[Guest]

A jury of twelve has been deliberating for some time when the process breaks down. The jurors are tired and irritable and begin arguing and talking over one another, when one juror has a suggestion. "why don't we line up the chairs in two rows of six and each sit accross from each other juror for five minutes and share are thoughts, so that every juror can hear what every other juror has to say? In less than an hour we could each hear everyones opinion!"

Like so... (where h's represent chairs)

h h h h h h

h h h h h h

The jury agrees that this is a good idea, but in practice this becomes difficult as well. They start with each juror moving one chair to the right after each interview, but after meeting with only half of the other jurors they find themselves in front of the first person they spoke with again.

Help the jury get unhung so that the defendant can be. What is the simplest rotation in which each juror can speak with each other juror?

This puzzle actually can up in real life, although not on jury duty.

[Guest]

A jury of twelve has been deliberating for some time when the process breaks down. The jurors are tired and irritable and begin arguing and talking over one another, when one juror has a suggestion. "why don't we line up the chairs in two rows of six and each sit accross from each other juror for five minutes and share are thoughts, so that every juror can hear what every other juror has to say? In less than an hour we could each hear everyones opinion!"

Like so... (where h's represent chairs)

h h h h h h

h h h h h h

The jury agrees that this is a good idea, but in practice this becomes difficult as well. They start with each juror moving one chair to the right after each interview, but after meeting with only half of the other jurors they find themselves in front of the first person they spoke with again.

Help the jury get unhung so that the defendant can be. What is the simplest rotation in which each juror can speak with each other juror?

This puzzle actually can up in real life, although not on jury duty.

Move 5 seats to the right.

[Guest]

Move 5 seats to the right.

Whoops! Never Mind.

[Guest]

1 Row moves 1 to the right in rotation

Both rows move 1 to the right in rotation

[Guest]

Umm is this allowed?

Have everyone move one seat to the right 5 times then have the top row only move one seat to the right with the one on the far right moving to the far left.

Then have everyone move to the right 5 more times.

[Guest]

1 Row moves 1 to the right in rotation

Both rows move 1 to the right in rotation

Whoops! Just checked it, doesn't work

[Guest]

12 individuals each need 11 conversations. Therefore 66 unique conversation pairings are required.

The important parameter here is that both rows are moving in opposite directions - therefore each move skips one in the sequence (expect when they move rows) as follows:

A B C D E F _\ G A B C D E _\ H G A B C D L K J I H G

G H I J K L / H I J K L F / I J K L F E ...... F E D C B A

So by the time we join A has spoken to G, I, K, F, D & B !

Therefore the simplest approch is for one row only to switch places with the person next to them, as follows:

L K J I H G _\ L K J I H G

F E D C B A / E F C D A B ...... and then to the previous pattern.

In which case A will now converse with H, J L, F, E & C.

Edited March 20, 2009 by PaulE

[Guest]

PaulE is correct, and that is a solution that I had not found. This also points out a flaw in the wording of my puzzle. What I was looking for was the simplest way for twelve people to rotate to converse in this manner from the beginning. Sorry, this is my first puzzle.

Not everyone has to move

[Guest]

If you rotate them through like a belt, you get the upside down configuration of your starting position after 5 moves (6 conversations). If you leave one person in their chair, however, and rotate around them, you will get each possible conversation pairing without having to change your rotation pattern.

Here's what I mean (A stays in place):

A B C D E F  |  A C D E F L  |  A D E F L K  |  etc...

G H I J K L  |  B G H I J K  |  C B G H I J  |

[Guest]

If you rotate them through like a belt, you get the upside down configuration of your starting position after 5 moves (6 conversations). If you leave one person in their chair, however, and rotate around them, you will get each possible conversation pairing without having to change your rotation pattern.

Here's what I mean (A stays in place):

A B C D E F  |  A C D E F L  |  A D E F L K  |  etc...

G H I J K L  |  B G H I J K  |  C B G H I J  |

I regard this as a much purer solution than mine. One small refinement though - it is important that the static person be on the end of a row. If in the middle (i.e. B) then after six conversations the pairs on the ends will again be facing one-another.