Magic is really not easy task its needed full determination, discipline and bla bla. Stop thinking Much just do it
Wednesday, April 21, 2010
Homing Coins
Secret: On two sides of a triangular stand is a ledge to hold four coins. Those on one side are loose, the
others are glued in place. The stand is on your table with the loose coins on show. Pretend to take the first
coin away but really let it fall behind the stand. Put the imaginary coin in a paper bag. Do the same with the
other coins. As you cover the stand with a scarf, tip the stand backwards. Blow up the bag and burst it.
Whisk the scarf away and the coins have returned.
Friday, April 9, 2010
Binary Numbers Magic Trick
Here is a trick that you can do at home.
- Cut out the 5 cards below. You are now ready to do the trick.
- Give the 5 cards to a friend, and ask them to pick a secret number between 1 and 31, and to give you back all the cards that have their number on it.
- You can figure out their secret number by adding together all of the first numbers on the cards they gave back to you. For example, if they gave you back the top and middle card, then their number would be 20, because the first numbers on these cards are 16 and 4, which add up to 20.
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Why does it work?
Remember how to write the numbers from 1 to 31 in binary? See the chart below if you forgot. The sequence of 1's and 0's in a binary number tell us which powers of 2 add up to make the number. For example, 19 = 16+2+1, so in binary we write 10011.
Now notice that the number 19 appears only on the first, fourth, and fifth cards above. That is, 19 appears on the cards with first numbers 16, 2, and 1, and it does not appear on the cards 8 or 4.
The 5 cards correspond to the powers of 2. The numbers that are on the first card (with "16" as the first number) are the ones that have a "1" in the 16's position when we write it in binary. The numbers on the "8" card are those with a "1" in the 8 position in binary. And so on for the other cards. So, when you add up first numbers on the cards that a "secret" number is on, you are adding up the powers of two that add up to the secret number!
Counting in Binary:
Math Telepathy
This is a stunning magic performed by the computer.
Follow the instructions. In the process you will be requested to compute the difference of two natural numbers (although on second thought, the omission of the decimal point appears not at all important.) See that you do not make a silly mistake. The magic fails in the face of ill preparedness. (As is well known in the magic circles, if a spell may go wrong, it will.) So, if you wish, you can use a calculator to compute that difference. In any event, it may be a good idea to double check your result.
Number Guessing Game
Calendar Magic
Arithmetic Magic Matrix
Barcode Magic
Magic in a Square
An Arithmetic Magic Trick
Thursday, April 8, 2010
The Trained Fly
The set up
This trick requires:
a drinking straw
a clear container
and an ordinary fly
The act
The magician places ten sugar cubes spaced from on a flat dry surface like a table, and presents the ordinary fly in the clear container. He then tells the audience he can make train this fly to go to any sugar cube he wishes through hypnotism or something of that nature. He then asks any audience member to select a sugar cube. After the audience member picks the magician pulls out his wand (straw) and constantly taps the sugar cube with his wand while telling the fly what to do for about a minute or so. After the magician finishes the training he opens the jar and releases the fly, after flying for a little bit the fly will pick the sugar the magician tapped.
How the Trick Works
What makes the trick interesting is the magician literally trained the fly. The fly is attracted to sugar but dry sugar like the cubes the magician used has no scent until it is wet. The straw (wand) is used to bring a small amount of moisture to the selected the sugar cube, since it was the only one that has any moisture the scent stands out to the fly and attracts it more than the rest of the cubes
Disappearing Quarter magic trick
What you need :
- a quarter
- napkin
How to do this Disappearing Quarter magic:
- To do this trick, hold the quarter in your hand, between your thumb and your index finger. The palm of your hand should be facing your body.
- Now practice passing the quarter from your right hand to your left hand. If you're left handed, you can hold the quarter in your left hand. It's good to do this so you know what it's supposed to look like when you pretend to pass the quarter. That way you can fake it better.
- Now, for the magic. This time instead of passing the quarter to your other hand, you're going to say the magic words, " abra ca dabra" , Make this coin leave the room now!" and use the index and middle fingers on your empty left hand to knock the quarter into your right hand. You still pretend to grab the quarter with your left hand, as you are dropping it into your right hand.
- Keep practicing and soon you will be able to learn this magic trick like a pro!
