**Welcome to the
Princeton Math Circle! **

**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 2:00 pm to 5:00 pm for middle-school students and from 3:00 pm to 6:00 pm for high school students at Fine Hall 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.**

**This program is NOT to supplement what is learned at school, or to improve test scores, or grades, but rather means to**** foster interest in mathematics among local school kids to help them become tomorrow's scientists, economists, engineers and mathematicians.**** **

First come - first served,

space permitting.

Current Status:

Registration is now closed.

3. Maitreyee DasGupta (7th Grader) - Distinction

4. Matthew Pan (8th Grader) - Distinction

6. Sharon Zhang (7th Grader) - Honor Roll

7. Xiutong Wu (7th Grader) - Honor Roll

8. Jeremy Zhang - Honor Roll

9. Shuvam Chakraborty - (8th Grader) - Honor Roll

10. Rhea Khatry (7th Grader) - Honor Roll

11. Jay Yalamanchili (7th Grader) - Honor Roll

12. Hasit Dantara (6th Grader) - Honor Roll and Achievement Roll

13. Michael Bi (7th Grader) - Honor Roll

14. Phoebe Wang (8th Grader) - Honor Roll

15. Anish Visaria (8th Grader) - Honor Roll

16. Julian Zhang (6th Grader) - Honor and Achievement Roll

17. Vadym Glushkov (8th Grader) - Honor Roll

18. Divyansh Devnani (7th Grader) - Honor Roll

19. Brian Wang

20. Nikhil Parchuri (5th Grader) - Achievement Roll

21. Vishaal Anand (6th Grader) - Achievement Roll

22. Ashwin Dandamudi (6th Grader) - Achievement Roll

23. Divya Unnam (7th Grader)

24. Disha Hegde (7th Grader)

2010 AMC 8 Winners:

Our Top Scorers:

1. Abhishek Lingineni (8th Grader) -

Perfect Score and Distinction

2. Tyler Shen (6th Grader) - Distinction

and Achievement Roll

3. Thomas Draper (5th Grader) - Honor

Roll and Achievement Roll

4. Byron Chin (6th Grader) -

and Achievement Roll

6. Ryan Kola (8th Grader) -

Roll

9. Matthew Pan (7th Grader)

10.Ananya Swaminathan (6th Grader) -

Achievement Roll

11.Aslesha Parchure (7th Grader)

12.Tanmay Rao (8th Grader)

13.Warren Saengtawesin (8th Grader)

14.Isha Shah (7th Grader)

15.

2011 AIME Qualifiers:

1. Abhishek Lingineni

2. Jason Shi

**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]

Contact us at info@princetonmathcircle.org