My Math Forum Inequalities important problem

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 February 12th, 2018, 10:54 AM #1 Newbie   Joined: Dec 2017 From: Spain Posts: 18 Thanks: 1 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] b<((a+c)/2) 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?? Thanks
 February 12th, 2018, 12:25 PM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,884 Thanks: 1088 Math Focus: Elementary mathematics and beyond You've already posted this. If you post it again I'll be forced to take remedial action. Thread closed. See here.

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