Mathematics, Magic And Mystery

1956
Written by Martin Gardner
Work of Martin Gardner
177 pages (Paperback), published by Dover Publications
Illustrated with photographs and drawings
Language: English
132 entries
This publication has been reviewed by
Cover photograph
Creators Title Comments & References Page AA Categories
Martin Gardner Preface
xi
Martin Gardner Tricks with Cards - Part One chapter intro
 		1
Martin Gardner The Curiosities of Peirce History of mathematical card tricks, history of Charles Peirce's work
 		2
The Five Poker Hands Five spectators dealt five cards each, think of one, put back and re-dealt, divine all the selections
 		3
The Piano Trick Piano card trick, standard
Variations 4
The Estimated Cut Trick That Fooled Einstein
 		5
Arthur Finley Findley's Four-Card Trick four cards secretly placed in pocket as prediction, pull out the necessary cards to form suit and value (using binary system)
Also published here 6
A Baffling Prediction forming four piles using the number ten, then count down the sum of the cards to the 40th card to match prediction
Variations 7
Henry Christ Henry Christ's Improvement same as A Baffling Prediction, but with a selection controlled to the 40th position, and the count is done backwards from ten
Inspired byRelated toVariations 8
Lloyd E. Jones The Cyclic Number A packet containing six cards forming the number 142857, when multiplied by any number from 2 to 6, gives a result which the cards themselves reveal
 		9
The Missing Card method to clock the deck to find missing card
Variations 10
Charles T. Jordan, Martin Gardner Jordan's Method Charles Jordan's method for clocking a deck (can be used to clock for four removed cards), with a tip from Martin Gardner to use the feet or fingers to help keep track of the suits
Inspired byRelated to 11
Stewart James Stewart James' Color Prediction Miraskill, three phases, magician predicts outcome each time
 		13
The Royal Pairs Packet of Kings and Queens are cut many times and held behind back, magician can take out the matching King/Queen pairs of the same suit
Variations 15
Bob Hummer Matching the Colors Deck shuffled face up and face down, magician can separate into two piles containing the same number of face up cards. Alternative is to shuffle red and black cards.
 		17
Bob Hummer, Oscar Weigle Hummer's Reversal Mystery CATO trick, magician can name correctly number of face up cards after cut and turn over procedure. Oscar Weigle variation: colors are also separated
Variations 17
Bob Hummer The Little Moonies CATO trick, uses cards with drawing of either smiling/frowning face. Two cards are marked on the back and after mixing, shown to be the only ones frowning while other cards are smiling
Inspired byAlso published here 19
Billy O'Connor O'Connor's Four-Ace Trick 10-20 force to find four Aces one by one
 		20
Bill Nord The Magic of Manhattan cut the deck into two piles, one pile is counted, the two digits in the number of cards is added together to get a single digit, count down to that number in that pile to find selection, the phrase THE MAGIC OF MANHATTAN is spelled to find selection, ten-twenty force principle as control
Related toVariations 20
Martin Gardner Tricks with Cards - Part Two chapter intro
 		20
Predicting the Shift Packet of thirteen cards (Ace to King), spectator shifts any number of cards from top to bottom, magician can immediately take out a card with a value corresponding to the number of cards shifted
 		21
Charles T. Jordan The Keystone Card Discovery two numbers named, predicted card is found at position equal to the difference between the two numbers after two failed count-downs
Related toAlso published here 22
Two-Pile Location Card selected via some dealing into two piles. Later will spell THIS IS THE CARD I SELECTED to find the card
Variations 22
Charles T. Jordan Spelling the Spades Packet of Ace to King of Spades, spell Ace to King one after another, originally titled The Improved Chevalier Card Trick
Related toAlso published here 23
Alex Elmsley, Dai Vernon Elmsley's Card Coincidence deck cut into two piles, a card selected in each pile, later shown to turn up at the same position, handling is by Vernon
Variations 25
Charles T. Jordan Magic by Mail Divination of selected card by mail, deck is sent through the post, deck is shuffled and card is selected, only half the cards are sent to the magician, yet card is divined. Uses interlocking chains
