Description
the game
This game consists of a row of cans.
Alernatively, player and computer remove 1- or 2 adjacent cans.
Winner is who removes the last can.
The player can win every game.
levels
There are 10 levels.
Starting level is 0.
After two won games, the level is increased by 1.
When a game is lost, the level decreases by 1.
"test" mode
Each higher level is more difficult.
"free" mode
Cans are placed randomly.
hall of - fame
When level 10 is reached in "test mode" the player can
register - as a master player- for the hall - of -fame.
Complete the form and click "register".
the board with "CANs"
Click with mousebutton on a can to remove.
Click between cans to remove both.
About this game
Cans belongs to the category of so called "Nim" games.
Many variations exist.
All these board games have the following common properties:
- 2 players move alternately
- a game ends with win or lose
- finite number of moves
- 2 type of board states:
- winning
- losing
- an algorithm recognizes a winning board state
The Canadian mathematician Charles L. Bouton analysed Nim games in 1902.
Cans is slightly more difficult then other Nim games :
the algorithm needs an extra step to evaluate a board state.
A breakthrough was found in 1936 by the German mathematician Roland Sprague.
Independenly, in 1939 P.M.Grundy obtained the same result.
"CANs" is geprogrammed in Javascript. By the nature of a script language,
the speed is slow. However, because simple arithmetic operations suffice
to analyse a game, little processor power is needed.
the board with "CANs"