Quick Coin Vanish trick
A coin is placed onto the table. It is picked up and it magically vanishes. cool eh ?
Method of doing the magic trick :
easy magic trick ! Set the coin onto the table with your left hand. Say something like "Check this out" and reach over with your right hand. Then press down on the coin with your index, middle, and 3rd fingers with your hand and arm parallel with the table. Slide the coin towards you keeping in mind it should be completely covered up.
Slide the coin off the table so it falls into your lap. Touch your thumb to your middle finger as if you are picking up the coin as it reaches the edge of the table. Keeping all your fingers closed still. Stare at where the coin should be as you slowly move your hand away from you back to about 6 inches above where the coin originally was. Start moving your thumb in a circular motion as if the coin is disappearing. Slowly turn your hand around and spread your fingers apart. Now the rest is up to you. The more surprised you act and if you act like you were all fortunate to see a miracle, people will believe the magic trick even more and remember it !
Ice Baby magic trick
Effect of magic trick : Pour some water into a cup, blow on the cup and then turn it upside down where out pops some ice cubes. You need a cup or glass that you can't see through. You also need a small sponge and and some ice cubes.
Method of magic trick : Prepare the cup by placing the sponge into the bottom of the cup. Then, drop a few ice cubes on top of the sponge and you're ready to go. To perform pour a small amount of water (about an inch) into the cup. The sponge will absorb the water. Blow into the cup, wave your hands over it and dump out the ice cubes. If you are using a disposable plastic cup for the trick, just throw it away at this time. Watch the look of surprise on your friends faces with this magic performance.The Floating Ring - an magic trick
Make some really thick salt water. REALLY thick.
Soak a piece of thread in it somewhere between 45 and 60 minutes. Take it out and let it dry.
Now you are ready. Ask someone for a ring.
Tie it to the end of the thread. Hold the string so its like a pendulum. Now take a match and light the string down by the ring.
The string will burn but the salt crystals can hold up a fairly light ring. An awesome magic effect.
A TRICK FOR PALM PRACTICE
THE uses of the palm will make themselves manifest in every trick in which money is used as a medium, but the beginner can astonish his friends, and, at the same time, make himself perfect, by any of the following minor tricks: (a) Throw the coin backwards and forwards, from hand to hand, three or four times, in a careless manner, always taking care that the left hand is shut well over each time the coin is contained in it; and then make a feint of throwing, but, in reality, palm the coin after the method that best suits its size. The hand (in most cases it would be the left, as the majority of conjurers palm with the right; with left-handed people it would be, of course, reversed) which is supposed to receive the coin must be closed smartly, so as to make a noise similar to that caused by a coin thrown into the palm. This is effected by the ends of the two middle fingers striking the fleshy part of the thumb (Fig. 7). If this is properly executed, the illusion is perfect, and all eyes will be directed to the left hand, when the coin can be quietly placed in a side or tail pocket, to which receptacle it may afterwards be made to pass from the left hand, where it is supposed to be, in a magical manner. I would recommend the beginner to practice this movement sedulously in private, as it teaches quick and neat palming, and will prove a most useful auxiliary to many important tricks. By "passing" a coin from place to place in a magical manner" is implied the act of pretending to do so; it being an accepted axiom amongst conjurers never to "pass" anything invisibly to any given spot until the article is already safely located there. This practice will, of course, commend itself to all as avoiding untoward mistakes. To pass a coin from the hand, wave the wand over it, and say whatever you think will go down best with the particular audience you have before you. A sharp rap on the knuckles will complete the operation, but always take care to show the hand empty, otherwise the trick is spoilt. If the wand is not handy, pretend to rub the coin away between the fingers, or affect to give it to one of the audience. (See Figs. 8 and 9 for an effective method.) | |
TO "SLEEVE" COINS
But, before taking a temporary leave of coins, I must put my readers up to a few wrinkles in connection with the use of the sleeve-a portion of the conjuror's attire which is but rarely employed, notwithstanding the popular exclamation of "Up his sleeve," which is usually made use of when the operator has vanished some trifle in the shape of a cauliflower or rabbit, for the reception of which articles the sleeve of a dress coat is so admirably adapted. Now the sleeve is only used when its coadjutorship is unsuspected; and, in the case of coins, only when the palm is suspected of containing the coin. So many people have a misty idea of palming, that one frequently hears whispered, "In his palm." Should the whisperer be wrong, of course you will at once prove him to be so by exhibiting your palms empty; but should he be right, you will then feign not to hear the whisper. Sometimes, though, the announcement is not made in a whisper, but in the form of a challenge to you, and this you must be prepared to meet. Suppose the coin is palmed and you are challenged; you are close to or among the audience, and the challenger is importunate. Nothing remains but to sleeve the coin. This manoeuvre is executed by shooting the arm straight out, the palm open and downwards, with such force as will carry the coin up the sleeve. Of course, you must not stand in middle