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Putnam problem of the day

putnam problem
Each day, one of currently 612 different Putnam, national or international Olympiad problems is displayed here.

Putnam competition 2019

Please join to congratulate the Harvard's team for finishing second place in this year's Putnam competition. Harvard ranked second among the 570 participating institutions and Laura Pierson was named an Elizabeth Lowell Putnam Prize Winner, an award honoring the top-performing woman in the competition. See the MAA page.

Putnam competition 2018

Daniel Kim, David Stoner and Shyam Narayanan, Putnam Fellows, March/1/2019, Click on a picture to get a large 3200x2400 pixel version.
From the announcement:: There were 4,623 participants from 568 institutions in this competition on December 1, 2018. 2018 Top Five Putnam Teams:
  1. Harvard University
  2. Massachusetts Institute of Technology
  3. University of California, Los Angeles
  4. Columbia University
  5. Stanford University
2018 Putnam Fellows, listed in alphabetical order: Elizabeth Lowell Putnam Prize Winner is Danielle Wang, Massachusetts Institute of Technology.

Putnam competition 2017

The 78th Annual Putnam Exam took place on Saturday, December 2, 2017. Congratulations to Harvard's team for finishing second place in this year's Putnam competition. Special congratulations to David Stoner for being named a Putnam Fellow. Congratulations also to Ravi Jagadeesan and Dong Ryul Kim for being among the top 15 ranking individuals, and to George Han, Jacob Klegar, Shyam Narayanan and Stefan Spataru for honorable mentions. Results [PDF] The first five teams were:
  1. MIT
  2. Harvard
  3. Princeton
  4. University of Toronto
  5. University of California, LA

Putnam competition 2016

The 77th Annual Putnam Exam took place on Saturday, December 3, 2016. Please join in offering congratulations to our team members and outstanding individuals in this year's Putnam Competition. Special congratulations to Dong Ryul Kim for being a Putnam Fellow (a top-five finisher in the individual competition). Congratulations to Calvin Deng and Ravi Jagadeesen, Stefan Spataru, David Stoner and Scott Wu for being among the next 25 highest ranking individuals, and to Pakawut Jiradilok, Jacob J. Klegar, Jeffrey Yan and Shyam Narayanan for honorable mentions. In the team competition, Harvard's team came in 3rd overall. The first five teams were:
  1. Carnegie Mellon University
  2. Princeton
  3. Harvard
  4. MIT
  5. Stanford
Please congratulate our team members: Pakawut Jiradilok, Dong Ryul Kim, and David Stoner.

Putnam competition 2015

The 76th Annual Putnam Exam took place on Saturday, December 5, 2015. Congratulations to our team members and outstanding individuals in this year's Putnam Competition. Special congratulations to Pakawut Jiradilok for being a Putnam Fellow (a top six finisher in the individual competition) Congratulations to Calvin Deng, Dongryul Kim, Stefan Spataru, David Stoner, Xiaoyu He, Vikram Sundar and Scott Wu for being among the next 27 highest ranking individuals and to Noah Fechtor-Pradines, Ravi Jagadeesan, Shyam Narayanan, In the team competition, Harvard's team came in fifth overall and the first five teams were:
  1. MIT
  2. Carnegie Mellon
  3. Princeton University
  4. Stanford University
  5. Harvard
Please congratulate our team members, Calvin Deng, Ravi Jagadeesan and David Stoner.

Putnam competition 2014

The 75th Annual Putnam Exam took place on Saturday, December 6, 2014. Congratulations once again to our team members and outstanding individuals in this year's Putnam Competition!
Special congratulations to Ravi Jagadeesan (Freshman) for being a Putnam Fellow (a top-six finisher in the individual competition). Congratulations to Calvin Deng and Malcolm Granville for being among the next 27 highest ranking individuals, and to Evan Chen, Rahul Dalal, Octav Dragoi, Xiaoyu He, Pakawut Jiradilok, Aaron Landesman, Zihao Wang and Allen Yuan for honorable mentions. In the team competition, Harvard's team came in 2nd overall. The first five teams were:
  • MIT
  • Harvard
  • Rensselaer Polytechnic Institute
  • University of Waterloo
  • Carnegie Mellon University
Please congratulate our team members. Calvin Deng, Malcolm Granville, and Xiaoyu He.


