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Olympic question posted on METU confession page

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Published on Oct 20, 2024

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Happy birthday Derincesi! On the night of Wednesday, October 16th, an Olympiad question suddenly appeared on Instagram. And it was coming from a place I would never have expected: @odtu_metu_itiraf_. After getting over the shock of realizing that an Olympiad question could be thrown as a confession, I solved the question and decided to set up a camera in the METU Mathematics Department building and share this solution with you. Enjoy watching! In the room where I took the shot, I was accompanied by my friend Urşen from METU Mathematics, Burak, who had won METU Chemistry this year and whom I had met only 1 hour before the shooting started, Emin from METU Electrical-Electronics Engineering, and Arsen (our venue sponsor), who dropped out of Bilkent EE in the 3rd year and studied METU Mathematics from beginning to end. This question thrown in the confession seemed like a direct application of Jensen's inequality. I used this situation as an opportunity to give the definitions and properties of convexity and to give a geometric proof of Jensen's inequality. However, we could not fit these beautiful arguments into our video time. We will upload the parts of the video that we did not include today as a separate video a week later. We expect you there too. 00:00 Those who know the incident 04:42 Question thrown in the confession 06:13 First approaches to the question 08:46 General state of the problem 13:02 Intervention from the future 14:01 Convexity and Jensen's inequality (summary) 20:56 Mental preparation for the solution 24:31 Solution of the problem 31:53 Efforts to show convexity

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