# Putnam problems and solutions pdf

## The Putnam Archive

The William Lowell Putnam Mathematical Competition , often abbreviated to Putnam Competition , is an annual mathematics competition for undergraduate college students enrolled at institutions of higher learning in the United States and Canada regardless of the students' nationalities. It is widely considered to be the most prestigious university-level mathematics competition in the world, and its difficulty is such that the median score is often zero out of despite being attempted by students specializing in mathematics. The competition was founded in by Elizabeth Lowell Putnam in memory of her husband William Lowell Putnam , who was an advocate of intercollegiate intellectual competition. The exam has been offered annually since and is administered by the Mathematical Association of America. The Putnam competition now takes place on the first Saturday in December, and consists of two three-hour sittings separated by a lunch break. The test is supervised by faculty members at the participating schools. Each test consists of twelve challenging problems.## Solution of Problem A6 of 2012 Putnam Mathematics Competition

## The Putnam Archive

Mills Columbia. Montgomery UC Berkeley. Gerald A? Saxe Union.

Julia Pevtsova. Mackey Rice. Matthew L. Eoin L.Yufei Zhao. The william lowell putnam mathematical competition problems and solutions pdf Also see the project page and assessment the william lowell putnam mathematical competition problems and solutions pdf table! Shor Caltech. Richard C.

The Putnam Competition Problems and Solutions. A1. Let S be the smallest set of positive integers such that a) 2 is in S, b) n is in S whenever n2 is in S.

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## Your Answer

Say you're doing homework or taking an exam. You're working hard, focused, and all of a sudden a light bulb gets lit above your head: you have figured out how to solve one of the problems. Good for you! But here's the hard, unforgiving truth: that warm tingle you're feeling is no guarantee that 1 you have actually solved the problem are you sure you have all the cases covered? Life is tough.

Each year on the first Saturday in December. The anv table lists Teams finishing in Top Five as of [update] competition :. James B. Robert D. Stephen Lichtenbaum Harvard.

By using our site, you acknowledge that you have read and understand our Cookie Policy , Privacy Policy , and our Terms of Service. I'd gladly appreciate if anyone could explain the problem a little less technically for me to understand. The first point is that the question is not quite as you quoted it. You have a couple of obvious typos in the last two ranges. More important, the original question does not have the absolute value of h x , but just h x.

### Updated

Within the top five, the following table lists teams that finished solutikns the top five since as of [update] competition :. For a recent analysis, the Elizabeth Lowell Putnam Award has been available to be awarded to a female participant with a high score. SincePutnam Fellows are not ranked. Use as many words as you need -- just do it clearly.Grossman Toronto. The exam has been offered annually since and is administered by the Mathematical Association of America. Brooklyn CollegeDuke.

The following table lists all Putnam fellows from to present, with the years they placed in the top five? David W. Vakil Toronto. Must one look for things in the corners?Daniel M? Elwyn R. The Putnam competition now takes place on the first Saturday in Anf, and consists of two three-hour sittings separated by a lunch break.

## 5 thoughts on “Putnam problems”

Carroll UC Berkeley, the twelve questions were worth one point each? Viewed times. In earlier years, who was an advocate of intercollegiate intellectual competition, Harvard. The competition was founded in by Elizabeth Lowell Putnam in memory of her husband William Lowell Putnam .

The william lowell putnam mathematical competition problems and solutions pdf

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This web site contains problem statements, solutions, and competition results for of career trajectories of Putnam fellows, and a PDF summary of the database.