Putnam competition 2013

The 74th Annual Putnam Exam took place on Saturday, December 7, 2013 The sign-up sheet is posted on the undergraduate bulletin board on the third floor Of the Science Center, in the Math Dept. opposite rooms 322 and 323. The deadline for signing up is October 4, 2013 The examination will consist of two, three hour sessions. There will be a two hour break between sessions. The Morning Session begins at 10:00 AM and ends at 1:00 PM The afternoon Session begins at 3:00 PM and ends at 6:00 PM.
Congratulations once again to our team members and outstanding individuals in this year's Putnam Competition! Special congratulations to Evan O'Dorney for being a Putnam Fellow (a top-five finisher in the individual competition) for the third straight year. Congratulations to Calvin Deng, Malcolm Granville and Xiaoyu He for being among the next 14 highest ranking individuals, and to Octav Dragoi, Pakawut Jiradilok, Aaron Landesman, David Liu, Toan D. Phan, Barry Tng and Jeffrey Yan for honoroable mentions. In the team competition, Harvard's team came in 4th overall. The first five teams were: 1. MIT 2. CMU 3. Stanford 4. Harvard 5. Caltech Please congratulate our team members, Evan O'Dorney, Octav Dragoi and Allen Yuan.


Putnam competition 2012

Congratulations once again to our team members and outstanding individuals in this year's Putnam Competition! Harvard's team came top (for the 29th time). The first five teams were: 1. Harvard 2. MIT 3. UCLA 4. Stony Brook 5. Carnegie-Mellon Please congratulate Eric Larson, Evan O'Dorney and Allen Yuan. Each receives $1,000, as members of the top-ranked team. Special congratulations to Eric Larson and Evan O'Dorney for being Putnam Fellows (top-five finishers in the individual competition, with an award of $2,500). This is the second year in which Evan has been a Putnam Fellow. Congratulations to Octav Dragoi for finishing amongst the next eleven individuals (for an award of $1,000), and to Xiaoyu He, Aleksandar Makelov and Allen Yuan for honorable mentions.


Media:
Photo 1 (3648x2736 px) (April 5, 2013)
Photo 2 (3648x2736 px) (April 5, 2013)
Photo 3 (3648x2736 px) (April 5, 2013)
Photo 4 (3648x2736 px) (April 5, 2013)

From left to right: Eric Larson, Evan O'Dorney and Allen Yuan.
(Click on thumbnail for large picture).


Putnam competition 2011


Alex Zhai, Eric Larson and Evan O'Dorney. (Click for large picture). 		Congratulations to our team members and outstanding individuals in this year's Putnam Competition. Harvard's team won for the 28th time. The first five teams were: Harvard, Carnegie Mellon, Caltech,Stanford, MIT. Please congratulate our team members, Eric Larson, Evan O'Dorney and Alex Zhai. Each receives $1000. Congratulations to Evan O'Dorney for being a Putnam Fellow (a top-five finisher, which carries an award of $2,500). Congratulations to Alex Zhai for finishing amongst the next 18 individuals (and an award of $250), and congratulations to Eric Larson and Allen Yuan for honorable mentions.

