Another USAMO tip

by rrusczyk, Jun 17, 2006, 3:21 PM

Put down your pencil (or pen). One of my favorite tactics when working one-on-one with a student in person is to take away his/her pencil when they're stuck on a problem. This is particularly important on the USAMO. You're swimming in oceans of time on the USAMO - take the time to put the pencil down and think. Don't be afraid to go for a walk. Conversely, don't get stuck staring into space the whole time, either - at some point you have to do something. But most people err by doing too much and thinking too little rather than thinking too much and doing too little.

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Besides computations/algebra, what should we be writing down?

Also, what do you think people should try to do when they have around 1.5 to 2 hours left, and they haven't solved #2--go on to #3 or keep going for #2?

by probability1.01, Jun 17, 2006, 3:22 PM

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probability1.01 wrote:

Other things to write: If you have a random idea while working on something else, write the idea down and come back to it. Write down things that, if proven, will finish the problem for you (especially important in geometry problem - usually I keep a forwards and a backwards list separately). Draw lots of pictures (precisely) for geometry problems. Write a brief outline of your proof before writing it up.

For your time management question, you should have read all three problems much earlier. After knocking off #1, you might spend 5-10 minutes brainstorming on each of #2 and #3 (something else for you to write), so the back of your mind works on one problem while the front works on the other. If you're dreadfully stuck on the one with an hour left, I'd switch, particularly if I had any good ideas at all on the other during brainstorming.

by rrusczyk, Jun 17, 2006, 3:22 PM

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Agreed about putting down your writing utensil!

I've found that the bulk of the USAMO is just thinking, and then once you've thought enough, you come up with the solution. Geometry problems might be the exception. I actually tended to use very little scratch paper during the exam; for trying out crazy ideas, test cases, and the like, I used a whiteboard. Last year, I think I only used a couple of sheets of actual scratch paper, not counting rough drafts of solutions.

Also, if you're not gunning for MOP or anything, and rather just trying to get points, I highly recommend doing drafts of your proofs if you have time (which you probably do). Although if you're planning on solving more than one problem each day, this is probably not a good use of time.

by Sly Si, Jun 17, 2006, 3:22 PM

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Have you ever had a situation in school on a math test where you get a problem wrong, but you are sure it is right, and you are sure the teacher made a mistake? Then you go up to her desk, talk her through the problem, and see that you were wrong after all. However, doing written work, you never noticed the flaw in your solution. Talking out a problem is another strategy I find extremely helpful.

by mysmartmouth, Jun 17, 2006, 3:22 PM