Ivan Wangsa C.L.’s Blog

Welcome to the jungle, Mr Liu. Hope you enjoy your stay in the wilderness, Indonesia.

*actually, what is this?*

I’ll explain in a few moment.

Yesterday, is just a day. Very very busy day. I would like to call it Hell-a-day, instead of Holiday.

The day before yesterday, I was told by my teacher to teach some students in a topic of Math Olympiad: The Extremal Principle, and The Invariant Principle.

Basically, my comment were just like this

I don’t master Invariant and Extremal, so why should I take the job?

But, at the end, I said, “Yes.”

So, basically, I haven’t prepared the resources for teaching, I haven’t prepared the handout, and fortunately, I can only prepare those things in the night. Damn.

And finally, I prepared all of them until 3 am. Yes, 3 am. And since my job’s started on 8 am, outside Jakarta, I must wake up at 5.30 am. Basically, I only got 2 and a half hours of sleep. Damn.

I must wake up at 5.30. It’s just crazy. After waking up, I brush my teeth and do anything else unconsciously. And after I get into the car, I sleep. Peacefully.

Because I finished preparing those things at 3 am, I can’t copy those handouts. So my teacher was copying those materials, while I waited in the class.

Almost 8 am, more than 20 attended my classes, and yet my teacher didn’t came because all of the photocopy centers were closed. Dammit. So I instructed all my students, for all of them who bring Arthur Engel’s book, Problem-Solving Strategies, please read it.

It’s about 8.05 am, when I think that my class was suspended to long (although it’s only 5 minutes), so, I started to teach. I remember my first words:

Hello, my name’s Ivan, and I’m going to teach you 2 basic principle in Mathematics Problem Solving.

Basically, there are 3 basic principle that could really help you solve some problems out there:

1. The Pigeonhole Principle
2. The Extremal Principle
3. The Invariant Principle

*underline number 2 and 3* so, I will teach you these 2 principles, Extremal and Invariant Principle. We’ll also use some pigeonhole principle, I’ll also teach the basics of pigeonhole principle, but let’s save the advanced topic of pigeonhole principle for some days later and focus on the last two topics.

The first thing is Extremal Principle. *explains the definition and how to use extremal principle* And so, let me begin by showing some problems involving Extremal Principle.

Given 2 sets of points, R and B, such that R contains all red points, and B contains all blue points. If there exist 2 points of same color, connected by a segment, then there exist a point lying on the segment with a different color. Show that R and B both lie on a line.

And after I showed the problem, my teacher comes. Thank God.

And the session continues. I explained all of them, while after 2 and a half hours, I finished both of the materials. I got 30 more minutes, and I got no idea. I asked my teacher, “Should I explain the third principle, Pigeonhole principle, or should I teach a more advanced topic of invariant?”

And I went with advanced topic of invariant. Saved pigeonhole for the last thing.

And I closed the session with the following problem involving monovariants:

Given n cards in a deck, each numbered with 1,2,…,n. I opened the first card, and let the number be k. Then, I reversed the first k cards, and repeat the same procedure, again and again. Prove that the process will halt (that is, if the first card is 1).

After I finished the session, some of us go to mall, to eat some foods. After that, we go to Puspiptek (Pusat Pengembangan Ilmu Pengetahuan dan Teknologi ; Science and Technology Research Center) to meet Mr. Andy Liu. Mr. Andy Liu is a world-class problem solver from Canada. He’s a genius. He writes most of the solution of the Tournament of Town’s book, and currently the vice-president of Tournament of Towns.

Welcome to the jungle, Mr. Andy Liu

But unfortunately, he teaches only the basic thing, which I already covered. Ah, I hope in some next time, he’ll teach us a more advanced topic, since his teaching style was quite cool.

And so, after teaching session with him, which ended at 5 am, we prepared to go to dinner with Prof. Andy Liu. And finally, I go home. Very tired. *sigh*

One of his problems is a cool one:

The Magician’s Trick.

The magician goes to the back of stage, he’s blindfolded, while his assistant chooses an audience; the audience then arranged a set of n coins, and the audience then chooses a number , such that . After that, the magician’s assistant flips a coin, and the magician summoned back to the stage. If the magician and his assistant had an agreement beforehand, could the magician guess the number ? And how?