Putnam competition 2010

Congratulations to our team members and outstanding individuals in this year's Putnam Competition. Our team placed third (congratulations to Caltech and MIT this year), and we had outstanding individual results, with four students placed in the top 15. The top five teams were:
  1. Caltech
  2. MIT
  3. Harvard
  4. UC Berkeley
  5. U Waterloo
Please congratulate our team members, Kevin Lee, Arnav Tripathy and Alex Zhai. Each receives $600. Congratulations to Alex Zhai for being a Putnam Fellow (a top-five finisher, which carries an award of $2,500). Congratulations to Iurie Boreico, Eric Larson and Arnav Tripathy for being among the next ten highest ranking individuals (for a prize of $1000), and congratulations to Sherry Gong for an honorable mention. -Peter Kronheimer



The 71st Annual Putnam mathematical competition took place on December 4, 2010 in the Science Center, Hall C. All signed up students should come at 9:30 am to the Science Center. Students who have not signed up in advance are welcome also. We will have extra copies of the exam.

Saturday, December 4: Morning Session 10 AM - 1 PM Saturday, December 4: Afternoon Session 3 PM - 6 PM

Putnam competition 2009

The Putnam Mathematical Competition in 2009 took place on Saturday, December 5, 2009.

1. MASSACHUSETTS INSTITUTE OF TECHNOLOGY Qingchun Ren, Bohua Zhan, and Yufei Zhao
2. HARVARD UNIVERSITY Iurie Boreico, Arnav Tripathy, and Alex Zhai
3. CALIFORNIA INSTITUTE OF TECHNOLOGY Jason C. Bland, Sam Elder, and Gjergji Zaimi
4. STANFORD UNIVERSITY Young Hun Jung, Seok Hyeong Lee, and Jeffrey Wang
5. PRINCETON UNIVERSITY Peter Z. Diao, Adam C. Hesterberg, and John V. Pardon


Source and more details.

Putnam competition 2008

Zachary Abel, Arnav Tripathy and Iurie Boreico Zachary Abel, Arnav Tripathy and Iurie Boreico
The winning Putnam team: from left to right: Zachary Abel, Arnav Tripathy and Iurie Boreico Photo: April 1, 2009, Harvard University. Click to see a large version of the photo. The winning Putnam team: from left to right: Iurie Boreico, Zachary Abel and Arnav Tripathy Photo: April 1, 2009, Harvard University. Click to see a large version of the photo. See also AMS, news for students.
The Putnam Mathematical Competition in 2008 took place on Saturday, December 6. 2008. Harvard has won the Putnam competition yet again! Congratulations to our winning team members and outstanding individuals: Our winning team members, Zachary Abel, Iurie Boreico, and Arnav Tripathy, each receive $1000 for the team competition. The top five teams are: 1. Harvard, 2. Princeton, 3. MIT, 4. Stanford, 5. Caltech. Congratulations to Arnav Tripathy, for being among the five highest ranking individuals (a Putnam Fellow) for the second time. He receives a prize of $2,500. Congratulations to Iurie Boreico and freshman Alex Zhai for being among the next eleven highest ranking individuals (for a prize of $1000), and to Zachary Abel for being amongst the next nine. Honorable mentions go to Kevin Carde, Zhou Fan, Rosen Kralev, Yi Sun, Dmitry Vaintrob, Ameya Velinger and Neal Wadhwa. A total of 3627 students from 545 colleges in Canada and the United States participated in the competition. See the photos. Also the MCM competition results are now official. One of our teams: Yi Sun, Chris Chang and Zhou Fan, was one of the four outstanding teams, and was the SIAM prize recipient. Photos.


The Putnam problems of 2008 [HTML] and [PDF].

Putnam competition 2007

The Putnam Mathematical Competition in 2007 took place on Saturday, December 1. 2007. Congratulations to our winning team members and outstanding individuals: Harvard is once again top of the heap in the Putnam competition! Our winning team members, Tiankai Liu, Alison Miller and Zachary Abel, each receive $1000. The top five teams are: 1. Harvard, 2. Princeton, 3. MIT, 4. Stanford, 5. Duke. Congratulations to Arnav Tripathy, for being among the six highest ranking individuals (a Putnam Fellow), and receiving a prize of $2,500. Congratulations to Alison Miller, Tiankai Liu and Justin Bae for being among the next ten highest ranking individuals (for a prize of ). Alison is also the winner (for a third time!) of the Elizabeth Lowell Putnam Prize. Congratulations to Zachary Abel, Iurie Boreico, and Shrenik Shah for being amongst the next eight highest ranking individials; and congratulations to Zhou Fan, and Rishi Gupta for Honorable Mentions. A total of 3753 students from 516 colleges in Canada and the United States participated in the competition.


