Tchoukaillon

From Wikimanqala

Multitchouka
Mancala ad infinitum
© 1977, Véronique Gautheron
France
Variant of tchuka ruma
Published rules
Used in maths research
This game is a solitaire
One cycle
Single lap
Stores are sown into
n holes per row
One row

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.

Rules

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.

References

Ahmad, I. & Khan, S. U. 

(2004) 'Some Preliminary Results on Three Combinatorial Board Games', in Bull. Eur. Assoc. Theor. Comput. Sci.; 84. Pages 159-166.

Broline, D. & Loeb, D. 

(1995) 'The Combinatorics of Mancala-Type Games: Ayo, Tchoukaillon, and 1/Pi', in UMAP Journal; 16. Pages 21-36.

Campbell, P. J. 

(1995) 'Tchuka Ruma Solitaire', in The UMAP Journal; 16 (4). Page 343-365.

Deledicq, A. & Popova, A.

(1977) Wari et Solo: Le Jeu de Calculs Africain (Collection Les Distracts 3), Paris: Cedic. Page 180-183.

Khan, S. U. 

(2003) 'Tchoukaillon', in Geombinatorics(2); 13. Page 106-108.

Preisser, G. 

(1998) Mancala Ad Infinitum, DeLand. [Pdf document]

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