The conversing club has lost more members as other problems came up such that now they only had 9 members. To help settle down the club, the club decided to get a series of 6 speakers to come in for 6 days of the week.

The chairs were arranged in 3 rows of 3, with space between each row, but less space between each chair in a row. The members wanted to talk to anyone to their immediate left or right during the performance, but felt it would be too rude to lean all the way forward or back to talk to anyone not on their immediate left or right. (Each day 6 people can talk to 1 person during the speech, and 3 people can talk to 2 people during the speech)

The schedule for where everyone would sit each day was created such that everyone would be able to talk to everyone once during the 6 days. The first day's schedule is as follows:

A B C
D E F
G H I

(So on the second day, B A E would be disallowed because A could talk to B again. DCB would not be allowed either, because B could talk to C again. ACF would be allowed because C would need to reach across B in order to talk to A, so C couldn't talk to A the first day. This means C could talk to A another day instead. DFB, BEI, CFG would be an allowed combinations, but GHA and FDE would not be allowed.)

What are schedules for all 6 days?

A B C
D E F
G H I

E A C
H D F
B G I

E C D
H F G
B I A

F A H
E B D
I C G

A D G
B F C
H E I

A G E
B H C
D I F

But, of course there's gonna be numerous answers. For any of the days you can reverse any row or switch rows and it will still work. And if you switch the days around too (except the 1st one, cuz that's part of the question) I'd say there's... what? 5760 different ways...8*6*120=5760. I think that's right.

Edited on May 22, 2004, 5:51 pm

Posted by Danny on 2004-05-21 23:22:19