Also published here 27
Steve Belchou Belchou's Aces Poker Player's Picnic, four Aces found via dealing and transferring cards between four piles, credited to Steve Belchou
Related to 27
Don Costello, Dai Vernon, Martin Gardner The Tit-Tat-Toe Trick Packet of nine cards used to play tic-tac-toe with a spectator (face up and down cards). Finale is revealed that the result is a magic square, each row/column/diagonal adds up to fifteen
Related toVariations 28
Martin Gardner Other Tricks of Interest suggested reading list
 		31
Joseph Diez Gergonne From Gergonne to Gargantua Chapter intro, describes Gergonne's Pile Problem, which is basically the 21 card trick using twenty seven cards, see following entries
Related toVariations 33
Naming the Position of the Card 21 card trick with twenty seven cards, spectator can assemble the piles in any way
 		34
Bringing the Card to a Named Position 21 card trick with twenty seven cards, spectator can name what the final position of the selection should be in the packet
Variations 35
Thomas Walker Walker's Method Easier method for Gergonne's Pile Problem, lets spectator name the position of the selected card
Inspired by 36
Naming the Card 21 card trick with twenty seven cards, magician can name the selection at the end
 		38
Mel Stover Relation to Ternary System 21 card trick with twenty seven cards, mathematical relation to ternary counting system
Variations 39
Mel Stover Gargantua's Ten-pile Problem 21 card trick but done with TEN BILLION PLAYING CARDS
Inspired by 40
Martin Gardner Dice intro
 		42
Martin Gardner Magic With Common Objects Chapter Intro
 		42
Guessing the Total Divination of sum of numbers from three dice
 		43
Frank N. Dodd Frank Dodd's Prediction Number "selected" with dice is predicted by number of matches
Also published here 43
Positional Notation Tricks Divine the faces of three rolled dice after some mathematics
 		44
Bob Hummer Hummer's Die Mystery Magician uses dice to divine number thought of by spectator, principle is similar to 21 card trick / Gergonne's Pile Problem. spectator thinks of a number between one and six, a die is put under performer's hand and without looking at it the performer shows three sides of the die several times and asks if the selected number is visible, number is eventually divined
Related to 45
Martin Gardner Dominoes intro
 		46
The Break in the Chain Predict the two numbers at the ends of a long domino chain
 		47
The Row of Thirteen Spectator secret shifts around a number of dominoes from a row of thirteen dominoes, magician divines how many have been shifted
 		47
Magic Squares Three by three square drawn on calendar, magician is told smallest number in square, can then divine total sum of the nine dates in the square
Related toVariations 48
Walter B. Gibson, Royal Vale Heath Gibson's Circled Dates Five dates are circled on a calendar month, magician asks how many Mondays/Tuesdays... are circled, magician can divine the sum total of the circled dates
Also published here 48
Martin Gardner Calendars intro
 		48
Mel Stover Stover's Prediction four by four square drawn on calendar, four circles drawn (draw circle and cross out row and column each time), magician divines the sum, Matrix Force
Also published here 49
Martin Gardner Calendar Memorizing Bibliography and suggested reading list for memorizing calendars
 		50
, Eddie Joseph Tapping the Hours Spectator think of any hour on the clock, magician tap the clock at random points, eventually will end counting on the thought-of hour. Variation by Eddie Joseph using blank cards with words
Variations 50
Martin Gardner Die and Watch Mystery Die is used to start counting clockwise and anticlockwise on a clock, count to thought-of number, the two hours are added together and magician can divine the number on the die
 		51
Royal Vale Heath Heath's Bill Trick Serial number divination, very mathematical
Also published here 52
The Three Heaps start with three heaps of matches, magician can (without looking) form a single pile of matches equal a number called out by spectator
VariationsAlso published here 55
Fred DeMuth Match Folder Mind-reading Divine thought of number with matchbook of twenty matches, spectator is instructed to tear out matches in some mathematical way
