Mancala is a board game originating in Africa, with many different rules.
The basic rules I play with are the following (mostly copied from an internet site), and the board looks like this:
http://www.centralconnector.com/images/Mancill1.GIF
OBJECT: Collect the most stones in your mancala (mancalas are the large bowls at each end of the board).
SET UP: Place 4 stones in each small bowl. Do not place stones in the mancalas. Set aside any extra stones (you will not use these). Place the board between the players, with the mancalas on the left and right. To play, use the general rules plus one of the other sets of rules.
Each player "owns" the mancala on his right and the six small bowls closest to him (see Diagram 1). Player 1 starts by scooping up all the stones from one of his small bowls (players may never start from a mancala or from the opponent's six bowls). Player 1 drops one stone into the next bowl on the right, one stone into the second bowl on the right, continuing around the board (counterclockwise) until he has no more stones in his hand. If Player 1 reaches his own mancala, he drops a stone into it. Players do not drop stones into their opponents' mancalas, they skip them and continue dropping stones, one at a time, from their hand until they run out of stones. Players take turns moving. At the end of the game, players count the stones in their mancalas - the player with the most stones wins.
One important addition to the rules in my version is that if the last stone you put down ends in your mancala, you get to go again.
Lastly, when either person has no stones on their side the game ends, and all the left over stones go to the player who ran out first.
For clarity, Ill consider pit 1 as the pit closest to the mancala, and pit 6 the farthest.
The puzzle Im curios about is if there is a pattern between the number and types of arrays of stones that will lead to a finish in one turn. For example, with 1-4 stones I can only see one combination, but after that there are more, and in the very high numbers things could probably get very complicated. (Im ignoring the rule of only 4 stones per pit, you can have any number of stones in any arrangement you want.)
Im also wondering if anyone can find a mathematical or programming method that will find the number of possible combinations for a given number of stones on one side.
If anyone can figure this out, Id be interested in your reasoning steps (though if its above very basic calculus I probably wouldnt understand it)
One more thing: For clarity, if youre talking about a combination we could all use the same format:
See my example in the next post, each number between the dash represents a pit.
Lastly, if you have any other interesting mancala rules, feel free to share them.
And if this is unclear, ask and I'll try to clarify it.
The basic rules I play with are the following (mostly copied from an internet site), and the board looks like this:
http://www.centralconnector.com/images/Mancill1.GIF
OBJECT: Collect the most stones in your mancala (mancalas are the large bowls at each end of the board).
SET UP: Place 4 stones in each small bowl. Do not place stones in the mancalas. Set aside any extra stones (you will not use these). Place the board between the players, with the mancalas on the left and right. To play, use the general rules plus one of the other sets of rules.
Each player "owns" the mancala on his right and the six small bowls closest to him (see Diagram 1). Player 1 starts by scooping up all the stones from one of his small bowls (players may never start from a mancala or from the opponent's six bowls). Player 1 drops one stone into the next bowl on the right, one stone into the second bowl on the right, continuing around the board (counterclockwise) until he has no more stones in his hand. If Player 1 reaches his own mancala, he drops a stone into it. Players do not drop stones into their opponents' mancalas, they skip them and continue dropping stones, one at a time, from their hand until they run out of stones. Players take turns moving. At the end of the game, players count the stones in their mancalas - the player with the most stones wins.
One important addition to the rules in my version is that if the last stone you put down ends in your mancala, you get to go again.
Lastly, when either person has no stones on their side the game ends, and all the left over stones go to the player who ran out first.
For clarity, Ill consider pit 1 as the pit closest to the mancala, and pit 6 the farthest.
The puzzle Im curios about is if there is a pattern between the number and types of arrays of stones that will lead to a finish in one turn. For example, with 1-4 stones I can only see one combination, but after that there are more, and in the very high numbers things could probably get very complicated. (Im ignoring the rule of only 4 stones per pit, you can have any number of stones in any arrangement you want.)
Im also wondering if anyone can find a mathematical or programming method that will find the number of possible combinations for a given number of stones on one side.
If anyone can figure this out, Id be interested in your reasoning steps (though if its above very basic calculus I probably wouldnt understand it)
One more thing: For clarity, if youre talking about a combination we could all use the same format:
See my example in the next post, each number between the dash represents a pit.
Lastly, if you have any other interesting mancala rules, feel free to share them.
And if this is unclear, ask and I'll try to clarify it.