of the room shooting your arm out, or the audience will either divine what you are about or will think you are taking leave of your senses. The action must be covered by an advance towards the challenger, which must be done as boldly as if you had never even seen the coin, much less concealed it in your palm. As you advance, say something; for example, "What! in my palm, sir? I don't understand you. How can anything be in my palm? If you don't believe me, see for yourself." With this, make the shoot, and turn the hand over. Care must be taken that the arm is quite level, or the coin will slide gracefully on to the floor. You must not stop here, but say, "Perhaps you would like to see my other hand as well, sir" (show left hand, at same time allowing coin to fall back in the right, where palm it), "or maybe you think the coin is up my sleeve." Shake both arms vigorously, which, as the coin is again in your palm, you can do with impunity, and ask someone to feet your sleeves. An extra effect is given by your asserting that the cause of the gentleman's anxiety was that he himself had basely pilfered the coin, and wished to pass the odium on to you. With this remark, produce the coin from some part of his person. Barring the disturbance to the equilibrium of one's feelings of security whilst the performance is going on, this little interlude, promptly carried out, is as good as any set trick. Of course there must be no bungling. Should the sleeves be turned back, as they often will be, they must fi1'st be unrolled, with great deliberation. In such an instance you would, of course, show that your sleeves are guiltless of any deception, before exonerating the palm. Practice will enable you at once to perceive the nature of the objection about to be raised, so that ordinarily you can anticipate, and turn down one sleeve at least. It is not often that the exigency occurs, but it will infallibly do so at some time or other, so one must be prepared to meet it, or be looked upon as an impostor. A second method for sending a coin up the sleeve is to place it almost on the ends of the fingers (Fig. 16) palm upwards, and, turning the hand rapidly over, close it (Fig. 17). This will throw the coin up the sleeve, whereas the appearance is that it is enclosed in the hand. A third method is to hold the coin between the thumb and middle finger (Fig. 18) and "flip" it up the sleeve. A fourth method is to place the coin on the edge of the table and cover it with the ends of the fingers, which draw smartly back and shut, when the coin will be shot up the sleeve. This somewhat resembles the second method. A fifth method is to spin the coin high in the air, and as it descends make a "grab" at it as if catching, but in reality allow it to fall down the sleeve, keeping the hand shut as though holding it. This is one of the most thorough deceptions I know of. It is so perfect that the operator himself cannot see the coin enter the sleeve. I am quite aware that it seems improbable, but a trial will be conclusive on the point. A pleasing variety of the first method is to place a coin (the heavier the better) on the palm of the hand. Turn the hand over briskly, at the same time thrusting it well forward, and the coin will slide up the sleeve. In performing any of these tricks be careful to have the shirt cuff pulled well up and out of the way, and do not wear large links or solitaires, against which the coin will infallibly clink, if only for the simple reason that it is not wanted to do so. No one but a bungler would use the sleeve in his regular performances, except when driven by necessity; but it is highly essential for a conjuror to be perfect in all the minutiae of his art, and he must practise them as the pianoforte-player practises the scales which he never plays to the public. In using marked coins, always take the greatest care that the marking is done in such a manner as to render it impossible for the coin not to be recognised on making its reappearance; and also let several people see the mark. It is very disheartening, when you have performed an elaborate trick, in which a Mr. Interference has given you no end of trouble, to hear the owner of the coin say that he cannot recognise his mark. I have seen people put some trivial mark on a coin in pencil, which would rub off immediately. It is also advisable to have a quantity of cheap coins by you. In such tricks as trick d, large, thin, and showy silver Turkish coins are the best. They possess every advantage; the milled edge gives a firm hold for the palm, whilst the substance of the coin allows of a large number being held in the hand. Besides this, thin coins give a good business-like clink; whilst a large coin is always more effective than a small one. Pennies plated over make very fair substitutes, and do not entail much loss of capital if kept aside ready for use, as they always should be, which can hardly be said to be the case with florins or half-crowns. | |
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METHOD FOR CONCEALING MANY COINS
Spread the handkerchief out upon the table, and place a coin, not heavier or larger than a shilling (borrowed and marked), in the centre of it. Beneath the nail of the middle finger of the right hand (which hand is immaterial, but for the purpose of illustration it is necessary to use the terms "right" and "left") you have a small piece of bees wax (on no account (Fig. 12). cobblers' wax) which you have previously made tolerably adhesive by working it about. Place this finger on the coin, saying, "Now, in order that all may see that I do not for one instant move the coin from its position, I place this finger upon it," and, taking up one of the corners of the handkerchief in the other hand, fold it over the coin so as to well cover it, and press it down hard, allowing the wax to come off on the coin, and to cause a mutual adherence between it and the handkerchief.