Also published here 55
Martin Gardner Matches intro
 		55
The Tramps and Chickens Using matches to tell story of tramps stealing chickens, matches seem to travel from hand to hand
 		56
The Purloined Objects Penny, ring, key distributed to three spectators. Each spectator then takes a number of matches corresponding to some rules, magician then divines who has which object
Related to 57
The Nine Mystery coins placed in a Q shape, spectator counts clockwise and anticlockwise, predict the endpoint of the count
VariationsAlso published here 59
Which Hand? divining which hand holds dime and which hand holds penny
Variations 59
Martin Gardner Coins intro
 		59
Royal Vale Heath Heath's Variation Which Hand, divine which hand holds nickel and which hand holds penny, required length of calculation as tell
Inspired byRelated to 60
, Walter B. Gibson Heads or Tails? Determine whether hidden coin is heads or tails after spectator has turned over the coins randomly, provides variation by Walter Gibson using pieces of colored cardboard
Variations 61
Bob Hummer Hummer's Checker Trick Spectator moves three checker pieces around on the board via spelling, magician can divine the starting positions of the checker pieces
 		62
Bob Hummer Hummer's Three-object Divination Three objects switched around, spectator then thinks of one and switches the other two, magician can divine thought of object (Mathematical 3 card monte 1951)
Variations 63
Jack Yates Yates' Four-Object Divination three matches facing one way and one match facing the opposite way. After moving matches around, magician correctly can divine which is the reversed match without looking
Inspired byAlso published here 66
Martin Gardner Topological Tomfoolery Chapter Intro
 		69
Various The Afghan Bands Moebius strip used for magic, provides the basic method and a history/bibliography of the Moebius strip in magic (Afghan Bands was named by Prof Hoffmann)
 		70
Finger Escape Handkerchief wrapped around finger, penetrates finger, topological
 		73
Edwin Tabor Tabor's Interlocked Handkerchiefs Two handkerchiefs wrapped around each other, penetrates through each other, topological
 		76
Knotty Problems Knot tied in handkerchief without letting go of either hand
 		80
Martin Gardner String and Rope intro
 		81
Garter Tricks Pricking the Garter, basic version, can use belt too
 		81
The Giant's Garter More complex version of Pricking the Garter using a closed loop of string
 		82
More String Tricks Examples of knots in strings/ropes that can allow penetration effects or escape effects
 		84
Martin Gardner Clothing Chapter intro
 		86
The Puzzling Loop Topological puzzle, loop of rope can escape from loop formed by a person's arm (person must be wearing vest)
 		86
Reversing the Vest Person wearing vest, hands are clasped together. Vest can be turned inside out without unclasping hands.
 		86
Removing the Vest Vest can be removed from body without removing coat
 		87
Martin Gardner Rubber Bands
91
Fred Furman The Jumping Band Rubber band jumps from index finger to middle finger
 		91
Alex Elmsley The Twisted Band Puzzle to remove the twists in a wide rubber band
Also published here 91
Martin Gardner Tricks With Special Equipment
95
Number Cards Set of cards with numbers, spectator thinks of a number and chooses cards that has the thought of number. Magician divines the number. Binary system
Variations 95
Window Cards More complex version of Number Cards with holes cut out in the card to be stacked up
Inspired byVariations 96
Sam Lloyd Sam Loyd's Version New version of window cards that reveal your age
Inspired by 100
Tom Hamilton Crazy Time Tapping the Hours but with a wooden board with holes in it
Inspired by 101
Royal Vale Heath Heath's "Tappit" Tapping the Hours type of trick, but with colored tiles and numbers printed on them
Inspired by 102
Martin Gardner Tap-a-drink Tapping the Hours but with names of different drinks in a clock shape
Inspired by 103
Martin Gardner Tap-an-Animal Tapping the Hours but with animal names in a clock shape
Inspired by 104
Martin Gardner The Riddle Card Tapping the Hours type of trick with a card with riddles
Inspired by 106
Royal Vale Heath, Ed Balducci Heath's "Di-ciphering" five dice with different three digit numbers on each face. Roll the dice, magician can very quickly give the sum of the numbers rolled
