# The Putnam Exam

Are you a math nerd???? Check this out! The National William Lowell Putnam Exam will be held this Saturday, Dec. 3rd, from 10-1 and 3-6 p.m.  Six problems are posed in each session, for a total of 12 problems.  The modal score on the exam is 0 (out of 120), because the problems are hard, but fun.  There is always an elegant way to find the answer, even though it is not obvious at first glance.  The topics of the problems range over all kinds of math.

If you are interested in attending all or part of the exam, please let Karen Collins (kcollins(at)wesleyan(dot)edu) know!

Date:   Dec. 3
Time:   10:00 AM – 1:00 PM, 3:00 PM – 6:00 PM
Place:  Exley Science Tower 405

Follow the jump for examples of  Putnam problems:

A-2-2000 Prove that there exist infinitely many integers n such that n, n+1, n+2 are each the sum of two squares of integers.

A-1-1998 A right circular cone has base of radius 1 and height 3.  A cube is inscribed in the cone so that one face of the cube is contained in the base of the cone.  What is the side-length of the cube?

A-1-1994 Suppose that a sequence a(1), a(2), a(3), … satisfies 0 < a(n) <= a(2n) + a(2n+1) for all n >= 1.  Prove that the series Sum a(n) from n=1 to infinity diverges.

A-2-1991 Let A and B be different n x n matrices with real entries. If A^3 = B^3 and A^2B = B^2A, can A^2+B^2 be invertible?

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