A PUZZLE FOR CARD-PLAYERS.
(
Combination and Group Problems)
Twelve members of a club arranged to play bridge together on eleven
evenings, but no player was ever to have the same partner more than
once, or the same opponent more than twice. Can you draw up a scheme
showing how they may all sit down at three tables every evening? Call
the twelve players by the first twelve letters of the alphabet and try
to group them.
Answer:
In the following solution each of the eleven lines represents a sitting,
each column a table, and each pair of letters a pair of partners.
A B -- I L | E J -- G K | F H -- C D
A C -- J B | F K -- H L | G I -- D E
A D -- K C | G L -- I B | H J -- E F
A E -- L D | H B -- J C | I K -- F G
A F -- B E | I C -- K D | J L -- G H
A G -- C F | J D -- L E | K B -- H I
A H -- D G | K E -- B F | L C -- I J
A I -- E H | L F -- C G | B D -- J K
A J -- F I | B G -- D H | C E -- K L
A K -- G J | C H -- E I | D F -- L B
A L -- H K | D I -- F J | E G -- B C
It will be seen that the letters B, C, D ...L descend cyclically. The
solution given above is absolutely perfect in all respects. It will be
found that every player has every other player once as his partner and
twice as his opponent.
