SIMO Retiree Blog

 Hi! It's Glen again. So I was supposed to write a post for next weekend, but I woke up this morning to pictures of this year's SMO Open Round 2 in my messages, and I figured I might as well give them a go. And then I figured that I should just release my solutions to beat everyone else to the chase. Hence, this blog post is a week early.

(Gabriel here) Occasionally, while I am solving a maths olympiad problem, I will be suddenly reminded of another problem I have done in the past before. I'm sure this has happened to many of you too. I think each of these connections presents valuable learning opportunities, and can help to make your subconscious intuition more concrete.

(David here.) Here's a more frivolous topic for this week: have you ever read a problem and just felt like it was way too convoluted?

(KY here.) In this blog we look at two problems. If you have not done them before, I would highly recommend trying them first before continuing with the rest of the blog.

(Jeck here.) Consider an arrangement of $n$ lines on the plane, which do not necessarily need to be in general position. There are many combinatorial problems one can explore with such configurations: If no three lines are concurrent, the number of regions into which these lines divide the plane is given by $1+\binom{n+1}{2}$. If not all lines are concurrent, there is always at least one intersection point that is shared by exactly two lines.

(Aloysius here.) I love doing many things, and two of those things are mathematics and puzzles. There are puzzles that use basic mathematics, such as Kakuro or Tomtom puzzles that require summation/basic mathematics. But there are several puzzles that require other tricks that are reminiscent of Math Olympiad techniques, and in this post I will be giving several examples.

(Click on "read more", if not this page won't render.)