Bulgarian solitaire

From Wikimanqala

Bulgarian solitaire
Deterministic Bulgarian solitaire
© 1983, Martin Gardner
USA
Variant of Carolina solitaire
Published rules
Used in maths research
This game is a solitaire
Reverse sowing
n holes per row

Bulgarian solitaire, also known as deterministic Bulgarian solitaire, was invented by the famous American recreational mathematician Martin Gardner in 1983.

Many variants were created, such as Austrian solitaire (Ethan Akin & Morton David Davis (USA), 1985), Montreal solitaire (Chris Cannings & John Haigh (England), 1992), random Bulgarian solitaire (Serguei Popov (Brazil), 2003) and two-handed Bulgarian solitaire (Tim Bancroft (USA), 2004). Gardner's game is based on a traditional Bulgarian game that is known as Carolina solitaire. His game and its variants are extensively researched in Combinatorial Game Theory (CGT). It employs reverse sowing.

Prof. Su Dorée of Augsburg College, Minneapolis, USA, called Bulgarian solitaire "a somewhat distant relative of the two-player African pebble games Mancala".

Rules

The game is played by just one person.

In the game, a group of N cards is divided into several decks.

Then one card is removed from each deck.

The removed cards are collected together to form a new deck (piles of zero size are ignored).

The decks are not ordered, so it doesn't matter in which order the cards are being removed or where the new pile is placed.

The game ends when the same position occurs again.

External links

• Martin Gardner

References

Akin, E. & Davis, M. 

(1984) 'Bulgarian Solitaire', in American Mathematical Monthly; (2); 92. Pages 237-250.

Bentz, H.-J. 

(1987) 'Proof of the Bulgarian Solitaire Conjectures', in Ars Combinatoria; 23. Pages 151-170.

Gardner, M. 

(1983) 'Mathematical Games. (a.k.a Bulgarian Solitaire and Other Seemingly Endless Tasks)', in Scientific American; 249. Pages 8-13 or 12-21.

Gwihen, E. 

(1991) 'Tableaux de Young et Solitaire Bulgare', in Journal of Combinatorial Theory; (2); 58. Pages 181-197.

Hobby, J. D. & Knuth, D. 

(1983) 'Problem 1: Bulgarian Solitaire', in A Programming and Problem-Solving Seminar, Stanford: Department of Computer Science, Stanford University; (December). Pages 6-13.

Igusa, K. 

(1985) 'Proof of the Bulgarian Solitaire Conjecture', in Mathematical Magazine; (5); 58. Pages 259-271.

Nicholson, A. 

(1993) 'Bulgarian Solitaire', in Mathematics Teacher; 86. Pages 84-86.

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