## MATH PROBLEM SOLVING WEB PAGE

Web page for the Northwestern University Math Problem Solving Group.

### Goals

1. Acquire basic math problem solving skills.
2. Help in training future candidates for the yearly Putnam Competition.

### Activities

1. Solve math problems proposed in magazines like Math Horizons, College Mathematics Journal and the Mathematics Magazine. Ideally we should solve at least one problem from each issue.
2. Discuss solutions to problems and study mathematical subjects related to problem solving.

Unless otherwise stated, the level of the problems and results shown here should be undergraduate.

### Announcements

(There are no announcements at this moment.)

### MathPSG Emailing List

Subscribe to the Math Problem Solving Group emailing list by sending an email to listserv@listserv.it.northwestern.edu with the following line in its body:
subscribe MathPSG Your Name


Alternatively, please click in one of the following links, depending on whether you want to

Clicking on one of those links will fire up the mail program associated to your browser with the appropriate command for the listserver already typed in. Note however that if your choice is to subscribe MathPSG, you must add your name at the end of the line "subscribe MathPSG", otherwise the listserver will reply with an error message saying that the name is missing.

Note: Problems from magazines discussed and solved in the MathPSG emailing list may be submitted to the magazines in the name of the Northwestern University Math Problem Solving Group.

The MathPSG emailing list is moderated. Postings sent to the list will not be automatically forwarded to its members, they must await approval by the moderator.

### How the group works

The Math PSG works on problems proposed by various math magazines (see below), and submits solutions to the magazines. The process works like this:
1. Pick a problem not yet solved by the group, and for which the deadline for submission has not arrived yet.
2. If you solve the problem, you can post your solution sending it by email to
MathPSG@listserv.it.northwestern.edu
or mailing it directly to the group coordinator. If you want to give a chance the other members of the group to think the problem too, instead of a complete solution you may post only some hints first.
3. Some discussion of the solution may follow. After the solution is considered correct, and if nobody has anything to add, the coordinator will write a final version and submit it to the magazine in behalf of the group. If there is some discussion, or more that one solution posted, the coordinator will try to compose a "combined solution" with the different contributions.
Problems solved by the group and submitted to a magazine appear below in the column "submitted solutions".

### Proposed Problems

These are problems proposed in magazines like Math Horizons, College Mathematics Journal, the Mathematics Magazine, Pi Mu Epsilon Journal, and Harvard College Mathematics Review. Ideally we should try to solve at least one problem from each issue and submit it to the magazine before the deadline.

Note: Downloading the lists of proposed problems requires authentication by password. I will distribute periodically the necessary username and password among the members of the Math Problem Solving Group. If you are a member of the group and have forgotten the password, let me know at MATHPSG-request@listserv.it.northwestern.edu.

- 2013 -
Math Horizons, Vol. 20, No. 2, Nov 2012 January 11, 2013 283
College Mathematics Journal, Vol. 43, No. 5, Nov 2012 February 15, 2013 990
Mathematics Magazine, Vol. 85, No. 4, Oct 2012 March 1, 2013 1901
Pi Mu Epsilon Journal, Fall 2012 (external link) March 1, 2013 1266, 1267
College Mathematics Journal, Vol. 44, No. 1, Jan 2013 April 15, 2013 993, 995
Mathematics Magazine, Vol. 85, No. 5, Dec 2012 May 1, 2013 1909
Math Horizons, Vol. 20, No. 3, Feb 2013 May 31, 2013 286, 289
College Mathematics Journal, Vol. 44, No. 2, Mar 2013 June 15, 2013 1000
Mathematics Magazine, Vol. 86, No. 1, Feb 2013 July 1, 2013 1912
Math Horizons, Vol. 20, No. 4, Apr 2013 August 10th, 2013 293
College Mathematics Journal, Vol. 44, No. 3, May 2013 Aug 15th, 2013 1004
Mathematics Magazine, Vol. 86, No. 2, Apr 2013 September 1, 2013 1919
Pi Mu Epsilon Journal, Spring 2013 (external link) October 1, 2013 1282
Mathematics Magazine, Vol. 86, No. 3, Jun 2013 November 1, 2013 1921
Math Horizons, Vol. 21, No. 1, Sep 2013 November 9th, 2013 295
College Mathematics Journal, Vol. 44, No. 4, Sep 2013 Dec 15th, 2013 1009
- 2014 -
Math Horizons, Vol. 21, No. 2, Nov 2013 January 11th, 2014 299
College Mathematics Journal, Vol. 44, No. 5, Nov 2013 Feb 15th, 2014 1011
Mathematics Magazine, Vol. 86, No. 4, Oct 2013 March 1, 2013 1926, 1927
College Mathematics Journal, Vol. 45, No. 1, Jan 2014 April 15th, 2014 1016, 1017
Mathematics Magazine, Vol. 86, No. 5, Dec 2013 May 1, 2014 1933
Math Horizons, Vol. 21, No. 3, Feb 2014 May 31st, 2014 305
College Mathematics Journal, Vol. 45, No. 2, Mar 2014 June 15th, 2014 1025
Mathematics Magazine, Vol. 87, No. 1, Feb 2014 July 1, 2014 1936
Math Horizons, Vol. 21, No. 4, Apr 2014 August 10th, 2014 309
College Mathematics Journal, Vol. 45, No. 3, May 2014 August 15th, 2014 1030
Mathematics Magazine, Vol. 87, No. 2, Apr 2014 September 1, 2014 1942
Mathematics Magazine, Vol. 87, No. 3, June 2014 November 1, 2014 1947
Math Horizons, Vol. 22, No. 1, Sep 2014 November 9th, 2014 312
College Mathematics Journal, Vol. 45, No. 4, Sep 2014 December 15th, 2014 1032
- 2015 -
Math Horizons, Vol. 22, No. 2, Nov 2014 January 11th, 2015 315
Mathematics Magazine, Vol. 87, No. 4, October 2014 March 1, 2015 1951, 1952, 1954
College Mathematics Journal, Vol. 45, No. 5, Nov 2014 April 15th, 2015 1039
Mathematics Magazine, Vol. 87, No. 5, December 2014 May 1, 2015 1956, 1957, 1958
Math Horizons, Vol. 22, No. 3, February 2015 May 31st, 2015 318, 321
Math Horizons, Vol. 22, No. 4, April 2015 Aug 10th, 2015 322

(*) Color red means that the solution submitted by us was selected for publication.

