Circular composition
From Wikimanqala
Circular Composition
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| © 1995, Rocco Servedio Yeong-Nan Yeh |
| Taiwan |
| Variant of Stones in cups |
| Published rules |
| Used in maths research |
| This game is a solitaire |
| One cycle |
| Single lap game |
| First seed in the same hole |
| n holes per row |
| One row |
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 colouring 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.
Rules
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.
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| 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.
References
- Servedio, R. & Yeh, Y.-N.
- (1995) 'A Bijective Proof on Circular Compositions', in Bulletin of the Institute of Mathematics Academia Sinica; 23. Pages 283-293.
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