The Putnam problems of 2007 [HTML] and [PDF].

Putnam competition 2006

The Putnam Mathematical Competition in 2006 took place Saturday, December 2, 2006. Congratulations to our team members, and all who competed in the 2006 Putnam competition, for another outstanding performance. Harvard's Putnam team came in second, behind Princeton. Congratulations to: Tiankai Liu, Alison Miller and Tong Zhang. Each member of the team will receive $800.

The 5 winning teams were: 1. Princeton, 2. Harvard, 3. MIT, 4. U. Toronto, 5. U. Chicago Congratulations to Tiankai Liu, for being again among the five highest ranking individuals (a Putnam Fellow), and receiving a prize of $2,500. Congratulations to Alison Miller for being among the next ten highest ranking individuals (for a prize of $1000). Alison is also the winner (again!) of the Elizabeth Lowell Putnam Prize. 		Congratulations to Zachary Abel, Jae Bae, Jared Bass, Steven Byrnes, Charles Chen, Ben Conlee, Rishi Gupta, Daniel Jerison, Joel Lewis, Mark Lipson,, Dragos Michnea, Gregory Price, and Tong Zhang. They are among the Honorable Mention Individuals. A total of 3640 students from 508 colleges in Canada and the United States participated in the competition.

The Harvard Team are the winners in the 2007 Mathematical Contest in Modeling: The Harvard team (Ben Conlee, Abe Othman, and Chris Yetter) earned the award of Outstanding Winners on the 23rd annual Mathematical Contest in Modeling (MCM) "A" problem. This year 949 teams representing institutions from 12 countries participated in the contest. 351 teams worked on the Problem "A". They were asked to develop a model for "fairly" and "simply" determining congressional districts for a state.
The problems of 2006 [HTML] and [PDF].

Putnam competition 2005

Harvard is the winner of the Putnam Competition 2005. Congratulations to our team members Tiankai Liu, Alison Miller, and Tong Zhang.. Each member of the team will receive $1,000. The 5 winning teams are: Harvard, Princeton Duke MIT and Waterloo
Congratulations to the Ricky Liu and Tiankai Liu. They are among the six highest ranking individuals, and they will receive $2,500 each. Congratulations to Steven Byrnes and Alison Miller are among the next ten highest ranking individuals. They will receive $1,000 each. Alison Miller is a winner of Elizabeth Lowell Putnam Prize, and she will receive $1,000. Congratulations!. Congratulations to Jae Bae Joel Lewis, Tong Zhang and Yan Zhang. They are among Honorable Mention Individuals. 3545 students from 500 colleges in Canada and the United States participated in the competition. The results on our undergraduate bulletin boards. If you want to know your personal result, ask Svetlana.
We also have good news from the annual Mathematical Contest in Modeling (MCM) and the Interdisciplinary Contest in Modeling (ICM). Over 900 teams competed this year. The Harvard team of Christopher Yetter, Neal Gupta, and Benjamin Conlee was designated as Outstanding Winner SIAM Award.

Old Exams and links to Archives

Kiran Kedlaya's Putnam Archive

About the competition

William Lowell Putnam, Image source: math.scu.edu/putnam/ The Putnam competition annualy takes place in December. From the description:
The Putnam examination tests originality, technical competence and familiarity with the formal theories embodied in undergraduate mathematics. Questions cut across the bounds of various disciplines, and include self-contained questions that do not fit into any of the usual categories. These self-contained questions can involve elementary concepts from group theory, set theory, graph theory, lattice theory, number theory or cardinal arithmetic.

