SIMO Retiree Blog

Wee Kean here. Happy New Years Eve! Lately, my only interaction with math has been through doing Project Euler. So... here's some cool things I've learnt! Unfortunately, there is hardly any structure to this blogpost so I apologize if this comes off as verbal diarrhea.

(Yu Peng here) For this post, I'll go through a common idea in competitive programming - dynamic programming - and some of my thought processes when I apply it to problems.

(This is Lucas.) Hi! In this post, I'm going to try and highlight a small but important part of my thought process when attempting Olympiad problems. 

(It's Glen again!) This post is going to be long, and as the title suggests, contain very many circles. Relatedly, most of the diagrams in here are hand-drawn and scanned because no way am I going to figure out how draw all of these diagrams on computer. You have been warned.

(Etienne here.) The date was 24 October 2021. It was late at night, and I was just about to tuck myself in. After all, the next day was the A-Level Physics practical! I needed to be well-rested (spoiler alert - I actually didn't). I was lying comfortably and about to bid a temporary farewell to the waking world, when suddenly, out of nowhere, I was attacked by a sudden thought: For what $r$ could I tile a square with rectangles whose sides had ratio $r$?

Hey! Choo Ray here. I've been involved in giving sessions for the SIMO National Team and other trainings recently, so naturally I have to hunt for suitable problems. I feel that I've been looking at more problems recently than I have in the lead-up to my participations in IMO/other competitions! Of course, I spend less time on each problem, as my objectives are geared towards discovering problems with good ideas and instructive value rather than solving them myself. However, sometimes I find myself being led down a long rabbit-hole of theory that I apparently ought to know about. In this post I'd like to share about one of these experiences. One day, I was browsing contest collections on Art Of Problem Solving (AoPS). A question from the 2020 Bulgarian National Olympiad caught my eye: P4. Are there positive integers $m>4$ and $n$, such that a) ${m \choose 3}=n^2$ b) ${m \choose 4}=n^2+9$ I clicked on the link, thinking that it seems a rather routine proble...

(This is Yan Sheng.) Today's blog post will be a change of pace from the usual contest math content: one day I was wondering to myself how many digits of $\sqrt2$ I could calculate by hand (who hasn't?). Math is more fun when you try stuff out for yourself, so here's some warm-up: