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18-yes, 17-maybe (Posted on 2010-08-06) Difficulty: 2 of 5
Prove that among any 18 consecutive 3-digit numbers there must be at least one which is divisible by the sum of its digits.

No Solution Yet Submitted by Ady TZIDON    
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Hints/Tips re: solution Comment 4 of 4 |
(In reply to solution by Praneeth)

Absolutely true, but case 1 is included in case 2.

Erasing the first four rows  and the words "case 2" does not affect the validity of your proof.

Your solution boils down to a shorter text:

In a row of 18 consecutive numbers  two are divisible by 9:
one is an even multiple and the other is odd.
Both 2 and 9 divide the even one.


q.e.d.


  Posted by Ady TZIDON on 2010-08-06 23:31:50
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