Mancala World
Circular Composition
Inventors: Rocco Servedio &
Yeong-Nan Yeh, 1995
Variant of Stones in Cups
Ranks: Circle
Sowing: Single laps
Region: Taiwan

Circular Composition was invented in 1995 by the mathematicians Rocco Servedio and Yeong-Nan Yeh of the Academia Sinica in Taipei, Taiwan (Republic of China). Its invention was motivated by the study of coloring circular-arc graphs. The game is a variant of Stones in Cups. Although it is often compared to Bulgarian Solitaire, the game does not use reverse sowing.


The board consists of any number m of circularly labeled "positions" around a disk.

A non-negative integer n of "units" is distributed in an arbitrary manner on the positions.

Circular composition.jpg

Initial Position with n=15 and m=7

A move consists of distributing the contents of a position, one by one, in a clockwise direction into the succeeding positions. The first unit is dropped to itself, the position that was just emptied.

The game ends when a "composition" (= board position) repeats.


Servedio, R. & Yeh, Y.-N.
A Bijective Proof on Circular Compositions. In: Bulletin of the Institute of Mathematics Academia Sinica 1995; 23: 283-293.


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