Chomp instructions
Chomp is a known two player board game involving mainly logic, but also some strategy and ... a little mystery.
It exists in various versions and names e.g. Munch, which is a synonym of Chomp. In this version, the board consists of a certain number of chocolates arranged in rows and columns (Fig. 1). Each player in turn eats (removes) a rectangular block of these chocolates. All the chocolates are the same, good and tasty, except the one on the top left corner, which is stale.
The game is played as follows: Each player in turn selects a chocolate, e.g. row 4, column 2. Then he/she eats that chocolate and all the chocolates below it and to the right of it (Fig. 2), which are removed from the board (Fig. 3). Playing is mandatory (you cannot "pass").
The goal is to leave the stale chocolate alone to be eaten by the opponent. Simple as that. Or not?
Here comes the "mystery" element: Is there a certain winner? Can the first or second player play in a way that he/she always win? Well, it can be proven that the first player can always win if he/she plays perfectly. (Hint: If the move of the first player is not a winning move, but the move of the second player is, it means that the first player could have chosen the move of the second player at the first place!)
However, except if you are trained in the game, you will see that playing against the machine is very tough. In fact, the machine always wins, esp. against the beginners. This is of course because the machine knows how to make a winning move. But don't get disappointed , which is natural, if you are new to the game. You can make progress in a short time.
Playing options
By touching "SELECT" in the action bar, a dropdown menu appears with board size and tracing options (Fig. 4).
Start with a 4x3 board if you are new to the game. It is easier then to explore the way the machine responds so that you can finally do the same thing!
Another thing that helps exploring the response by the machine is using "tracing". This leaves marks at the chocolates you and the machine are removing at each move (H = human, M = machine) (Fig. 5).
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Fig. 4 |
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Fig. 5 |
Please leave your comments on the game.
You can also contact the developer at a_pis @ otenet.gr.
References for Chomp
- https://en.wikipedia.org/wiki/Chomp
- http://lpcs.math.msu.su/~pentus/abacus.htm
- https://plus.maths.org/content/os/issue14/xfile/index
- http://www.math.cornell.edu/~mec/2003-2004/graphtheory/chomp/howtoplaychomp.html
- https://www.win.tue.nl/~aeb/games/chomp.html
- http://www.math.uci.edu/icamp/summer/research_11/mojica/chomp.pptx
- https://www.emis.de/journals/INTEGERS/papers/fg7/fg7.pdf
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