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 12 digit number (Posted on 2007-01-22)
A 12 digit number is formed using these rules:

* You can only use digits 1,5 and 9 (base 10)
* The number is divisible by 37

Prove that the sum of the digits is not 76

 No Solution Yet Submitted by atheron No Rating

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 unsatisfying proof, by exhaustion, but may serve as a hint | Comment 1 of 2
I'm sure what's wanted is a deductive proof, rather than a proof by testing all the qualifying numbers for their sum of digits. However, a tabulation of how many of each possible sum of digits might give someone a lead on a deductive proof:

`sum of digits   number of occurrences 12                     1 24                    64 36                  1000 48                  4096 52                   192 56                   228 60                  6859 64                   228 68                   192 72                  4096 84                  1000 96                    64108                     1`

 Posted by Charlie on 2007-01-22 11:26:10

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