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February 12th, 2018, 10:54 AM   #1
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Inequalities important problem

Good Morning,
I've recently been working on a problem, which I haven' been able to solve:

"Find the biggest positive integer with the following property: each digit except for the first and the last one must be smaller than the average mean of the two immediately adjacent digits.
The veracity of the result must be proved"

So for instance for a number [abc]

I've found out that the biggest natural digit with this condition has to be 96433469.
My maths teacher told me that the result was the right one. He also said that I now only have to prove that there is no 9-digit number that satisfies this condition.

Does anybody have an idea how to solve this??

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February 12th, 2018, 12:25 PM   #2
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