Fold the remaining three corners over one another with great deliberation, exhibiting a portion of the coin each time, to show that there is "no cheating." When all four corners are folded over, the handkerchief will still be in the shape of a square, but of course much smaller than it was at the commencement, and it will have an aperture running from the centre to each corner. Note the portion of the handkerchief to which the coin is stuck, and place the two hands, side by side. in the aperture formed by this portion and the one next to it
If the hands are now separated briskly, and the sides of the handkerchief allowed to slide through the fingers, it stands to reason that, the coin being fast to the corner of the handkerchief, it will, when the corner is reached, find its way into the hand. The handkerchief must be shaken hard, as soon as the coin is safe in the hand, for effect. The operations of opening the handkerchief and shaking it must be practised until they can be compassed both smoothly and quickly in one movement.
The trick is easy, but requires some little practice. Common soap is an excellent substitute for wax, but it has the disadvantage of being less portable. The beauty of the wax is that it can be so easily concealed beneath the nail, and comes off the coin cleanly. The coin successfully vanished from the handkerchief, it rests with the performer to reproduce it in what manner he pleases. If he has already found coins in the heads of the audience, the reproduction can be varied.
For instance, if a tiny piece of wax be affixed to the flat end of the wand, and that end brought into contact with the coin whilst in the palm, and a little pressure used, the coin will adhere. Then, if the wand be passed rapidly behind a curtain. or inside the coat of one of the audience, a great effect call be caused by slowly producing the vanished article from its supposed place of concealment at the end of the wand. The trick can be further prolonged by having about 15in. of human hair, with a tiny bead of wax at the end, affixed to a waistcoat button. Affix the coin to the waxed end, and place it in a wineglass, in which it can be easily made to dance by slightly moving the glass or depressing the hair with the wand, which is supposed to be beating time. Such a combination of tricks, each one easy in itself, affords invaluable practice to the beginner.
The conjuror, like the chess-player, must always see, in his mind's eye, two or three moves ahead, so that no hitch or hesitation occurs. For example, the instant the coin reaches the hand from the handkerchief, it must be palmed, the wand taken up, and the handkerchief ostentatiously given round for inspection to show that there is no hole in it, or for any other plausible reason. Perhaps you will only gain five seconds by this, but that is time enough to enable you to press the wand against the coin. You must not, after this, allow the least pause to occur, but at once seize someone, and have your wand inside his coat before he knows what you are about; for it must be remembered that, if the action is noticed, the coin will be noticed too, as it is in a tolerably conspicuous position at the end of the wand. Then, whilst you are rating the individual soundly for having endeavoured to spoil your trick by concealing the coin, and drawing universal attention to him, one hand will be busily employed in pressing the waxed end of the hair against the coin.
The trick of dancing a coin in a glass is so well known that no one with any desire for a reputation as a prestidigitateur would introduce it by itself; but, in the illustration I have just given, the coin has been in such a variety of places and situations, that the idea of its being fixed to anything does not enter the minds of the audience. Half-a-minute's dancing is quite sufficient, and at the end of it the attention of the audience must be at once drawn into another groove by your showing the coin to be the veritable one marked some time since, the wax being removed by a finger nail.
TO PASS A MARKED COIN THROUGH A TABLE
The following makes an excellent "follow" to the preceding trick: Suppose that you have sixteen coins in all in the hat; conceal four of them in one hand. If the hat is then held by the same hand, it will not be noticed that it contains any coins.
