Beginning Olympiad Mathematics

If you've ever looked through anything remotely Olympiad-ish, you might have been one of three types of people:

  1. People who say "This looks pretty simple..."
  2. People who say "This is waaaaaay too hard!"
  3. People who go from saying the first, to saying the second, then never touching another problem again.

If you're in the first group, good on you! Maybe this post will be too simple for you. If you're in the second or third groups, this post is for you. We want to stop you from running away and actually giving it a fair shot!

Here's a question:

You have three opaque boxes on a table. It is known that one of them contains two white balls, another has two black balls, and the last has one black and one white ball. The boxes have labels "2 white", "black and white", and "2 black", but you know that the muppet who put them on got them ALL wrong (so none of the boxes have the right label on them!). You are allowed to pick just one ball (without looking) from one of the boxes. Can you work out which boxes should have which labels?

It looks like a lot of reading and, if you're like me (the person who edited Natalia's post), you might not get it the first time. But read it again until you get it! Draw a picture too (I did)! Give it your best shot, and on the next instructional post, we'll go over the solution.

Ok, now for a crash course in Maths Olympiad (Molympiad). We can roughly divide everything we do into four sections:

  • Geometry (circles, triangles and shape stuff)
  • Algebra (inequalities, finding variables...)
  • Number Theory (divisibility, breaking the confines of society)
  • Combinatorics (everything we're too lazy to sort)

Even though each section is pretty distinctive, there's often some crossover between them. Over the next few months, we'll go over different tools you might find useful for these topics. Just FYI, the problem above was a combinatorics question.

People ask me whether Molympiad is closer to Calculus or Statistics. It's actually neither. The further you go into Molympiad, the more you realise that calculus is frowned upon and that statistics is completely irrelevant. Molympiad is just pure logic using cool tools (and barely any arithmetic), meaning that anyone can be good at it!

I hope I've given you a peek into this massive area of maths. If you want another question to chew on, here's another combinatorics question:

Two friends, Ann and Bill, are shown three pieces of paper, two pieces have the number 1 on it, and one piece has the number 2 on it. One piece is now attached to Ann's back and one to Bill's back; both Ann and Bill have the number 1 on their backs, and the piece with number 2 is hidden. Each person can see the other's number but not their own number, and neither Ann nor Bill know what we put on their back and which number we hid. Assuming that both the contestants are good at problem solving, can one of them be the first to deduce logically (not guess) what number is on his/her back?