Difficulty of the Putnam compare to the IMO

原文链接：

https://www.quora.com/How-does-the-difficulty-of-the-Putnam-compare-to-the-IMO?

www.quora.com

Shuai Ye, Finance PhD student, Cornell University

It』s harder to score a perfect score on Putnam, but as for the difficulties of the problems, I have to disagree with Akaki and say IMO is harder on average.

Putnam is done in 2 three-hour sessions in a day, with 6 problems in each session. The first 2 problems of each sessions are usually give-away questions that can be done in 10 minutes each. A competent participant would have a fair shot at problem 3–4 if he/she is familiar with the topic, and problem 5–6 of Putnam is usually around mid (and sometimes high) difficulty level of IMO. One interesting feature of Putnam problems is that they can usually be solved in just a few lines of writing. They are usually trick questions that only require you to be clever once to be able to solve.

On the other hand, IMO is done in 2 days, with 3 problems each in 4.5 hour sessions. IMO problems are often quite deep and require very long solutions (esp. the number theory questions). On the positive side, you have much more time to solve each problem.

You asked if IMO6 is the same difficulty of B6 on Putnam. I would say if you allow the same amount of time to solve each, then IMO6 is for sure harder. But you usually have much less time in Putnam because you want to get all the points from previous problems. Easy problems count just as much as the last difficult problem, and you easily get in top 25 by solving just 9 problems in total (see this for historical high scores) so there is not that much incentive for contestants to go for the A6 and B6 problems.

What makes it hard to get a high score in Putnam is that it requires a much broader knowledge of math than IMO. The format of IMO is pretty fixed. You know there will usually be 1 geometry, 1 inequality, 1 number theory, 1–2 algebra questions so you can prepare specifically for these topics. Putnam questions can be quite wild, and it』s hard for a freshman or sophomore to know all the areas of college math topics.

Akaki Margvelashvili, works at Google

Putnam is harder.

I have done IMO 3 times and Putnam once. So I think I am qualified enough to answer.

Here are the major differences:

The most significant difference is that Putnam requires some expertise in college level math while at IMO sometimes the hardest problems can be solved with only middle school math.
Timing also makes a lots of difference. Putnam has twice more problems than IMO has to be solved in 2/3 of IMOs time (3 hours compared to 4.5). Its worth noting that first 2 problems of each contest (there are 2 contests each with 6 problems) are relatively easier than the easiest problem at IMO not taking too much time.
The last 2 problems of each contest of Putnam tend to be tough being as challenging as 3rd/6th problem of IMO. This makes Putnam extremely hard to nail even for the ones who have gotten top scores at IMO.
Finally, pool of students taking the exams are extremely different. IMO participants already are one of the best math guys in their countries while an only requirement of taking Putnam exam is being an US college student. This makes Putnam exam takers to be very diverse having some students getting 110+/120 (usually old IMO 40+s) when an average score is around 2/120 every year.

Putnam is also tougher psychologically - puts you on the ground. At IMO you can get a medal if you make into the first half of the participants while at Putnam maximum 15-20 students are awarded while only top 5 scorers get well published. Thus, if you work hard for Putnam in college and make in top 10-20 (among all US college kids), you still have a feeling of not accomplishing anything great while analogous result would guarantee you the high Gold at IMO. Thats why lots of my IMO friends are not motivated not only to work, but also even to take the Putnam exam.

So although Putnam is harder than IMO (and by no means Ive nailed IMO), I personally take Putnam when I can because it is fun, lets me check problem-solving skills and most importantly, reminds me the old days.

评论：

Putnam:本科生。难度跨度很大。差异性大，技术性强，观赏性中。较为片段化。偏向于纯数学。

IMO:高中生。难度跨度较大。差异性中，技术性中，观赏性强。较为整体化。偏向于应用数学。

如果说绝对难题的话，Putnam的某几届的5或6（一个简单地标志性的标记是7分以上人数为0）相对于历届IMO的3和6的难度而言是碾压级的。但是，Putnam有更多异常简单的题目。