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2*6=12

8+12 = 20

20+4 = 24

or 

2*6+8+4 = 24

The 24 Game is math game in which the object is to find a way to manipulate four numbers from one to nine so that the end result is 24.

Students will:

  • set up deck from a standard set of 52 playing cards: ACE= 1, elimate all other face cards, 
  • deal four playing cards face up on their table 
  • disreguarding suit, use the number value from each card to determine the 4 numbers for the play 
  • get busy solving for 24 

Students  must use each card once and only once.  They can use Addition, subtraction, multiplication, or division. For example with the numbers 1, 2, 4, 4, the solution is: ((1x2)+4) x 4

1x2=2

2 +4 =6

6 x 4 = 24

Note that in many cases, there are more than one solution

The 24 game solution to the numbers 1  1  1  8 is ((1+1)+1)x8

The 24 game solution to the numbers 1  1  2  6 is ((1+1)+2)x6

Players, Cards and Deal  From a standard international pack remove all picture cards and jokers leaving just 40 cards: the numbers from ace (1) to 10 in each suit.  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 Play: 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.

4 Player Game: The deck is divided equally between the players. Each player places a card face up. A player who has a solution slaps the table but says nothing. When three players have slapped the table, the fourth player must select one of them. If the selected player gives a correct solution, the fourth player must take the four cards; if not the selected player must take the four cards. In this version it is possible to bluff by slapping the table when you do not in fact have a solution, in the hope that you will not be selected. As in the two-player game, if no one slaps the table, the players can agree that there is no solution. Then all players put their cards on the bottom of their decks and turn up a new card.

Card collection version, for 2,3,4 players

In this version, the first player to call a correct solution takes the four cards and places them under his or her stack. Players who run out of cards can still call solutions and thereby win some cards back. If there are four players with cards, each places one card face up. When there are three players with cards, the player who won the previous set places two cards and the others one each. (To start a three-player game 13 cards are dealt to each player and one card is placed face up; the three players each contribute one card to the first set.) When there are two players with cards each player places two cards. When only one player has cards, this player has won the game.Players should try to show their two cards at the same time as each other, and should place the cards so that they are clearly visible, being careful not to cover the cards with their hands.

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.

Other Variations: A version of 24 can be played by more than two players. In this case the 40 cards are kept in a single shuffled stack and one player (the dealer) drops four cards face up on the table. In China, it is quite usual simply to play a series of throws in which the first player to find a solution calls it out, or the players agree that there is no solution, without keeping any kind of tally of the overall score. If you prefer to keep score one possible method is as follows. The first player who finds a way to make 24 from the four numbers scores a point. If no solution can be found, the first person to call "no solution" wins a point - but if another player finds a solution after "no solution" was declared, then the player who claimed no solution gets nothing and the finder of the solution scores 2 points.

Some players allow additional operations, such as powers and roots. For example you could use two 3's to get 27 (3 to the power 3). A square root requires a 2 - for example 9 and 2 can then be combined to make 3 (square or 2nd root of 9). Some people even allow logarithms - for example the base 2 log of 8×4 is 5. Factorials are never allowed - each operation must use at least two numbers - and approximations are never allowed. The result always has to be exact, without rounding.

Some players include the Jack, Queen and King in the pack, valued at 11, 12 and 13 respectively, or at 10 each.