Yann's Mancala Problem

Yann's Mancala Problem
Inventor: David Yann, 1997
Ranks: Circular
Sowing: Single laps
Region: France

Yann's Mancala Problem was created by the French mathematician David Yann in 1997. It was first posted on the newsgroups, sci.math and rec.puzzles. This very interesting solitaire is based on the mancala group of games. It was solved by the mathematician Bill Taylor a short time after. Taylor, who is living in New Zealand, has invented another Mancala game called Superwari. The proof, a theorem about finitely checkable procedures, is utterly non-constructive. The solution shows that there is always a series of moves which can bring the game from a distribution A of the tokens to a distribution B.


The game is played on a circular board that consists of a finite number of boxes.

A box may contain any number of tokens (including none at all).


A "Typical" Initial Position (D. Eppstein)

The game is played by just one person.

At his turn the player takes all the tokens from one of the non-empty boxes and redistributes them clockwise, one token at a time, into the boxes, starting with the one following the emptied box - and without omitting that box.

The goal is to bring the game from a given position A to another position B. This is defined as "mancala connectivity".


Taylor, B. 
Yann's MANCALA problem - solved!. Donald Bren School of Information and Computer Sciences (University of California), Irvine CA (USA) 1997.
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