March 21, 2006

Mathematical Telepaty

Posted in Computers, Mathematics at 12:26 pm by pmatos

My girlfriend sent me the other day the following link:

The play is nice but as usual nothing more than a trick with basic number theory (and as it is normal, with the number 9).
The instructions are as follows:

  • Choose a number with two digits, let’s call it z. z is composed of the two digits x and y and is given by:
    [tex]z = 10x – y[/tex]
  • Now, subtract from z both digits and you’ll obtain the final number, f.
    [tex]f = z – x -y[/tex]
  • The next step is to search the table for f and it’ll guess which symbol associated with it.

The trick is now very obvious since [tex]f = z -x -y = 10x – x -y = 9x[/tex]. Basically all multiples of 9 are associated with the same symbol, which will be the symbol given as the guess (which will always be correct, by the way). All the other symbols are randomly chosen.

Well, this is not new. 9 has several nice properties but none are used in this trick. For example, it could say to subtract from z, two times the first digit and one time the second and f would be a multiple of 8. You would just have to put the same symbol in every multiple of 8. But 9 is nice for tricks? Why? Because the sum of the digits of a two-digit multiple of 9 is 9. I’ve read about some tricks which used this property. I can’t remember any but I can make up one. Imagine an integer between 10 and 99 (inclusive). Multiply by 4, sum all its digits, subtract 1, multiply by 8, sum all its digits, if the number is less than 10 sum all its digits again until you have a 1-digit number. Now, multiply by nine. Sum its digits, and take 4. I’ll guess the number you have is 5! And it will always be… all the mambo-jambo I just invented tricked your mind into thinking you’re doing something useful when it was plain useless. The kernel of the operation is the multiplication by 9 and the sum of its digits. You sum them and you’ll get 9 (I know that!) and then I ask you to take 4 and I’ll guess 5 which will be correct. You’ll be thinking I’m a magic and I only know the basic property of multiples of 9. :)

Have fun!


1 Comment »

  1. der blaue reiter said,

    ah, o que se aprende quando se procura um pouco !
    obrigado !

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