THOUGHT NUMBERS—MYSTICAL NINE—MAGIC HUNDRED—KING AND COUNSELLOR— HORSE-SHOE NAILS—DINNER PARTY PUZZLE—BASKETS AND STONES, ETC.
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 remains 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.
ANOTHER WAY
Tell the person to take 1 from the number thought of, and then double the remainder; desire him to take 1 from this double, and to add to it the number thought of, in the last place, ask him the number arising from this addition, and, if you add 3 to it, the third of the sum will be the number thought of. The application of this rule is so easy that it is needless to illustrate it by an example.
A THIRD WAY
Ask the person to add 1 to the triple of the number thought of, and to multiply the sum by three; then bid him add to this product the number thought of, and the result will be a sum from which if 3 be subtracted, the remainder will be ten times the number required; and if the cipher on the right be cut off from the remainder, the other figure will indicate the number sought.
Example—Let the number thought of be 6, the triple of which is 18; and if 1 be added, it makes 19; the triple of this last number is 57, and if 6 be added it makes 63, from which if 3 be subtracted, the remainder will be 60; now, if the cipher on the right be cut off, the remaining figure, 6, will be the number required.
A FOURTH WAY
Tell the person to multiply the number thought of by itself; then desire him to add 1 to the number thought of, and to multiply it also by itself; in the last place, ask him to tell the difference of these two products, which will certainly be an odd number, and the least half of it will be the number required.