24 Game
Encyclopedia
The 24 Game is an arithmetical 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 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.
Robert Sun
commercialised the game and copyrighted it in 1988, introducing dedicated game cards bearing four numbers each, and sold it through his company, Suntex International Inc.
There are nine official editions of Suntex's 24® Game. A tournament-style competition, referred to as the 24 Challenge®, is based on the 24 game.
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.
, 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.
and paper will slow down a player, and are generally not allowed during play anyway.
There are
four-card "hands" when played with a standard 52-card deck. It is impossible to make 24 with some of these, for example 1,1,1,1 while others can be difficult, such as 3,3,8,8 (8/(3-(8/3))=24).
With practice, the ability to spot useful patterns increases. These typically target pairs of factors (2 x 12, 3 x 8, 4 x 6), obvious pairs of summands (18 + 6, 16 + 8, and 10 + 14 appear often) or combinations of these involving the number 1 such as:
6 x 4 = 6 x (3 + 1) = 6 x 3 + 6 (9 - 1) x 3 = 9 x 3 - 3
The number 1 (or Ace) is also useful as a throwaway card. Since a number times 1 (or divided by 1) is itself, a solution in which only three digits are needed to create 24 is possible by multiplying the 1 by any of the remaining cards. If a 1 is not provided on the card, two numbers may be subtracted (such as 8-7) or divided (6/6) to make a 1.
Possible solutions can be found on the back of 24 Game deck boxes.
and in other countries. The tournaments were very popular in Pennsylvania, where many participating schools held school competitions. Each school then sent one or two students to compete at a regional level, and the top four went on to the state level Championship. In many states, there was no state-level competition.
Official, Suntex-sposored tournament events were suspended after the 2008 season due to lack of corporate funding, which had provided 24 Challenge Math Program materials to participating schools. Today, many schools continue to conduct their own 24 Challenge® events. Over a period of months preceding the event, teachers use the 24® Game in their classrooms to help students hone their mathematics skills. Schools or districts that hold regional or district-wide events schedule playoffs to determine which students will advance to their Championship event.
In tournament
play, several extra rules apply:
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.
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.
A Pre-test/Post-test module called JUST THE FACTS records each student’s proficiency with basic facts, as players try to complete the addition, subtraction, multiplication, and division tables in under 5 minutes. Three KNOW & SHOW modules provide a unique way for students to experience the type of problems found in standardized tests. Students solve problems from nine categories that tie to national math standards. A workout GYM module helps build automaticity with addition, subtraction, multiplication and division facts, and progress to include fractions, decimals and integers. MEASUREMENT WORLD showcases games and activities that focus on Money, Time, Length, Distance, Area, Volume and Weights.
The First In Math® site allows players to compete individually or as a classroom "Team" and then compare their score to other players on their Team, in their school, school district, state and nationally. Players earn virtual "stickers" that accrue to their personal and classroom score by correctly solving problems on the site.
With the increasing popularity of smart phones, a number of 24 applications have been ported to mobile devices such as S60 phones with J2ME support, 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. The officially-licensed version of the 24® Game became available on iTunes in December of 2010. Currently, only the Single Digits version is available.
Also available as a Google Chrome App.
Card game
A card game is any game using playing cards as the primary device with which the game is played, be they traditional or game-specific. Countless card games exist, including families of related games...
in which the object is to find a way to manipulate four integers so that the end result is 24.
Addition
Addition
Addition is a mathematical operation that represents combining collections of objects together into a larger collection. It is signified by the plus sign . For example, in the picture on the right, there are 3 + 2 apples—meaning three apples and two other apples—which is the same as five apples....
, subtraction
Subtraction
In arithmetic, subtraction is one of the four basic binary operations; it is the inverse of addition, meaning that if we start with any number and add any number and then subtract the same number we added, we return to the number we started with...
, multiplication
Multiplication
Multiplication is the mathematical operation of scaling one number by another. It is one of the four basic operations in elementary arithmetic ....
, or division
Division (mathematics)
right|thumb|200px|20 \div 4=5In mathematics, especially in elementary arithmetic, division is an arithmetic operation.Specifically, if c times b equals a, written:c \times b = a\,...
, 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.
