Preparing for Olympiad Exam: Tips & Suggestions

[jobsism]

I had already posted an earlier thread, asking anyone if they could tell me whether a set of questions were high-level Olympiad questions, and whether I could prepare for such questions (for a certain examination) in 3 months.

However, this post is on a completely optimistic note; after looking at the ingenuity of the questions asked, and the fun in the math involved to solve them, I'm well damn determined to go to whatever extent to learn the math to solve such problems! :D

All I want to know now is whether my current preparation is sufficient; I'm currently studying from a book named "Mathematical Circles: A Russian Experience" by Dmitri Fomin, Sergey Genkin and Ilia Itenberg. The theory is easy to understand and the problems are intriguing. However, I'm still not at a level to solve the "high-level" ones (perhaps I will be able to, after completing the book). And I think the theory is a bit limited too. To have an idea of these "high-level" (atleast for me!) questions, here's a sample:-

1. Show that there are exactly 16 pairs of integers (x, y) such that 11x + 8y + 17 = xy.

2. A function g from a set X to itself satisfies g^m = g^n for positive integers m and n with m > n. Here g^n stands for g ◦ g ◦ · · · ◦ g (n times). Show that g is one-to-one if and only if g is onto.

3. Let a1, a2,...a100 be 100 positive integers. Show that for some m,n with 1<=m<=n<=100, ∑[i=m to n] a(subscript)i is divisible by 100.

4. In Triangle ABC, BE is a median, and O the mid-point of BE. The line joining A and O meets BC at D. Find the ratio AO : OD.

Are there any other beginner-level books, that cover most topics? I've already glanced at some of the famous ones like "Mathematical Olympiad Challenges" by Titu Andreescu, "The Art and Craft of Problem-Solving" by Paul Zeitz and "Problem-Solving Strategies" by Arthur Engel, but I don't feel comfortable using them.

Any other book suggestions/tips, anyone? Please help.

Thanks! :D

 

[disregardthat]

If you don't feel ready to start reading a problem solving book, find problems from less difficult competitions. You should be doing 99% problem solving, and 1% reading.

 

[5416339]

Looks like your preparing for CMI as well! Good luck !

 

[Bill Simpson]

In "Talent is Overrated, What REALLY separates World-Class Performers From Everybody Else" Geoff Colvin makes a very strong case for a method called "deliberate practice", which is very different from how most people "practice", and for finding a very qualified coach/trainer/tutor who can see your weaknesses much better than you can and who will work you mercilessly.

I should have/would have done that twenty years ago if I'd had the sense to realize it.

If anyone wants to dispute Colvin's argument then I'd love to see the evidence to back it up.

As I think I've written several times on these competition questions before, after listening to a couple of presentations by individuals who were long time graders and trainers for the Putnam, at least for the Putnam, being trained and coached by an individual who really understands what it takes to make the difference between getting one or two points versus getting almost full points on a problem... skilled coaching will make all the difference, assuming you have already developed an adequate skill set in problem solving.

If you want to score really really highly you should obviously go verify all this information with someone who is highly qualified.