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Amount prediction. Focus secret

Spectacular tricks and their clues

Directory / Spectacular tricks and their clues

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Focus Description:

Is it possible to know in advance the amount that will result from the addition of numbers arbitrarily given by those present in the audience? Magicians have come up with many ingenious solutions to this problem, which we do not intend to deal with here, since they are based on the use of figureheads, sleight of hand, and other non-mathematical tricks.

Focus secret:

If the demonstrator is given the right to name the terms, alternating with the viewer, then he can get the desired amount without using any non-mathematical means. The simplest and oldest method for doing this is as follows: let's say you want 23 in your answer. Drop the first digit, i.e. 843, and then add it to the remaining number, you get 2. You write this number first.

Now ask the viewer to sign any four-digit number below:


Under these two numbers, you write, as it should seem to the audience - at random, the third four-digit number. In reality, under each number written by the viewer, you write its complement to nine:


Next, the viewer writes his second four-digit number. You write the third number, and, as in the previous case, you make it up from numbers that complement the numbers of the viewer to nines.

Focus Predict Sum

The sum of the five numbers written out is exactly 23843. In the example just considered, the first digit of the predicted answer was 2. It corresponded to two pairs of numbers in which the sum of the digits standing one above the other was 9, and there were five terms in total. If the first digit of the assigned amount is the number 3, then you need to take three pairs of numbers with the sum of the digits standing one above the other equal to 9, etc. In all cases, you get the first number to be written down by discarding the first digit of the predicted amount, and then adding it to the remaining number. Focus can be shown with numbers made up of any number of digits. It is only necessary that in all terms it be the same.

There are many variations of this focus. For example, the viewer can write the first number. Then your number, which you write down under the number of the spectator, must be chosen so that the numbers standing one above the other add up to nine. Then the viewer writes the third number, you write the fourth number according to the same principle. The viewer writes the fifth and last number, after which you draw a line and instantly sign the amount. Or, if you find it more efficient, while the spectator adds up the numbers, turn your back, and then, without looking at what you wrote down, announce the result. The answer is obtained, of course, as follows: subtract two from the last written number and put it in front of the resulting number.

You can delay the summation process if you wish. For example, together with the viewer, you can write down six pairs of terms, each of which adds up to nine. The last "number that the viewer writes down will bring the number of terms to 13; to get the answer now, you need to subtract 6 from the thirteenth number, and then write 6 in front of the number obtained in the remainder. If you imagine that the addition will extend to, say, 28 pairs numbers before the last number is written, the trick principle remains the same: subtract 28 from the last number and put 28 in front of the resulting remainder.

There is another version of the trick, when the viewer writes down the prediction. Suppose he chose the number 538. Drop the five and add it to the remainder, you get 43. You write this number first.

Now, in turn with the viewer, using the principle of nine, you write the numbers in a column until there are five pairs under the first number:

Focus Predict Sum

The answer, of course, is the number predicted by the spectator.

Author: M.Gardner

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