Mathematics, Magic And Mystery

Written by Martin Gardner

1956
Work of Martin Gardner

177 pages (Paperback), published by Dover Publications
Illustrated with photographs and drawings.
Language: English

(132 entries)

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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
Unknown The Five Poker Hands Five spectators dealt five cards each, think of one, put back and re-dealt, divine all the selections 3
Unknown The Piano Trick Piano card trick, standard 4
Unknown The Estimated Cut Trick That Fooled Einstein 5
Arthur Finley, Findley 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
Unknown A Baffling Prediction Form four piles using the number ten, then count down the sum of the cards to the 40th card to match predictionVariations 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 tenInspired by 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
Unknown The Missing Card Method to clock the deck to find missing cardVariations 10
Charles T. Jordan, Martin Gardner Jordan's Method Charles Jordan's method for clocking a deck, with a tip from Martin Gardner to use the raising of your fingers to help keep track of the clockingInspired by 11
Stewart James Stewart James' Color Prediction Miraskill, three phases, magician predicts outcome each time 13
Unknown 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 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 separatedVariations 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 smilingInspired 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 20
Martin Gardner Tricks with Cards - Part Two chapter intro 20
Unknown 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. 22
Unknown Two-Pile Location Card selected via some dealing into two piles. Later will spell THIS IS THE CARD I SELECTED to find the card 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 TrickRelated to 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 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 chainsAlso 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 BelchouRelated 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 fifteenRelated 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 cardsRelated toVariations 33
Unknown Naming the Position of the Card 21 card trick with twenty seven cards, spectator can assemble the piles in any wayRelated to 34
Unknown 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 packetRelated toVariations 35
Thomas Walker Walker's Method Easier method for Gergonne's Pile Problem, lets spectator name the position of the selected cardInspired byRelated to 36
Unknown Naming the Card 21 card trick with twenty seven cards, magician can name the selection at the endRelated to 38
Mel Stover Relation to Ternary System 21 card trick with twenty seven cards, mathematical relation to ternary counting systemRelated toVariations 39
Mel Stover Gargantua's Ten-pile Problem 21 card trick but done with TEN BILLION PLAYING CARDSInspired byRelated to 40
Martin Gardner Dice intro 42
Martin Gardner Magic With Common Objects Chapter Intro 42
Unknown 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 matchesAlso published here 43
Unknown 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 divinedInspired byRelated to 45
Martin Gardner Dominoes intro 46
Unknown The Break in the Chain Predict the two numbers at the ends of a long domino chain 47
Unknown 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
Unknown 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 squareRelated 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 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 49
Martin Gardner Calendar Memorizing Bibliography and suggested reading list for memorizing calendars 50
Unknown, 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 wordsVariations 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 52
Unknown 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 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 wayAlso published here 55
Martin Gardner Matches intro 55
Unknown The Tramps and Chickens Using matches to tell story of tramps stealing chickens, matches seem to travel from hand to hand 56
Unknown 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 57
Unknown The Nine Mystery Coins placed in a Q shape, spectator counts clockwise and anticlockwise, predict the endpoint of the countVariations 59
Unknown Which Hand? Divine which hand holds dime and which hand holds pennyVariations 59
Martin Gardner Coins intro 59
Royal Vale Heath Heath's Variation Which Hand, divine which hand holds nickel and which hand holds pennyInspired by 60
Unknown, 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 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 lookingInspired 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
Unknown 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
Unknown Knotty Problems Knot tied in handkerchief without letting go of either hand 80
Martin Gardner String and Rope intro 81
Unknown Garter Tricks Pricking the Garter, basic version, can use belt too 81
Unknown The Giant's Garter More complex version of Pricking the Garter using a closed loop of string 82
Unknown More String Tricks Examples of knots in strings/ropes that can allow penetration effects or escape effects 84
Martin Gardner Clothing Chapter intro 86
Unknown The Puzzling Loop Topological puzzle, loop of rope can escape from loop formed by a person's arm (person must be wearing vest) 86
Unknown Reversing the Vest Person wearing vest, hands are clasped together. Vest can be turned inside out without unclasping hands. 86
Unknown 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 91
Martin Gardner Tricks With Special Equipment 95
Unknown 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 systemVariations 95
Unknown Window Cards More complex version of Number Cards with holes cut out in the card to be stacked upInspired byVariations 96
Sam Lloyd Sam Loyd's Version New version of window cards that reveal your ageInspired by 100
Tom Hamilton Crazy Time Tapping the Hours but with a wooden board with holes in itInspired by 101
Royal Vale Heath Heath's "Tappit" Tapping the Hours type of trick, but with colored tiles and numbers printed on themInspired by 102
Martin Gardner Tap-a-drink Tapping the Hours but with names of different drinks in a clock shapeInspired by 103
Martin Gardner Tap-an-Animal Tapping the Hours but with animal names in a clock shapeInspired by 104
Martin Gardner The Riddle Card Tapping the Hours type of trick with a card with riddlesInspired 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 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 shiftedVariations 110
Unknown Blocks of India Variation on Blyth's Domino Box, uses colored dominoesInspired 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
Unknown 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
Unknown 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 cardVariations 123
Martin Gardner The Vanishing Rabbit Geometrical vanish of a rabbitInspired by 125
Mel Stover Stover's Variations Geometrical Vanish / transformation of objects, face becomes beer mug or red pencil becomes blue pencilInspired by 125
Unknown 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
Unknown 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 CarrollRelated 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 seriesInspired by 137
Paul Curry Curry's Paradox Various geometrical vanishes of squares in rectangles and squaresVariations 139
Martin Gardner Curry Triangles Geometrical vanishes with trianglesInspired by 145
Unknown 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
Unknown Rapid Cube Root Extraction Find cube roots of numbers very quickly, mental calculation 157
Unknown Adding a Fibonacci Series Add up ten Fibonacci numbers very quickly, mental calculation 158
Unknown 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
Unknown Divining a Number Divine final answer of a series of calculations 161
Unknown, 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 moneyRelated to 163
Unknown Digital Roots Number force using digital rootsRelated to 164
Unknown Persistent Root Number force using digital roots of nineRelated to 165
Unknown Guessing Someone's Age Using digital roots to estimate the age of someoneRelated toVariations 166
Unknown An Addition Trick Divine digit that is not named in a long number using digital rootsRelated to 167
Unknown A Multiplication Trick Divine digit that is not named in a long number using digital rootsRelated to 167
Martin Gardner The Mysteries of Seven Explains why the number nine has such weird properties 168
Unknown Predicting a Sum Magician correctly predicts sum of numbers generated by spectator and magicianVariations 170
Al Baker Al Baker's Numero Convert the final sum into a word, which becomes the name of the spectatorInspired by 172
Unknown Psychological Forces Psychological forces with psychologically appealing numbers (37, 68) 173
Data entered by Harapan Ong.