HOW TO TELL ANY NUMBER THOUGHT OF.
Ask any person to think of a number, say a certain number of dollars; tell him to borrow that sum of some one in the company, and add the number borrowed to the amount thought of. It will here be proper to name the person who lends him the money, and to beg the one who makes the calculation to do it with great care, as he may readily fall into an error, especially the first time. Then say to the person: “I do not lend you, but give you $10; add them to the former sum.” Continue in this manner: “Give the half to the poor, and retain in your memory the other half.” Then add: “Return to the gentleman, or lady, what you borrowed, and remember that the sum lent you was exactly equal to the number thought of.” Ask the person if he knows exactly what remains; he will answer “Yes.” You must then say: “And I know also the number that remains; it is equal to what I am going to conceal in my hand.” Put into one of your hands 5 pieces of money, and desire the person to tell how many you have got. He will answer 5; upon which open your hand and show him the 5 pieces. You may then say: “I well knew that your result was 5; but if you had thought of a very large number, for example, two or three millions, the result would have been much greater, but my hand would not have held a number of pieces equal to the remainder.” The person then supposing that the result of the calculation must be different, according to the difference of the number thought of, will imagine that it is necessary to know the last number in order to guess the result; but this idea is false, for, in the case which we have here supposed, whatever be the number thought of, the remainder must always be 5. The reason of this is as follows: The sum, the half of which is given to the poor, is nothing else than twice the number thought of, plus 10; and when the poor have received their part, there remains only the number thought of, plus 5; but the number thought of is cut off when the sum borrowed is returned, and, consequently, there remain only 5. The result may be easily known, since it will be the half of the number given in the third part of the operation; for example, whatever be the number thought of, the remainder will be 36 or 25 according as 72 or 50 have been given. If this trick be performed several times successively, the number given in the third part of the operation must be always different; for if the result were several times the same, the deception might be discovered. When the five first parts of the calculation for obtaining a result are finished, it will be best not to name it at first, but to continue the operation, to render it more complex, by saying, for example: “Double the remainder, deduct two, add three, take the fourth part,” etc.; and the different steps of the calculation may be kept in mind, in order to know how much the first result has been increased or diminished. This irregular process never fails to confound those who attempt to follow it.