(related to Problem: A Puzzle for Card-players)

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.

$$\begin{array}{ccc} A B — I L&E J — G K&F H — C D\\ A C — J B&F K — H L&G I — D E\\ A D — K C&G L — I B&H J — E F\\ A E — L D&H B — J C&I K — F G\\ A F — B E&I C — K D&J L — G H\\ A G — C F&J D — L E&K B — H I\\ A H — D G&K E — B F&L C — I J\\ A I — E H&L F — C G&B D — J K\\ A J — F I&B G — D H&C E — K L\\ A K — G J&C H — E I&D F — L B\\ A L — H K&D I — F J&E G — B C \end{array}$$

It will be seen that the letters $B, C, D,\ldots, L$ 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.

Thank you to the contributors under CC BY-SA 4.0!



Project Gutenberg

  1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

This eBook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this edition or online at If you are not located in the United States, you'll have to check the laws of the country where you are located before using this ebook.