### Problems for the Brave

Problems from magazines like the American Mathematical Monthly are traditionally (but not always) harder than the ones proposed in the magazines mentioned above. I am including them here just in case someone wants to try them.

- 2013 -
American Mathematical Monthly, Vol. 119, No. 8, Oct 2012 February 28, 2013
American Mathematical Monthly, Vol. 119, No. 9, Nov 2012 March 31, 2013 11670
American Mathematical Monthly, Vol. 119, No. 10, Dec 2012 April 30, 2013
American Mathematical Monthly, Vol. 120, No. 1, Jan 2013 May 31, 2013
American Mathematical Monthly, Vol. 120, No. 2, Feb 2013 Jun 30, 2013
American Mathematical Monthly, Vol. 120, No. 4, Apr 2013 Aug 31, 2013
American Mathematical Monthly, Vol. 120, No. 5, May 2013 Sep 30, 2013
American Mathematical Monthly, Vol. 120, No. 6, Jun 2013 Sep 30, 2013
American Mathematical Monthly, Vol. 120, No. 7, Aug 2013 Nov 30, 2013
- 2014 -
American Mathematical Monthly, Vol. 120, No. 8, Sep 2013 Feb 28, 2014
American Mathematical Monthly, Vol. 120, No. 9, Nov 2013 Mar 31, 2014 11739
American Mathematical Monthly, Vol. 120, No. 10, Dec 2013 Apr 30, 2014
American Mathematical Monthly, Vol. 121, No. 1, Jan 2014 May 31, 2014
American Mathematical Monthly, Vol. 121, No. 2, Feb 2014 June 30, 2014
American Mathematical Monthly, Vol. 121, No. 3, Mar 2014 July 31, 2014
American Mathematical Monthly, Vol. 121, No. 4, Apr 2014 August 31, 2014
American Mathematical Monthly, Vol. 121, No. 5, May 2014 September 30, 2014
American Mathematical Monthly, Vol. 121, No. 6, Jun 2014 October 31, 2014
American Mathematical Monthly, Vol. 121, No. 7, Aug 2014 December 31, 2014
American Mathematical Monthly, Vol. 121, No. 8, Oct 2014 February 28, 2015 11800
American Mathematical Monthly, Vol. 121, No. 10, Dec 2014 April 30, 2015
American Mathematical Monthly, Vol. 122, No. 1, Jan 2011 May 31, 2015

(*) Color red means that the solution submitted by us was selected for publication.

### Lists of problems

Collections and archives with math problems (and some solutions).

### Mathematical Results

These are common mathematical results that can be used in the resolution of math problems.

### Solved problems

This is a collection of solutions to some problems.

### Bibliography

• G. Alexanderson et al.: The William Lowell Putnam Mathematical Competition problems and solutions: 1965-1984, The Mathematical Association of America, Washington, D.C., 1985.
• W. W. Rouse Ball and H.S.M. Coxeter: Mathematical Recreations and Essays (13th edition), Dover Publications, 1987.
• Benjamin Bold: Famous Problems of Geometry and How to Solve Them, Dover Publications, 1969.
• Heinrich Dorrie: 100 Great Problems of Elementary Mathematics, Dover Publications, 1989.
• Arthur Engel: Problem-Solving Strategies, Springer, 1998.
• Gelfand, Gerver, Kirillov, Konstantinov and Kushnirenko: Sequences, Combinations, Limits, Dover Publications, 1969.
• A.M. Gleason et al.: The William Lowell Putnam Mathematical Competition problems and solutions: 1938-1964, The Mathematical Association of America, Washington, D.C., 1980.
• Kedlaya, Poonen and Vakil: The William Lowell Putnam Mathematical Competition 1985-2000: Problems, Solutions and Commentary, The Mathematical Association of America, Washington, D.C., 2002.
• Kenneth Hardy and Kenneth S. Williams: The Green Book of Mathematical Problems, Dover Publications, Inc., 1997.
• Kenneth Hardy and Kenneth S. Williams: The Red Book of Mathematical Problems, Dover Publications, Inc., 1996.
• Frederick Mosteller: Fifty Challenging Problems in Probability with Solutions, Dover Publications, 1965.
• Donald J. Newman: A Problem Seminar, Springer, problem books in mathematics, 1982.
• G. Polya: How to Solve It, 2nd ed., Princeton University Press, 1957.
• Alfred S. Posamentier, Charles T. Salkind: Challenging Problems in Algebra, Dover Publications, 1988.
• Alfred S. Posamentier, Charles T. Salkind: Challenging Problems in Geometry, Dover Publications, 1988.
• D. O. Shklarsky, N. N. Chentzov, I. M. Yaglom: The USSR Olympiad Problem Book: Selected Problems and Theorems of Elementary Mathematics, Dover Publications, 1993.
• Hugo Steinhaus: One Hundred Problems in Elementary Mathematics, Dover Publications, 1979.
• Wayne A. Wickelgren: How to Solve Mathematical Problems, Dover Publications, 1995.