Carolina solitaire

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Carolina solitaire
Played in:
Bulgaria
This game is a solitaire
Reverse sowing
n holes per row

In the late 1990s, Andrey Andreev, a Bulgarian visitor, introduced Carolina solitaire to mathematicians of the University of South Carolina. This reverse sowing game could be a traditional game in Bulgaria, but so far its native name is unknown in the west. Bulgarian solitaire is a generalized version, which was invented by the famous mathematician Martin Gardner in 1983. It seems obvious that he knew the original game.

Rules

The game can be played with any number of (imagined) pits that are ordered in a row. Initially there are some seeds in each pit, the exact number can be varied.

board
Initial position discussed by Davalan

The game is played by just one player.

Each move the player takes one seed from every non-empty pit (empty pits are ignored) and puts them in a new pit at the end of the row, always in the same direction.

The game ends when the board position repeats.

References

Davalan, J.-P. 
(2004) Solitaire Bulgare. [Web site]
Gardner, M. 
(1983) 'Mathematical Games (a.k.a Bulgarian Solitaire and Other Seemingly Endless Tasks)', in Scientific American; 249. Pages 12-21.
Griggs, J. R. & Ho, C.-C. 
(1998) The Cycling of Partitions and Compositions under Repeated Shifts, Columbia: Industrial Mathematics Institute; March 2, 1998. [Pdf document]
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