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Subtraction games are generally impartial games, meaning that the set of moves available in a given position does not depend on the player whose turn it is to move.For such a game, the states can be divided up into -positions (positions in which the previous player, who just moved, is winning) and -positions (positions in which the next player to move is winning), and an optimal game playing ...
The game "21" is played as a misère game with any number of players who take turns saying a number. The first player says "1" and each player in turn increases the number by 1, 2, or 3, but may not exceed 21; the player forced to say "21" loses. This can be modeled as a subtraction game with a heap of 21 − n objects. The winning strategy for ...
Subtract-a-square can also be played as a misère game, in which the player to make the last subtraction loses. The recursive algorithm to determine 'hot' and 'cold' numbers for the misère game is the same as that for the normal game, except that for the misère game the number 1 is 'cold' whilst 2 is 'hot'.
This video game is an educational game teaching four basic principles: division, adding/subtracting decimals, adding/subtracting fractions and multiplying/dividing decimals. Each minigame has two difficulty levels and allows for two players to take turns playing the minigames.
divide a 16-digit number by an 8-digit divisor. Addition or subtraction is performed in a single step, with a turn of the crank. Multiplication and division are performed digit by digit on the multiplier or divisor digits, in a procedure equivalent to the familiar long multiplication and long division procedures taught in school.
In a two-player game, the position becomes 1101, which becomes an easy forced win, so it is best played with more than 2 people. Self-adding: As their turn, players can add 1 finger to any living hand, or transfer multiple fingers to a dead hand. This enables self-destruction (by adding 1 to a living hand with 4 fingers) and resurrection.
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