Robert Sun
Robert Sun
Omar A Mohamud , is the inventor and founder of the 24 Game. He invented the math card game in the 24 . He is also the chairman, president, and chief executive of Suntex....
commercialised the game and copyrighted it in 1988, introducing dedicated game cards bearing four numbers each, and sold it through his company, Suntex International Inc.
Suntex
Suntex International Inc. is a company based in Easton, Pennsylvania, founded by Ayub Mohamud; he is most famous for producing the 24 Game math card game....
There are nine official editions of Suntex's 24® Game. A tournament-style competition, referred to as the 24 Challenge®, is based on the 24 game.
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
War (card game)
War is a card game typically involving two players. It uses a standard French playing card deck. Due to its simplicity, it is played most often by children.-Gameplay:The deck is divided evenly among the two players, giving each a down stack...
; 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.
Overview of the commercial game
Cards are divided into three levels of difficulty. One-dot cards (with a single white dot in each corner, indicating an easy problem) are often solved by simple additionAddition
Addition is a mathematical operation that represents combining collections of objects together into a larger collection. It is signified by the plus sign . For example, in the picture on the right, there are 3 + 2 apples—meaning three apples and two other apples—which is the same as five apples....
, 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
Multiplication
Multiplication is the mathematical operation of scaling one number by another. It is one of the four basic operations in elementary arithmetic ....
and division
Division (military)
A division is a large military unit or formation usually consisting of between 10,000 and 20,000 soldiers. In most armies, a division is composed of several regiments or brigades, and in turn several divisions typically make up a corps...
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
Ratio
In mathematics, a ratio is a relationship between two numbers of the same kind , usually expressed as "a to b" or a:b, sometimes expressed arithmetically as a dimensionless quotient of the two which explicitly indicates how many times the first number contains the second In mathematics, a ratio is...
of one-dot cards to two-dot cards to three-dot cards is 1:2:1.
Variations
There have been many variations on the original Single Digits Edition 24® game, including standard 96-card editions and 48-card travel-sized editions. Some variations include:- Double Digits Edition — Cards include 2-digit numbers, from 1 to 24, 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.
- Fractions/Decimals, Algebra/Exponents and Integers(negative numbers) versions are also available and are recommended for ages 9 and up.
- Editions for ages 7/8 and up include: Add/Subtract Primer; Multiply/Divide Primer and Factors/Multiples. Primer editions have a "self-check" feature (answer on reverse side)
Strategy
Mental arithmetic and fast thinking are necessary skills for competitive play. PencilPencil
A pencil is a writing implement or art medium usually constructed of a narrow, solid pigment core inside a protective casing. The case prevents the core from breaking, and also from marking the user’s hand during use....
and paper will slow down a player, and are generally not allowed during play anyway.
There are
four-card "hands" when played with a standard 52-card deck. It is impossible to make 24 with some of these, for example 1,1,1,1 while others can be difficult, such as 3,3,8,8 (8/(3-(8/3))=24).With practice, the ability to spot useful patterns increases. These typically target pairs of factors (2 x 12, 3 x 8, 4 x 6), obvious pairs of summands (18 + 6, 16 + 8, and 10 + 14 appear often) or combinations of these involving the number 1 such as:
6 x 4 = 6 x (3 + 1) = 6 x 3 + 6 (9 - 1) x 3 = 9 x 3 - 3
The number 1 (or Ace) is also useful as a throwaway card. Since a number times 1 (or divided by 1) is itself, a solution in which only three digits are needed to create 24 is possible by multiplying the 1 by any of the remaining cards. If a 1 is not provided on the card, two numbers may be subtracted (such as 8-7) or divided (6/6) to make a 1.
Possible solutions can be found on the back of 24 Game deck boxes.
Tournament
In the 1980s through 2008, there were 24 Challenge® tournaments held throughout the United StatesUnited States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
and in other countries. The tournaments were very popular in Pennsylvania, where many participating schools held school competitions. Each school then sent one or two students to compete at a regional level, and the top four went on to the state level Championship. In many states, there was no state-level competition.
