24 Game

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This article is about the arithmetical card game. For the game based on FOX's television series, see 24: The Game.

The 24 Game is an arithmetical card game in which the objective is to find a way to manipulate four integers so that the end result is 24. Addition, subtraction, multiplication, or division, and sometimes other operations, may be used to make four digits from one to nine equal 24. For example, card with the numbers 4,7,8,8, a possible solution is the following: (7-(8/8))*4=24.

The game has been played in Shanghai since the 1960s, using ordinary playing cards. It is similar to the card game Maths24.

A Sample 24 Game Card

Original version[edit]

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 thrown and the first player that can achieve the number 24 exactly using only allowed operations (such as addition, subtraction, multiplication, division, and parentheses) wins the hand. Some groups of players allow exponentiation, roots, logarithms and/or additional operations.

For short games of 24, once a hand is won, the cards go to the player that won. If everyone gives up, the cards are shuffled back into the deck. The game ends when the deck is exhausted, and the player with the most cards wins.

Longer games of 24 proceed by first dealing the cards out to the players, each of whom contributes to each set of cards exposed. A player who solves a set takes its cards and replenishes their pile, after the fashion of War. Players are eliminated when they no longer have any cards.

A slightly different version includes the face cards, Jack, Queen, and King, giving them the values 11, 12, and 13, respectively.


Mental arithmetic and fast thinking are necessary skills for competitive play. Pencil and paper will slow down a player, and are generally not allowed during play anyway.

There are \tbinom {4+13-1}4=1820 four-card "hands" when played with a standard 52-card deck. Rule variations sometimes allow for square root and factorial operations to allow more combinations. If the additional operations are not included a card such as 1,1,1,1 would be impossible to manipulate an answer of 24. However, with the use of factorials, it is possible to get 24 using the cards 1,1,1,1 , i.e (1+1+1+1)!= 24. This gives an idea of the number of possible combinations on various cards.

See also[edit]

Krypto (game)


External links[edit]

An implementation in the "8th" language
An implementation in "4tH", a Forth dialect