digital roots. Effective trick and its solution

EFFECTIVE FOCUSES AND THEIR CLUES
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digital roots. Focus secret

Spectacular tricks and their clues

Directory / Spectacular tricks and their clues

Focus Description:

If you add up all the digits of a certain number, then all the digits of the sum just found, and so on far enough, you get one - the only digit, which is called the digital root of the original number. The fastest way to obtain a digital root is by using the so-called "rejection of nines" process. Suppose, for example, that we want to find the digital root of the number 87345691. First, add the numbers 8 and 7, it will be 15; then we immediately add 5 and 1, we get 6. The same result will be obtained if we subtract or "exclude" nine from 15.

Now we add 6 to the next digit, that is, to the three, we get 9. Nine plus 4 gives 13 - a number that, after eliminating the nine, again reduces to the number 4. We do the same until we reach the last digit. The number 7 obtained in this way will be the digital root of the given number 87345691.

A large number of number tricks are based on an operation that results in a seemingly random number, although in reality it has a nine as its digital root. If such an operation was performed, you can invite the viewer to circle any number of the answer (with the exception of the bullet), and name the remaining numbers in any order. After that, the demonstrator may announce the marked figure. To do this, he just needs to add up the numbers called by the viewer, subtracting nines along the way; thus, when declaring the last digit, he will already know the digital root of the totality of the numbers he has written down.

If this root turns out to be nine, then the same figure was marked with a circle. In other cases, to get the marked figure, you need to subtract the found digital root from nine. Here are some of the many operations that result in numbers whose digital root is 9.

1. Write a number (it can be arbitrarily large) and rearrange its digits in any order; Subtract the smaller of these numbers from the larger.

2. Write a number, add up all its digits and subtract the resulting amount from the original number.

3. Write some number. Find the sum of its digits, multiply it by 9 and add the result to the original number.

4. Write a number, multiply it by 9 or a multiple of nine. (All numbers that are multiples of nine have nine as their digital root, and vice versa, all numbers that have nine as their digital root are multiples of nine.)

5. Write some number, add the two numbers obtained from it by any permutation of the Numbers, and square the result.

Focus secret:

If you want to further obscure the method of obtaining numbers whose digital root is 9, you can enter arbitrary numbers and operations before the action essential in this method. For example, you can ask the viewer to write down the amount of change in his pocket, multiply this number by the number of people in the room, add the most significant year in his life to the result, etc., and finally multiply the result by 9. It is clear that only the last action is relevant to the case.

As soon as a number is obtained whose digital root is 9, you can invite the viewer to circle some digit of the result and show focus, as described above.

Author: M.Gardner

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