Putnam vs USAMO

The 2009 Putnam competition was in December 2009, and the results came out a few weeks ago. My score on the Putnam was much higher than my score on USAMO from April 2009, but I know I hadn’t improved much in contest math in the eight months between the USAMO and the Putnam; this increase in score is due primarily to the different formats of the tests. This leads to some interesting questions.

First, an overview of the differences between USAMO and Putnam. The USAMO is a 9 hour exam with 6 problems; that comes out to 90 minutes per problem. The Putnam, on the other hand, is a 6 hour exam with 12 problems, for 30 minutes per problem on average. The topics covered on USAMO and Putnam are similar, with only one major difference: geometry on USAMO is replaced by calculus and linear algebra on Putnam.

It seems that Putnam problems are more straightforward and more approachable. Since there are only 30 minutes per problem, each problem can usually be solved by one insight or one trick. USAMO problems, however, often require a series of insights. In the end, Putnam is more about being clever and writing solutions carefully, while USAMO is more about solving difficult problems. That’s not to say that USAMO is harder than Putnam; they are simply different. Some people are better at quickly finding clever tricks, while others are more persistent.

This difference is interesting because high school mathematics is usually thought of as the domain of clever trickery and quick problems, while college mathematics usually has harder problems that require more persistence — approaching the types of problems seen in research. I suppose that this seemingly contradictory difference in USAMO and Putnam is a result of tradition and not of conscious choice.

Another item of interest in USAMO and Putnam are the median scores. The median score on the 2009 USAMO is 4/42, while the median score on the 2009 Putnam is 2/120. By that measure, the Putnam seems to be even harder than USAMO despite the arguments above for why the Putnam should be more approachable. However, that’s not quite true. The USAMO in 2009 selected the top 500 students from AMC and AIME to take the test, so USAMO participants are already highly filtered. If it were opened to everyone, the number of people taking USAMO would be in the thousands and the median would be much lower, probably 0. This is in fact what happens to the Putnam: 4000 people took the 2009 Putnam, and 43% scored zero. Indeed, the median for the top 500 on Putnam is around 30/120, much higher than the median for USAMO.

So what do my Putnam score and USAMO score say about the way I think about math? It appears that I’m better at solving easier problems quickly than at working through hard problems (especially given the time limit of USAMO). Another possible explanation is that I’m much better at calculus than at geometry; I couldn’t solve 2009 USAMO Problem 1, but I could solve 2009 Putnam A2.

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3 responses to “Putnam vs USAMO

  1. Math March 19, 2012 at 5:25 pm

    HI, I am in fort wayne and I want to do the Putnam competition but I don’t know where to go for the registration.

  2. Silkjbcxx April 15, 2014 at 11:55 am

    In college, no one really cares about the Putnam because the problems in math classes are much deeper. ( Putnam covers really low level topics from a college math perspective if you think about it)

    Frankly, I don’t think you can draw any reasonable conclusion from comparing your Putnam score with your usamo score and there’s just so many variables to factor in. Putnam is not even remotely as important in college as usamo was in high school.

  3. The Ram March 13, 2015 at 1:41 pm

    Seems like academic mathematics attracts two types of students: theoreticians and problem solvers. The theoreticians are probably more successful on average at obtaining PhD’s, whereas the problem solvers either become world-class mathematicians or crash & burn as undergrads. I’d say that success on the Putnam or USAMO is directly related to problem solving ability (ie, I’m sure the great problem solver Paul Erdos would have done outstanding on those tests), but among USAMO qualifiers and the top Putnam finishers who are pursuing careers in math, it’s probably impossible to say which ones of those will become excellent mathematicians and which ones will prematurely burn out. And on the other side of the coin, I’d say those tests say next to nothing about a student’s theoretical potential. This is all my personal conjecture, of course…

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