24 Game
From Wikipedia, the free encyclopedia
The 24 Game is a mathematical card game in which the object 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 an 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[1], using ordinary playing cards. Robert Sun commercialised the game in 1988, introducing dedicated game cards bearing four numbers each, and sold it through his company, Suntex International Inc. There are nine official variations of the 24 Game. The tournament-style competition 24 Challenge is based on the game.
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[edit] The original version
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 addition, subtraction, multiplication, division, and parentheses wins the hand. Some groups of players allow exponentiation, or even further operations such as roots or logarithms.
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.
[edit] Overview of the commercial game
Cards are divided into three levels of difficulty. One-dot cards (with a single white dot in each corner) are often solved by simple addition, or contain three digits that can make 24, plus a 1 (in which case any other digit could be multiplied or divided by 1 to create the same digit). Two-dot cards (with two red dots) are slightly more difficult, and often require more multiplication and division than one-dot cards. Three-dot cards (with three yellow dots) are the most difficult cards, often having only one solution. In most decks of Math 24 cards, the ratio of one-dot cards to two-dot cards to three-dot cards is 1:2:1.
[edit] Variations
There have been many variations on the 24 Challenge game, as one deck of cards can be fairly easily memorized, thus creating a simple memory game instead of a skills tester. Some variations include:
- Two-digit cards — cards may have 2-digit numbers on them, leading to more difficulty as not as many students are as familiar with multiples of larger numbers.
- Variables — Cards have two wheels, each has three numbers with one number "missing." The object is to find a number (any integer 1 - 9) which, when used with the other numbers on each wheel, can make 24 on both wheels.[2]
- Fraction, Decimal, and Exponent versions are also available. They are used often in higher level tournaments.
[edit] Strategy
Mastering this game requires fast thinking, but with enough practice, the ability to spot useful patterns increases. Some experienced players can make 24 with almost any four numbers. There are several sequences that lead to 24 that players frequently try to obtain. For example, the solutions 6 X 4, 8 X 3, 2 X 12, 18 + 6, 16 + 8, and 10 + 14 often appear.
There are many common patterns that help a player to acquire a solution faster. It is beneficial to look for common multiplication patterns, such as 12 x 2, 8 x 3, and 6 x 4 in a card to equal 24. Similarly, multiplying a digit by another digit that is one more or less than the usual multiplicitive pair (for example, 4 x 5 or 4 x 7 instead of 4 x 6) then adding or subtracting the first number (20 + 4 or 28 - 4) is a common strategy for reaching 24. This strategy comes from the law of distributivity from elementary algebra. These are some more examples:
6 x 4 = ...
= 6 x (3 + 1) = 6 x 3 + 6
= 6 x (5 - 1) = 6 x 5 - 6
= (5 + 1) x 4 = 5 x 4 + 4
= (7 - 1) x 4 = 7 x 4 - 4
8 x 3 = ...
= 8 x (2 + 1) = 8 x 2 + 8
= 8 x (4 - 1) = 8 x 4 - 8
= (7 + 1) x 3 = 7 x 3 + 3
= (9 - 1) x 3 = 9 x 3 - 3
Possible solutions can be found on the back of 24 game deck boxes.
The number 1 is a powerful digit on a card. As stated above, a 1 may be used at any time to multiply or divide any number to equal itself. This is important in cards where only three digits are needed to create the value of 24. A player may simply multiply (or divide) 24 by 1 to create the final result of 24. If a 1 is not readily provided on the card, two numbers may be subtracted (such as 8-7) or divided (6/6) to make a 1.
Pencil and paper are generally not allowed during play; using such would only slow down a player anyway. Mental math is a necessary skill for playing this game.
[edit] Tournament
In Spring, there is an annual 24 tournament. The tournament happens mainly in Pennsylvania, but also is in New Jersey, California, and other states. In Pennsylvania, participating schools have a school competition. They then send one or two students to compete at a regional level, and the top four will go on to the state level. In other states, there is no state level.
Recently, some of the tournaments have not been taking place because of low funds.
In tournament play, several extra rules apply:
- A player, upon tapping the card, must state the final operation they used to reach 24 first. They then proceed to list the operations in normal order, subsequently repeating the final operation. If a player forgets to state the final operation first, they receive a penalty flag. If, in mentioning all steps they used to reach the card, they do not use the same final operation, they receive a penalty flag.
- Tapping a card with one finger, four or five fingers, or slapping with the whole hand results in a penalty flag, or a relinquishment of a card.
- Players must keep their hands (usually, only the tapping two or three fingers) on the blue region in the mat, about eight inches away from the card. Touching inside this area results in a penalty flag.
- Fake cards with no solution are slipped into tournament decks in the first round to discourage impulsive tappers. These cards are usually marked in such a way that the moderator can distinguish them from normal cards.[citation needed] Tapping one of these fake cards results in an automatic penalty flag.
When a player receives three penalty flags, they are disqualified from further play in that round, but they keep any points they have earned up to that point.
In order to win, the player must earn more points than everyone else in the competition. Usually there are two rounds. The players move from table to table playing other students in their same level. For each card that they receive, they get more points. The points are distributed based on the number of dots found in the corner of each card. The player at the end with the most points wins.
[edit] The Platinum Series
Several variations of Math 24 cards exist, and are used in the Platinum stages of tournaments.This level of play is highest in the 24 game, and only 7/8 graders can participate .The cards used are Algebra/exponents, fractions/decimals, and integers.They can be purchased at 24 game.com ( link located here [1]). These numbers are treated the same way as regular digits, and must be used in a solution once.
A special "integers" deck uses negative digits alongside positive numerals. (Cards in this version may be solved for positive or negative 24.)However, in the tournament, positive 24 must be found.
Algebra version cards contain values with a variable, such as 3y or 2x-4. In solving a problem, the player must state what each variable represents, then give the solution using that variable in it. Cards may contain more than one variable on a side; three-dot cards commonly use x, y, and z all on one card.
The "Exponent" version of Math 24 integrates roots and powers into game play.These cards have a special center marking, indicating that one digit (or result from a previous equation) must be squared, cubed, or have the square root or cube root taken. This results in a card requiring four operations, instead of the usual three. For example, a card with the digits 2, 3, 4, and 8 might be solved by stating that 2x8=16, the square root of 16 is 4, 4+4=8, and 8x3=24.
The last form of platinum play are the "fraction" cards. They involve fractions along with usually whole numbers, except in the case of some level three cards.
[edit] Online Game
In addition to the game produced by Suntex on small cards, there is also a 24 game online. In this game, the player finishes skill sets which earn "stickers" and include the different variations of the game. The players can then compare their score to other players in their school and even the schools in the surrounding areas.
With the increasing popularity of smart phones, a number of 24 applications have been ported to mobile devices such as iphone and android. These games use different user interfaces due to limited screen size, yet they're able to achieve the core objective of Game 24.
