Crossed out number. Effective trick and its solution

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EFFECTIVE FOCUSES AND THEIR CLUES
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Crossed out number. Focus Secret

Spectacular tricks and their clues

Directory / Spectacular tricks and their clues

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Focus Description:

Ask a willing member of the audience to think of some multi-digit number, and have them do the following:

write down the intended number;
rearrange the numbers in any order;
subtract the smaller number from the larger one;
cross out one of the digits of the difference (but not zero);
the rest of the numbers will tell you in any order.

In response, tell the viewer the number he crossed out.

Suppose the viewer thought of the number 3857. He then did the following:

3857; 8735;

8735 - 3857 = 4878.

Having crossed out the number 7, he calls you the remaining numbers in this order, for example:

8, 4, 8.

Based on these numbers, determine the crossed out number.

Focus secret:

The sum of the digits of any number, when divided by 9, gives the same remainder as the number itself. Two numbers made up of the same digits, but in a different order, so the remainder should be the same when divided by 9.

So, if you subtract the other from one, then the difference will be divisible by 9 without a remainder (equal remainders will give zero when subtracting). Based on the above, you can know that the viewer received as a result of subtraction a number whose sum of digits is a multiple of 9.

Since the numbers reported to you - 8, 4, 8 - add up to 20, the number 7 was most likely crossed out, in the amount of which 20 is divisible by 9.

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