SIMO Retiree Blog

(Choo Ray here.) I thought it may be a good idea to write about some of the more interesting problems that I have used in my recent sessions for students in the Singapore National Team.

(Yu Peng here) Sometimes, you feel like you should be on the right track in solving a problem, but your solution falls short a little, due to issues like having a suboptimal bound, or having a condition you need but isn't true. At other times, you could just be struggling to find the optimal construction. At such times, it would often do you good to take a step back, and think about how you can optimise your solution.

(David here.) I'm going to explore various versions of an idea, starting from where I first saw it in Olympiads, and going beyond.

(Yu Peng here) I'll be going through a pretty cool concept in graph theory: flows! I'll start off by explaining what a flow network is, then go on to demonstrate how we can make use of flows to easily prove some theorems in graph theory, for example, Hall's Marriage Theorem. Finally, we'll look at an olympiad problem.