Now ask someone to count the coins in the hat, and, of course, there will be twelve. Take four of these away, and give them to be held by another person. Hold the hat high in the air, and tell the person who bas the remaining eight coins to drop them into it when you have counted "three." Watch the action of his hand narrowly, and, as the eight coins fall, release the four concealed in the hand which holds the hat so that they all fall exactly together.
The great thing to avoid is the sound of two distinct drops, which would be fatal. Leaving the hat, covered with a handkerchief if you please, in the hands of your temporary assistant, who will, of course, be enjoined to "hold it very high," you take the four coins just previously given to be held, and "pass" them invisibly into the hat, where, of course, twelve coins will be found. The method for passing used is the same as that depicted at Fig. 7, with the difference that the coins are not palmed. They must be held in the fingers loosely (Fig. 11) so that when the false movement of placing them in the out-stretched palm is made they will come together with a clash, which is highly necessary for the success of the pass.
The hand actually containing the coins must instantly seize the wand, which article will then cause the magic journey from left hand to hat to be made. Be careful that the counting of the coins is done in a very deliberate manner, and in a loud voice, so that everyone in the room knows how many coins are supposed to be in the hat before you pass the rest into it. If this is not done, the effect of the trick is lost.
Here let me advise my readers to assiduously practise quick palming, for which purpose I would recommend trick a as a most effective exercise. So much depends upon it quick and secure palm, that too great a stress cannot be laid upon it. Indeed, I cannot too strongly impress the learner with the necessity of practising everything, to the minutest detail, in private, before venturing to perform before others. By so doing, much chagrin and disappointment will be averted.
THE USE OF THE WAND IN PALMING
The coins must not be jingled, or the trick will be exposed. Tell one of the audience that he must be very rich if he can afford to carry money about in such strange places as you perceive he does. Surprise will, of course, be expressed on his part, when you will fumble about in his hair, and eventually find the coin which you have had palmed. This is a much better method of commencing than merely saying, "I have here a penny." It is sure to amuse the audience, and put you on a good footing with them; besides which, it is always well to mingle as much with them as possible, as then people go home and say, "Oh! he came right down among us, and found money in people's heads," &c.
Also take care to find the money in an elegant and inoffensive manner. Having spun the coin in the air, in order to show that it is a real one, retire to the end of the room, as far away as you can, if the room is small, and hold the hat, still in the left hand, before you, with the crown towards the audience.
With the coin in the right hand, make a pass at the hat, palming the coin (Palm No.2), and letting one from the left hand fall. You will then appear to have passed the coin from the right hand into the hat, by way of the crown. Should the coin by accident fall on a soft place in the hat, and make no noise in so doing, shake the hat about to show that the coin really is inside, or no one will know what is supposed to have taken place.
Now advance a step or two, looking cautiously forward as if you saw something in the air, and suddenly make a dart out with the right hand, at the same time bringing the coin to the extreme ends of the fingers. The idea conveyed is that the coin has been caught in the air (Fig. 10). Pass it through the hat, letting another fall from the left hand, and shaking the hat so as to ensure the two that have been dropped jingling together, and find another in the air a little farther on. Proceed in this way till all the coins in the left hand are exhausted (varying the proceedings by occasionally finding one at your elbow or foot), and then show the hat with coins to the audience, a member of which will doubtless have "just one more" seated on the tip of the nose, which coin is put into the hat in the ordinary way.
The beginner should use shillings, seven or eight only in number, for this trick, although larger coins are certainly more effective at a distance. It is best to use two palms, viz., the finger palm when the coin is to be caught in the air or in the flame of a candle (a very pretty effect), as it is more readily brought to the ends of the fingers from that position; and either of the others (No.1 for choice), when the coin is to be found on the body or elsewhere. It is as well to occasionally pretend to put the coin into the hat in the ordinary way, instead of through the crown. Some conjurors object altogether to passing through the crown; but this is merely a matter of fancy.
It sometimes happens that the person in whose hair you find the first piece will, from his being a "funny man," or otherwise privileged person, ask you to give him back his property. Acquiesce at once with his request, of course after your own manner, which will be to palm the coin, and pretend to give it to him, much to his discomfiture.