Official, Suntex-sposored tournament events were suspended after the 2008 season due to lack of corporate funding, which had provided 24 Challenge Math Program materials to participating schools. Today, many schools continue to conduct their own 24 Challenge® events. Over a period of months preceding the event, teachers use the 24® Game in their classrooms to help students hone their mathematics skills. Schools or districts that hold regional or district-wide events schedule playoffs to determine which students will advance to their Championship event.
In tournament
Tournament
A tournament is a competition involving a relatively large number of competitors, all participating in a sport or game. More specifically, the term may be used in either of two overlapping senses:...
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 were included in "Tournament Decks"* in the first round to discourage impulsive tappers. Tapping one of these fakeFakeFake means not real.Fake may also refer to:In music:* Fake , a Swedish synthpop band active in the 1980s*Fake?, a Japanese rock band* Fake , 2010 song by Ai featuring Namie Amuro...
cards results in an automatic penalty flag. *(Special Tournament Decks (with non-working cards) were only used at official Suntex-sponsored events, and were not distributed to the general public or sold.)
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.
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 http://24game.com). 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
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
version cards contain values with a variable
Variable (mathematics)
In mathematics, a variable is a value that may change within the scope of a given problem or set of operations. In contrast, a constant is a value that remains unchanged, though often unknown or undetermined. The concepts of constants and variables are fundamental to many areas of mathematics and...
, 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
Square root
In mathematics, a square root of a number x is a number r such that r2 = x, or, in other words, a number r whose square is x...
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
Fraction (mathematics)
A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, we specify how many parts of a certain size there are, for example, one-half, five-eighths and three-quarters.A common or "vulgar" fraction, such as 1/2, 5/8, 3/4, etc., consists...
" cards. They involve fractions along with usually whole numbers, except in the case of some level three cards.
Online Game
In addition to the game produced by Suntex on small cards, there is also a 24® game online at firstinmath.com. The First In Math® Online Program (FIM) was introduced in 2002. The backbone of the FIM program is the 24® Game, but the 24 editions available online range from Addition Only to multi-step Algebra, and are organized into eight SKILL SETS™. Each Skill Set comprises three sequential 24 Games, labeled 1, 2 and 3. Each game builds upon the skills acquired in previous games. After completing certain Skill Set requirements, students can play BONUS GAMES. Bonus games offer various types of skill-building activities, such as sequencing and working with tens. Bonus Games are targeted to skills students need to master at each grade level, based on common core math standards.A Pre-test/Post-test module called JUST THE FACTS records each student’s proficiency with basic facts, as players try to complete the addition, subtraction, multiplication, and division tables in under 5 minutes. Three KNOW & SHOW modules provide a unique way for students to experience the type of problems found in standardized tests. Students solve problems from nine categories that tie to national math standards. A workout GYM module helps build automaticity with addition, subtraction, multiplication and division facts, and progress to include fractions, decimals and integers. MEASUREMENT WORLD showcases games and activities that focus on Money, Time, Length, Distance, Area, Volume and Weights.
The First In Math® site allows players to compete individually or as a classroom "Team" and then compare their score to other players on their Team, in their school, school district, state and nationally. Players earn virtual "stickers" that accrue to their personal and classroom score by correctly solving problems on the site.
With the increasing popularity of smart phones, a number of 24 applications have been ported to mobile devices such as S60 phones with J2ME support, 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. The officially-licensed version of the 24® Game became available on iTunes in December of 2010. Currently, only the Single Digits version is available.
External links
- Distinct solutions to all solvables
- www.24game.com The Official 24 Game website
- 24 at Pagat
- A fast 24 game solver: both executable program and source code
- Online 24 Game
- 24 Math Practice - A comprehensive iPhone App to practice finding 24
- iMath24s - A 24 game for S60 smartphones
- Slide 24 - The 24 game for iPod Touch and iPhone
- 24.roundskylab.com the iphone version of 24
- Cards Math by virtuesoft.com the iphone version of 24
- TwentyFour! - A multiplayer version of 24 for the iPhone
- 24 game scorers in over 40 different programming languages on the Rosetta Code site
- 24 game solvers in over 23 different programming languages on the Rosetta Code site
- itestu.com/24 An online 24 card game where users are ranked by how fast they solve a set of problems.
- game24.apphb.com An online 24 game and solver.
Also available as a Google Chrome App.