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Re: [Phys-l] The modulus mind reading trick



BC,
The trick works on a version of “Casting out nines” See, for instance: http://en.wikipedia.org/wiki/Casting_out_nines

For any integer, x, there is a digital root k (mod 9). Rearranging the digits of the integer, x, will still produce the same root k (mod 9). Example 2345 has a digital root of 5 (mod 9) and 5243 has the same digital root of 5 (mod 9).

Subtracting the two numbers always yields a digital root of 0 (mod 9) which means the number is a multiple of 9. When you throw out one of the digits in your answer and submit it to the server, all the computer has to do is subtract the digital root of your submitted number from 9. The result must be the digit that you threw out.

The only ambiguity arises when you throw out a 0 or a 9 which have the same effect. The program carefully rules this out by not allowing a 0 to be thrown out. Hope this helps.


---- Original message ----
Date: Wed, 20 Aug 2008 21:51:38 -0700
From: Bernard Cleyet <bernardcleyet@redshift.com>
Subject: [Phys-l] The modulus mind reading trick
To: Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>
Cc: Nancy Seese <nancyseese@redshift.com>

I think this trick was explained on PHYS-L, but I can't find it.

Please help!

bc


http://www.digicc.com/fido/


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THO

Thomas O'Neill
Physics Teacher in Residence
James Madison University
Shenandoah Valley Governor's School