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-- The Amazing Phone Number Trick

Posted by Kabby on Mar-10-2004 00:21:

The Amazing Phone Number Trick

HERE

Posted by A.J. on Mar-10-2004 02:10:

Sorry, but that is not amazing.

It's just lame......

Posted by St�phanie on Mar-10-2004 04:24:

the title was intriging...lol

Posted by O-RzA on Mar-10-2004 06:44:

umm...
yeah ..kinda lame

Posted by Mystre on Mar-10-2004 09:24:

weak

Posted by -=M=- on Mar-13-2004 03:08:

how'd that work?

Posted by Noisician on Mar-13-2004 04:02:

quote:
Originally posted by -=M=-
how'd that work?

elementary number theory

n1 - initial number
n2 - number formed by the same digits but in different oder

fact 1:

|n1-n2| ≡ 0 (mod 9)

fact 2:

∀k∈N, 9 | k ↔ 9 | (d1+d2+d3+d4+...+dn) where d1,d2,d3...dn are digits of k

in this case

k = |n1-n2|, therefore 9 | k, therefore 9 | (d1+d2+...+dn)

step v asks you to remove one digit. without loss of generality suppose it's d2.

then d2 = 9p - (d1+d3+d4+...+dn), where p∈N

fact 3:

∀d∈DIGIT, 0 ≤ d ≤ 9

in this case 0 ≤ 9p - (d1+d3+d4+...+dn) ≤ 9

it can be easily shown that d2 is uniquely defined by the above double inequality.