# Twenty-Four

The Chinese card game Twenty-Four requires
skills at mental arithmetic. It has been played in

From a standard international pack remove
all picture cards and jokers leaving just 40 cards: the numbers from ace (1) to

Shuffle the cards equally between the two players, each having a face down stack of 20 cards which they must not look at until they are played.

The two players simultaneously take the top two cards of their stacks and place them face up in front of them, to form a square of four face up cards. Now each player tries to think of a way to combine the four numbers using only addition, subtraction, multiplication and division to get a result of 24. For example if the four cards were 2, 3, 6, 9 then possible solutions would be (9+6-3)×2 or (9-3)×(6-2) or (9×3)-(6÷2).

The first player to think of a solution slaps the table and calls out the solution. If it is correct, the four cards are given to the other player to place at the bottom of his or her stack. Then each player again places two cards face up and players again try to make 24 from the four numbers showing. This process is repeated until one player has no cards. This player is the winner.

If a player slaps the table and then calls out a solution that is wrong, or cannot immediately give a solution, then this player must take the four cards as a penalty.

If neither player can make 24, they may agree after a little while that there is no solution. In this case, each player chooses one of their cards to take back, adds this card to the bottom of their stack, and replaces it with a new face up card from the top of their stack.

Players may shuffle or cut their card stacks any time they wish, but must not look at the cards in their stacks.

In the standard game the four numbers must be combined using only the arithmetic operations +, -, ×, ÷, with brackets ( ) if necessary to define the order in which operations are carried out. All four numbers must be used.

The total of 24 is often achieved by grouping the cards to make a two numbers that can finally be multiplied: 4×6, 3×8 or 12×2, but this is not always the case. A surprisingly difficult problem is to make 24 with the numbers 3, 3, 8, 8. Given the limited resources available it may seem impossible at first - most people take a considerable time to find the solution.

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