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How does this puzzle work?? Can someone explain the mathematics? I can't figure out how it works, but it always seems to be correct, (click on the guy in the lower right to turn pages): http://digicc.com/fido/
 

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Add the remaining numbers together, the missing number will always make that number divisible by 9.
 

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It's really obvious when you do it to a 2 digit number. ;) The trick actually works from 2-10 digits.
 

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Basically no matter what numbers you choose between 01 and 9876543210 the sum of the difference of any juxtaposition will be divisable by 9. Try this on any number yourself, no repeating of digits, jumble them up and subtract. Add up the digits in the answer and then divide by 9. If you do this trick on someone just add up the numbers they give you and divide by nine, the remainder of the equation is the number they chose.

10-01=9
20-02=18
30-03=27
40-04=36
50-05=45
60-06=54
70-07=63
80-08=72
90-09=81

See the pattern now?
 
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