(1); BLI(2); CDM(3); AHK(8); JEO(10);
Day 6: MEI(1); GKO(2); AFL(3); CNH(6); BDJ(8);
Day 7: BGM(4); JHF(5); AOI(7); CEK(9); DNL(10);

Posted by Penny on 2003-12-30 04:54:21