In borrowing the hat, be sure that it hides the left hand in the act of being taken, so that any accidental exposure of the coins held there, which might occur through inexperience, will be covered. Also observe the greatest caution in dropping only one coin into the hat at the first pass. After the first coin has fallen, it does not matter if two or more are accidentally let fall at once, as the error could not be detected; but at the commencement it would be simply fatal to do so. Under cover of the hat it is easy to separate one coin from the rest for the first drop. If the number of coins is very limited, you must give the hat a short, sharp shake, which will serve in lieu of letting one fall; but only do this now and then.
This trick will be treated in an enlarged form, under the head of "Grand Magic." When any number of coins are required for any other trick, they should always be collected in this manner, it being a most effective method. Always take a step in advance each time a coin is found. For this reason the performer should stand well to the right on the stage on commencing.
CHANGE A COIN
Now place the left hand under the table, the right hand remaining above. Covered by the action of bringing it on the table, execute Palm No.1 with the right hand, but keep the fingers formed as though they still held the coin, which you then pretend to lay on the table with a sharp click." This "click" is made by the coin in the left hand, under the table, in order that the illusion may be perfect. The right hand will then affect to rub the coin through the table, and eventually the one in the left hand, which has in reality never been out of it, will be produced.
The noise of rubbing is also made by the coin under the table, only it must not be continued too long; and care must be taken that the two hands act in perfect unison, as it will not do for the noise to continue when the action of rubbing with the right hand has ceased. This trick is not so difficult as it looks on paper, and is very effective. The whole trick consists in pretending to take the marked coin from the fingers of the left hand without doing so.
"PASS" A COIN INVISIBLY
At the same time, open the left hand, and the coin that has been snugly concealed there will look as if it had just left the right hand. By this means a change is effected which you can utilise according to circumstances. By fidgeting about among the audience, you may be able to place the marked coin under one of them; the other coin being held by someone who is directed to hold it very high, sir, very high, so that everyone can see it "-the real object being to keep him from examining it too closely.
By standing the holder of the coin on a chair, an opportunity for slipping the palmed coin into his pocket presents itself, and should be taken advantage of. The marked coin being once safely hidden, it is an easy matter to palm the unmarked one (which, of course, the audience has been led to believe is the marked one) and make it "pass" invisibly to wherever the other may be. The conjuror's own coin should always be provided with a very distinct mark - a cross is invariably a safe one to employ - as it is rarely that one meets with people who can refrain from instituting an illicit investigation so soon as the conjuror's back is turned.
When the holder of the coin is seen to be surreptitiously examining it for the mark, the conjuror should not prevent him, but call the attention of the audience to the fact, and ask if the mark be visible. The holder, seeing the cross, will answer in the affirmative; he not being aware, of course, that the borrowed coin was possibly marked with a very different sign. This incident will add to the effectiveness of the trick.
In tricks a and b the wand will be found very useful. It should always be carried under the arm, after the manner in which soldiers carry their canes; and when any palm has been effected, and the coin has to remain concealed in the hand, the wand should be taken in the hand containing the coin. Beginners, especially, will find this of great assistance, as in the case of a somewhat defective palm the coin can be pressed well home by clenching the wand hard. Besides this, the fact of carrying a wand in the hand keeps the idea of the coin being there from the minds of the audience; and the mind is what the conjuror has to deceive.
A Maths Magic Trick
Step 1: You will need | |
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Step 2: The trick
Tell the participant that you're going to think of a card, the identity of which will be revealed later. Deal one card onto the table face down. Now give the deck to your participant. Tell them to think of a number card in their head as they look through the deck. Tell them not choose a picture card such as a king or an ace. Tell them to find this card in the deck and place it face down on the table next to the other face down card. Now hand them the calculator. This is where the maths comes in. Ask them to double the number of the card they chose. then to add 2, multiply by 5, and finally subtract 7 from the answer. Now ask them to reveal their answer. In this case it's 23. Now ask your participant to turn over the card they selected. It's the first digit of their answer. Now turn over your prediction card, it's the second digit of their answer. Magic? or .... maths?
Step 3: Maths
The secret to this trick, is maths. The magician knows that with this special sum, whatever number the participant chooses, the answer will always end with a three. Knowing this secret, the magician need only select a three as his prediction card, place this face down on the table and the trick will always be a success. Apply the correct equation, and the result is guaranteed every time.