Guessing a number. Effective trick and its solution

EFFECTIVE FOCUSES AND THEIR CLUES
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Guessing a number. Focus secret

Spectacular tricks and their clues

Directory / Spectacular tricks and their clues

Focus Description:

This is one of the most wonderful mathematical tricks. It is distinguished from such tricks by the fact that not once during the entire demonstration, both when performing operations on the planned number, and after receiving the final result, the viewer does not tell the showman anything. And yet it turns out that, using skillfully created loopholes, you can gradually get close to the number conceived by the viewer.

Focus demonstration can be divided into the following steps:

1) You ask someone to think of a number between 1 and 10 inclusive.

2) Tell me to multiply it by 3.

3) Suggest dividing the resulting number by 2.

4) Now you need to find out if the viewer got a mixed fraction or an integer in the quotient. To get the right information, ask him to multiply the result by 3 again. If this is done quickly, without apparent effort, there is every reason to be sure that the viewer did not have to deal with fractions. If he succeeded with a fraction, he would stumble and perhaps be somewhat surprised. He may even ask how he should deal with the fractional part. In any case, if it seems to you that the viewer got a partial fraction, say something like this: "By the way, your last result contains a fractional part, doesn't it? It seemed to me that way for some reason. Please round your number up. Well, for example, if you get 101/2, take the number 11 instead."

Now, if the quotient was a fraction, remember the "key number" 1. If the quotient was an integer, you don't need to remember anything.

5) After multiplying by 3 according to the previous instruction, tell the viewer to divide the result by 2 again.

6) Then you again need to know if the quotient turned out to be a fraction or an integer. You say, for example, the following: "Now you have an integer in the quotient, don't you?". If the answer is yes, say "I thought so" and move on to the next step. If they answer you that you were mistaken, make a surprised face and immediately say: "Well, then get rid of the fraction, taking, like last time, the nearest larger whole number."

In this latter case, remember the next key number 2. If the quotient was an integer, nothing needs to be remembered.

7) Offer to add 2 to the result.

8) Ask to subtract 11. Of course, the last two steps mean nothing more than subtracting 9; however, these actions of yours are intended to mask the application of the principle of the nine.

9) If the spectator announces to you that the subtraction of 11 cannot be done because the last number he received is too small, you will immediately be able to name the originally conceived number. So, for example, if you had to remember only the key number 1, a unit was conceived; if you memorized the key number 2, a deuce was conceived; if you had to remember both key numbers, a triple was conceived (it can be considered as the result of adding both key numbers); if nothing had to be memorized, a four was conceived.

Suppose now that the subtraction of the number 11 can be done, this will mean that the intended number is greater than four.

Remember key number 4 and proceed as follows:

10) Ask to add 2 to the last result.

11) Tell me to subtract 11.

12) If this is not possible, then by adding the key numbers, you get the answer. If the viewer silently subtracted, add up the key numbers, add the number 4 again and you will get the intended number.

Focus secret:

At first glance, this trick may seem unreasonably complicated, but if you work it carefully, the whole procedure will seem quite easy to you. Of course, the subtraction of nines can be done in any way. For example, instead of adding two and subtracting 11, you could ask the viewer to add 5 and subtract 14, or add 1 and subtract 10. After a few demonstrations, you will be able to give instructions in such a way that the viewer will not have any suspicion that his answers he gives you the information you need about the intended number. After the series of operations proposed by you, which at first glance seem meaningless and the results of which are not reported, the viewer will be surprised to see the announcement of the number he has conceived.

Indexes 1, 2, 3, 4 mean the key numbers that the showman remembers. It can be seen from the diagram that the conceived number is the sum of the key numbers obtained by the end of the process. Interestingly, the number of numbers that can be conceived can be increased. So, for the number 11, the scheme remains unchanged, for 12, you will have to subtract 9 again, which will give the third four, etc.)

Author: M.Gardner

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