Variations 106
Eli Hackman, Stewart James Sure-Shot Dice Box Small box that allows dice in it to rattle but not turn over. Includes trick by Stewart James (sum prediction)
 		108
Will Blyth Blyth's Domino Box Dominoes in a box shifted, the spots on the dominoes will predict how many have been shifted
Variations 110
Blocks of India Variation on Blyth's Domino Box, uses colored dominoes
Inspired by 110
Bob Hummer Hummer Tricks Hummer's Poker Chip Trick: numbered poker chips, magician can divine sum of the numbers on three concealed poker chips
 		111
Martin Gardner Geometrical Vanishes - Part 1 chapter intro
 		114
The Line Paradox Line vanishes when paper is shifted
 		114
Sam Lloyd Sam Loyd's Flag Puzzle Geometrical Vanish, cut an American flag into two pieces, rearrange to form onto thirteen stripes instead of fifteen
 		117
The Vanishing Face Geometrical Vanish of a face
 		118
Sam Lloyd "Get Off The Earth" Geometrical vanish of a Chinese warrior by rotating paper globe
 		118
Theodore DeLand DeLand's Paradox Geometrical Vanish of a playing card
Variations 123
Martin Gardner The Vanishing Rabbit Geometrical vanish of a rabbit
Inspired by 125
Mel Stover Stover's Variations Geometrical Vanish / transformation of objects, face becomes beer mug or red pencil becomes blue pencil
Inspired by 125
The Checkerboard Paradox Geometrical vanish of a square on a checkerboard
 		129
William Hooper Hooper's Paradox Rectangle rearranged to apparently increase the area
 		131
Square Variation Area of square changes after pieces are rearranged
 		132
Martin Gardner Fibonacci Series About the mathematics behind geometrical vanishes where the area of a shape changes. Based on work by V. Schlegel, E.B. Escott and Lewis Carroll
Related to
  • V. Schlegel, Zeitschrift fur Mathematik und Physik, Vol. 24, p. 123 (1879)
  • E. B. Escott, Open Court, Vol. 21, p. 502 (1907)
Variations 		134
Harry Langman Langman's Version Rectangle changes in area when pieces are moved around, related to Fibonacci series
Inspired by 137
Paul Curry Curry's Paradox Various geometrical vanishes of squares in rectangles and squares
Variations 139
Martin Gardner Curry Triangles Geometrical vanishes with triangles
Inspired by 145
Four-piece Squares Cut square into four pieces, rearrange to get hole
 		151
Paul Curry Three-piece Squares Cut square into three pieces, rearrange to get hole
 		153
Paul Curry, Martin Gardner Two-piece Squares Cut square into two pieces, rearrange to get hole
 		153
Martin Gardner Curved and 3-D Forms Discusses the possibilities of geometrical vanishes with 3-D shapes
 		155
Martin Gardner Magic with Pure Numbers chapter intro
 		156
Rapid Cube Root Extraction Find cube roots of numbers very quickly, mental calculation
 		157
Adding a Fibonacci Series Add up ten Fibonacci numbers very quickly, mental calculation
 		158
Predicting a Number Think of a number, do some operations, predict final result
 		159
Paul Curry Curry's Version Think of a number, do some operations, predict final result, better presentation
 		160
Al Baker Al Baker's Version Predict sum of numbers
 		160
Divining a Number divining final answer of a series of calculations, required length of calculation as tell
 		161
T. O'Connor Sloane The Mysteries of Nine Number forces using the number nine (e.g. 1089), includes variation by T. O'Connor Sloane using money
Related to 163
Digital Roots Number force using digital roots
Related to 164
Persistent Root Number force using digital roots of nine
Related to 165
Guessing Someone's Age Using digital roots to estimate the age of someone
Related toVariations 166
An Addition Trick Divine digit that is not named in a long number using digital roots
Related to 167
A Multiplication Trick Divine digit that is not named in a long number using digital roots
Related to 167
Martin Gardner The Mysteries of Seven Explains why the number nine has such weird properties
 		168
Predicting a Sum Magician correctly predicts sum of numbers generated by spectator and magician
Variations 170
Al Baker Al Baker's Numero Convert the final sum into a word, which becomes the name of the spectator
Inspired by 172
Psychological Forces Psychological forces with psychologically appealing numbers (37, 68)
Related to 173
Data entered by Harapan Ong, September 2018.