Mancala World
Other Names: mancala ad infinitum
Inventor: Véronique Gautheron,
Variant of Tchuka Ruma
Ranks: One
Sowing: Single laps
Region: France

Tchoukaillon is a variant of Tchuka Ruma which was developed by the French mathematician Véronique Gautheron in 1977. The game received some attention in Combinatorial Game Theory. Duane Broline and Daniel Loeb found out in 1995 that the number of stones in a winning position is asymptotically bounded by n2/pi (given n pits). Tchoukaillon was called mancala ad infinitum by Gary Preisser, a student at Stetson University, Florida, who did a senior research project on the game in 1998.

Monokalah and Multitchouka are Tchoukaillon variants proposed by the same author.


The board consists of one row which can have any finite or even infinite number of playing pits known as "cases" ("squares") in French.

At the right end of the row is a store called "roumba" (often spelled "rumba" in English).

Initially each hole may contain any number of stones or can be be empty.


Possible Initial Set-up (Roumba Marked)

The game is played by just one player.

At his turn the player picks up the contents of a hole and sows them to the right, one by one, into succeeding holes. The last stone must be placed into the roumba.

The player wins the game when he eventually accumulates all stones in the roumba.


Ahmad, I. & Khan, S. U.
Some Preliminary Results on Three Combinatorial Board Games. In: Bulletin of the European Association for Theoretical Computer Science 2004; 84: 159-166.
Broline, D. & Loeb, D. 
The Combinatorics of Mancala-Type Games: Ayo, Tchoukaillon, and 1/Pi. In: UMAP Journal 1995; 16 (1): 21-36.
Campbell, P. J. 
Tchuka Ruma Solitaire. In: UMAP Journal 1995; 16 (4): 343-365.
Deledicq, A. & Popova, A.
Wari et Solo: Le Jeu de Calculs Africain (Collection Les Distracts 3). CEDIC, Paris (France) 1977, 180-183.
Jones, B., Taalman, L. & Tongen, A.
Solitaire Mancala Games and the Chinese Remainder Theorem (Paper). James Madison University, Harrisonburg VA (USA) 2011 (December 15).
Khan, S. U. 
Tchoukaillon. In: Geombinatorics 2003 (2); 13: 106-108.
Preisser, G. 
Mancala Ad Infinitum. DeLand FL (USA), 1998.
Taalman, L., Tongen, A., Warren, B. & Wyrick-Flax, F.
Mancala Matrices (Paper). James Madison University, Harrisonburg VA (USA) 2012 (June 15).


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By: Ralf Gering
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