SIMO Retiree Blog

 (Glen here.) I had the privilege of being a Coordinator at this year's IMO, which, along with some extra perks such as a lot of free food and being able to witness Singapore's 3rd-best ever team placement (!), came with the benefit of seeing this year's IMO problems a couple of days before everyone else. This also meant that I had a couple of days to make predictions about how each problem would be received, and I turned out to be wildly wrong about one problem in particular: Problem 3. I'd found this a lot easier than its single-digit solve-rate would suggest (this took me less than an hour without paper), and so I figured that I should write something about my thought process behind this problem. For obvious reasons, I don't have an actual record of solving the problem, but everything has been reconstructed to the best of my memory. The problem I first saw this problem on the Saturday before the IMO. There was a nice fancy dinner for Coordinators and Leaders, and...

(David here.) Continued from Day 1 here. Problem 4 (IMO 2024/Q4) Let $ABC$ be a triangle with $AB Prove that$\angle KIL + \angle YPX = 180^{\circ}$. We spent 25 min drawing diagram in Geogebra (heh). Diagram stolen and modified from Evan Chen's AoPS post. 1. The tangents through$X$and$Y$actually concur on$AI$. This is because with$AB$and$AC$, they form a rhombus. 2. The obvious thing to do to eliminate the two midpoints is to homothety$I$out 2x to$J$. This gives$\angle KIL =\angle BJC$. And we can safely erase$K$and$L$. 3. Maybe we could "push out"$PX$and$YX$- construct$Q$such that$BQ//PX$and$CQ // PY$, and maybe we'd have that$Q$is also on the angle bisector? But then we'd need$DX\cdot XB = DY\cdot YC$(where$D = AI\cap BC$), which seems false. 4. Maybe$K,X,P$collinear? But this is false. 5. After staring for a while: realize that$B,X,J,P$are concyclic. This is easy, because$\angle JXC = \angle C = \angle BP...

(David here.) Recently, Sheldon and I attempted the IMO questions (with AYS and Aloysius making guest appearances along the way). I've tried to document some thought processes and some mishappenings - compared to the cleaned up solutions you'd see on the AoPS thread, this would be instead a messier look at how one might go about the problems.

(Wee Kean here.) I recently learned some interesting game theory which may or may not (read: will not) be useful in your life. For starters, we begin with the classic game of Nim.

 (Dylan here.) With the IMO drawing near, I thought I'd stray from maths to do some rambling.  What is the IMO? What is tested at the IMO? Do I know enough maths? Why do people care about the IMO? Should I care about the IMO? How do I get to/train for the IMO? How do I know if I'm improving? What happens after the IMO?