Pawan’s Reviews > Problem Primer for the Olympiad > Status Update

I was excited about combinatorics because I wanted to try counting on a soroban. Of the problems that are application of Pigeon Hole Principle (79, 81, . . ., 98), my favourite was 86 because it combines trigonometry in a clever way. Problems such as 91, 97 can be answered directly without having to solve much. 83 is recursive combinatorics.

Scoring:
Combinatorics > Number Theory > Algebra > Geometry.

I need to pra

Getting the diagrams right enhances the ability to push through to a solution (problem 55, for instance).

Problem 57 is an application of Menelaus's and Ceva's theorem whereas Ptolemy's theorem is applied in 65. Drawing instrument box comes handy for problems 59 (and 60).

After a point I simply read through the solutions of some of the problems because I couldn't bear staring any longer.

Most of the problems require application of tricks, rearrangements or substitutions which makes looking for clues in the problem statement important. Few require a combination of theorems to reach the end result, whereas some problems such as 10, 11 (similar to 18) require none.

Problems 5, 20, 27, 30, 32, 37 could be solved in the head. I couldn't solve 9 and 17 or get the upper bound in 35 and 42 with aid.

My fav

Geometry has direct real world applications, and it is also the most dreaded (by me). Although the problems pertain to Euclidean geometry which is prevalent in architecture, I have found most use of differential geometry: machine learning (gradients), design (surfaces and 3d-modelling) and more.

Aiming for solving at least one in three without hints. I might want to share interesting problems.

It is important to disregard any presuppositions about the difficulty of the problems (especially those that are binned together) because one risks anchoring other problems with another difficult problem (which could not be solved), and they may not give enough thought to each subsequent problem before moving on or skipping the entire set.

Alright, I have come to a realisation that instead of memorising the toolkit (like I used to do before), deriving, to a certain extent, each of the mathematical assertions, likely expands intuition, and may improve success rate for coming up with solutions for the graded problems.