Results from the 2006 competition

The list of Winners is here

Results from the 2005 competition

The list of Winners is here

Results from the 2004 competition

The list of Winners is here

Results from the 2003 competition

The list of Winners here

Rank School Team Members (in alphabetical order)
1
 MIT Reid W. Barton, Daniel M. Kane and Yevgeny K. Zaytman
2 HARVARD UNIVERSITY Gabriel D. Carroll, George Lee, Jr., and Alexander B. Schwartz
3DUKE UNIVERSITY David G. Arthur, Nikifor C. Bliznashki and Oaz Nir
4 CALTECH Zhihao Liu, Po-Ru Loh and Po-Shen Loh
5 HARVEY MUDD COLLEGE David J. Gaebler, Jason Murcko and Andrew G. Niedermaier


RESULTS FROM the 2002 COMETITION

Winner list from here.

Rank School Team Members (in alphabetical order)
1
 HARVARD UNIVERSITY Gabriel D. Carroll, George Lee, Jr., and Alexander B. Schwartz
2 PRINCETON UNIVERSITY Stefan L. Hornet, Mihai Manea, and Radu H. Mihaescu
3DUKE UNIVERSITY David G. Arthur, Oaz Nir, and Melanie E. Wood
4 UNIVERSITY OF CALIFORNIA, BERKELEY Boris Bukh, James M. Merryfield, and Austin W. Shapiro
5 STANFORD UNIVERSITY Chee Hau Tan, Paul A. Valiant, and Daniel Wright

Results from the 2001 Competition

Winner list from www.unl.edu :
RankSchool Team Members (in alphabetical order)
1Harvard UniversityGabriel D. Carroll, George Lee, Jr., and Alexander B. Schwartz
2 Massachusetts Institute of TechnologyReid W. Barton, Abhinav Kumar, and Pavlo Pylyavskyy
3 Duke University David G. Arthur, Nathan G. Curtis, and Kevin D. Lacker
4 University of California, BerkeleyMaksim I. Maydanskiy, James M. Merryfield, and Austin W. Shapiro
5 Stanford University Kenneth K. Easwaran, Paul A. Valiant, and David T. Vickrey

Results from the 2000 competition

Winnerlist from www.unl.edu :
Rank School Team Members (in alphabetical order)
1 Duke University John J. Clyde, Jonathan G. Curtis, and Kevin D. Lacker
2 Massachusetts Institute of Technology Aram W. Harrow, Abhinav Kumar, and Ivan Petrakiev
3 Harvard University Lukasz Fidkowski, Davesh Maulik, and Christopher C. Mihelich
4 California Institute of Technology Kevin P. Costello, Christopher M. Hirata, and Michael Shulman
5 University of Toronto Jimmy Chui, Pavel T. Gyrya, and Pompiliu Manuel Zamfir

First place teams

A list of first place teams can be found here. The individual Putnam fellows since 1938 can be found on this website. The Harvard team won 29 times in the 73 competitions so far:

  • 7th,5/24/47
  • 9th,3/26/49
  • 13th,3/23/53
  • 15th,3/5/55
  • 16th,3/3/56
  • 17th,3/2/57
  • 19th,11/22/58
  • 26th,11/20/65
  • 27th,11/19/66
  • 43rd,12/4/82
  • 46th,12/7/85
  • 47th,12/6/86
  • 48th,12/5/87
  • 49th,12/3/88
  • 50th,12/2/89
  • 51st,12/1/90
  • 52nd,12/7/91
  • 53rd,12/5/92
  • 55th,12/3/94
  • 56th,12/2/95
  • 58th,12/6/97
  • 59th,12/5/98
  • 62th,12/1/01
  • 63th,12/7/02
  • 66th,12/3/05
  • 68th,12/1/07
  • 69th,12/6/08
  • 72th,12/3/11
  • 73th,12/1/12
Statistics starting 1938: Top five students (as of 2012 competition) 
Harvard 58
MIT     43
Caltech 32
First Place Teams (as of 2012 competition) 
29      Harvard
10      Caltech
6       MIT
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