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The original version of 24 is played with an ordinary deck of playing cards with all the face cards removed. The aces are taken to have the value 1 and the basic game proceeds by having 4 cards dealt and the first player that can achieve the number 24 exactly using only allowed operations (addition, subtraction, multiplication, division, and parentheses) wins the hand.
The game is played between two players on a board consisting of whole numbered tokens labeled 1 through N, where N is any positive whole number. During each turn, one player (deemed the tax payer) takes a number from the board, and the other player (deemed the taxman) removes all remaining factors of the tax payer's number from the board.
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The end of the game must contain the 4 standard result codes: "1-0", "1/2-1/2" "0-1", and "*". The codes must be the same as the Result tag pair. An annotator who wishes to suggest alternative moves to those actually played in the game may insert variations enclosed in parentheses.
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Answer: 1 bull and 2 cows. (The bull is "2", the cows are "4" and "1".) The first player to reveal the other's secret number wins the game. The game may also be played by two teams of players, with the team members discussing their strategy before selecting a move. Computer versions of the game started appearing on mainframes in the 1970s.
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The game chromatic number of a graph , denoted by (), is the minimum number of colors needed for Alice to win the vertex coloring game on . Trivially, for every graph G {\displaystyle G} , we have χ ( G ) ≤ χ g ( G ) ≤ Δ ( G ) + 1 {\displaystyle \chi (G)\leq \chi _{g}(G)\leq \Delta (G)+1} , where χ ( G ) {\displaystyle \chi (G)} is the ...