|Other Names: Mancala-game|
|Inventor: Roland Schröder, |
|Variant of Stones in Cups|
|Sowing: Single laps|
Mancala Solitaire, also known as the Mancala-game in the On-Line Encyclopedia of Integer Sequences™ (OEIS™), was invented in 2005 by OStR a.D. Roland Schröder, a retired math teacher in Celle (Germany). He was inspired by Klaus Hasemann's game Türme Bauen (i.e. "Building Towers"), a combinatorial math problem for 1st and 2nd graders. Research on the game's mathematical properties demonstrated that the lower Wythoff sequence can be constructed by playing it. Results were published in the OEIS™. Knott and Schröder also formulated in 2010 two assumptions for a game played on an infinite board.
The game inspired Rüdeger Baumann to create a close variant called Montenegrinisches Mancala in 2010.
The first hole (starting from the leftmost one) contains one stone, the second hole two stones, the third hole three stones and so on.
The object of the game is to discover mathematical laws.
The game can be played starting from different set-ups.
Roland Schröder gave the following positions:
- A finite board with all holes initially occupied. The last legal sowing finishes in the rightmost hole.
- A finite board with only the first holes occupied, the following ones being empty. Again the game stops, when the last stone of a sowing falls into the rightmost hole.
- An infinite board with all holes being occupied.
- Lower Wythoff sequence (a Beatty sequence)
- The Mancala Game and the spectrum of Phi
- A photo of Roland Schröder (center) with the winners of the Math Competition Celle
- Hasemann, K., Leonhardt, U. & Szambien, H.
- Denkaufgaben für die 1. und 2. Klasse. Cornelsen Verlag, Berlin (Germany) 2006.
"Actually it isn't a game, but the result of a playful activity. Of course, you can change the problem as you want and each time analyze its mathematical laws. Then it might be possible to call it a game. More precisely a playful matrix for mathematical discoveries."
Roland Schröder (2011)