Mathletes’ Greatest Secrets Finally Revealed Episode 5: Philippine Mathematical Olympiad

Mathletes’ Greatest Secrets Finally Revealed

Episode 5: Philippine Mathematical Olympiad
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Henry

Image Credit: "weird pi sculpture at the lavender farm" by Brian Ellin. Licensed under CC BY-NC-SA 2.0.

The letter pi is a apt motif that recurs in each yearly iteration of the PMO logo.

The Philippine Mathematical Olympiad is the premier mathematics contest for high school students in the country. Among the contests and programs we’ve discussed, only this one bears the legitimacy of being the country’s national Olympiad.

Format

The screening round is a multiple choice test. The catch is, one must shade one’s answers in ink; answers can still be changed by crossing the shade out (papers will be marked manually), but there’s no returning to a crossed-out answer. The top fifty scorers per area (the areas are NCR, Luzon, Visayas, and Mindanao) will be taken to the area Finals.

This, on the other hand, is a sit-down test with eighteen short answer questions and three full solution questions. The top twenty scorers overall, regardless of area, will be taken to the finals. The top three per area will be awarded on the evening of the finals, whether or not they are themselves among the national top twenty.

The national top twenty, regardless of their performance in the finals, will be invited to train under MOSC.

Preparation

The screening and area stages will be somewhat similar to AMC12/AIME; they will be at most pre-Olympiad in difficulty.

For the actual Olympiad portion, after you’ve done the previous PMOs, you’ll find it useful to do national Olympiads from countries that have roughly the same difficulty level as PMO (Canada and India, for example.) National Olympiads vary greatly in difficulty, so to be productive it’s important to practice at one’s own level.

If you’ve made it this far, chances are you’d be interested in continuing to IMO, so it’s prudent to begin training at that level. Personally I’ve found it unproductive to immediately train with an Olympiad problem in an unfamiliar topic (e.g. spiral similarities). It pays to study the topic itself at length, attempting many pre-Olympiad problems before trying the actual Olympiad question. It rarely pays to shove oneself into the deep end and surface empty-handed after a few hours. That being said, when in a contest and faced with an unfamiliar topic, don’t be afraid to give it everything at your disposal.

Resources

Good texts to start off would be Bautista and Garces’ Mathematical Excursions: A Problem-Solving Primer for Trainers and Olympiad Enthusiasts, along with Zeitz’ The Art and Craft of Problem Solving. The former is readily available locally and is patterned after the MOSC (see my next post) topics of the time. The latter is, in style and difficulty, a spiritual successor to Lehoczky and Rusczyk’s Art of Problem Solving.

Another indispensable resource is The IMO Compendium, but be aware that it’s a compilation, not a guided text (though the second chapter is an indispensable resource). Let’s also not forget Engel’s Problem Solving Strategies. For websites, there’s the forums at Art of Problem Solving, and high-quality resources at imomath.com.

Math professors who have conducted training may post the handouts on their websites; they’re worth a look for skills on specific topics.

As you may have probably noticed, unlike problems at intermediate and basic levels (where speed and accuracy are 'core' skills), it's pretty useless to drill the same kinds of problem again and again. At this level, once you have seen how to solve the problem, you cannot unsee it -- you may forget the approach after some time, but you will never recover the sense of seeing the problem fresh for the first time. This means it's not a good idea to 'waste' problems by directly looking at the solutions. That is no different from burning money.

Tips

Expect the unexpected.

Encountering rehashed questions is a guilty pleasure for most of us, but don’t expect that here. (In fact, don’t rely on rehashing anywhere. Being a problem-memorizer insults the art and craft.) This applies especially to the written round. Most of the content is either original, or adapted from material not yet publicly released.

Have a good gauge of difficulty.

Just because problems are out-of-this-world doesn't make it pointless to look at past year questions, both for the Written and Oral rounds. As mentioned above, there really is no dearth of resources in that area.
There's another good reason to do practice runs on complete problem sets - you sharpen your sense of how difficult a problem is, and know when it's time to bail. This is an important tool when torn between forging ahead to Question #3, or investing more time into Question #2.

Just really solve the problems already.

Someone once told me something along these lines: you can read the solutions to ten problems, it won't be a better use of your time than completely solving one by yourself.

Answer with a haiku, guess with a novel.

This is for questions requiring solutions. If you can solve a problem completely, streamline – you reduce your chances of making minor errors. If you can’t, write lots of clever observations – with any luck you’ll hit something worth partial credit.

Brush up on your trivia.

The last question of the first oral round is by tradition a trivia question (i.e. Notable mathematicians, Fields Medal winners, where the IMO is being held). It’s not worth too many points, but getting it right is an ego boost!