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The magic of number 1089. The secret of focus

Spectacular tricks and their clues

Directory / Spectacular tricks and their clues

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Focus Description:

You simply ask to guess any three-digit number so that the difference between the extreme numbers is 1. Now ask to swap the extreme numbers. You get the second number. Offer to subtract the smaller from the larger. The person performing this trick will also have to add to this result the number that differs only in the extreme numbers: they have swapped places. The magician gives an envelope, the spectator opens it and... there is the number he got!

Focus secret:

If you do that operation, you always get 1089.

For example:

851
- 158
693
+ 396
= 1089

Using the number 1089 from the previous example, hand the volunteer a calculator and ask him to multiply 1089 by any three-digit number without saying it. (Suppose he secretly multiplied 1089? 256 = 278) Now ask how many digits are in the answer. The answer is 784.

You say, "Say five of these six numbers out loud, in any order. I'll try to figure out the missing one." Suppose a volunteer lists out loud: “Two... four... seven... eight... eight.” You politely tell him that he missed the number 7.

The secret is based on the fact that a number is a multiple of 9 if and only if the sum of its constituent digits is a multiple of 9. Since 1 + 0 + 8 + 9 = 18 is a multiple of 9, then the number 1089 is a multiple of 9. Therefore, 1089 when multiplied by any an integer will give a multiple of 9. And since the numbers spoken add up to 29, and the next multiple of 9, greater than 29, is 36, then our volunteer missed the number 7 (since 29 + 7 = 36).

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