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Problem 6 (due Monday, April 28 )

Prove that if a,b,c are positive numbers such that abc=1 then

11+2024a+11+2024b+11+2024c115.

We received a solution from Emily (Qingyue) Liu, Josiah Moltz, and Andrew Zhou (a high school senior from Cincinnati, OH). Andrew's solution is based on a certain general result in elementary inequalities called the N-1 Equal Value Principle. The solution from Josiah Moltz is perhaps the simplest of all the solutions we have. For details and other solutions see the following link Solution.