Our Mission

Princeton Math Circle is a weekly program for the high school and the middle school students of Princeton and its surrounding communities. It meets on Saturdays from 1:00 pm to 4:00 pm on the Princeton University campus. 

The program is sponsored by the members of the Princeton University. Its mission is to:

• inspire, encourage and excite young students about mathematics,
  
• build a stronger foundation in math for success in their future careers, and
  
• prepare them to compete for American Mathematics Competitions (AMC 8/10/12), US Math Olympiad and International Math Olympiad Championships.

Registration for the Fall 2010  session of the Princeton Math Circle will start  in August (for new students only). Our former students need not re-apply. Please see the Contact Us section for more details.

Typical Math Quiz Problems (for Olympiads)

 Problem 1
Let a1, a2, a3, ..., an be distinct positive integers and let M be a set of n - 1 positive integers not containing s = a1 + a2 + a3 + ....+ an. A grasshopper is to jump along the real axis, starting at the point 0 and making n jumps to the right with lengths a1, a2, a3, ...., an in some order.

Prove that the order can be chosen in such a way that the grasshopper never lands on any point in M. [IMO, 2009]

Problem 2
Let ABCD be a convex quadrilateral with BA different from BC. Denote the incircles of triangles ABC and ADC by k1 and k2 respectively. Suppose that there exists a circle k tangent to ray BA beyond A and to the ray BC beyond C, which is also tangent to the lines AD and CD.

Prove that the common external tangents to k1 and k2 intersects on k. [IMO, 2008]

Problem 3
Let P(x) be a polynomial of degree n > 1 with integer coefficients and let k be a positive integer. Consider the polynomial Q(x) = P(P(...P(P(x))...)), where P occurs k times.

Prove that there are at most n integers t such that Q(t) = t.  [IMO, 2006]