MathDB

A9/B10

Part of 2008 Princeton University Math Competition

Problems(2)

2008 PUMaC Algebra A9 / B10

Source:

9/24/2019
If p(x)p(x) is a polynomial with integer coeffcients, let q(x)=p(x)x(1−x)q(x) = \frac{p(x)}{x(1-x)} . If q(x)=q(11−x)q(x) = q\left(\frac{1}{1-x}\right) for every x≠0x \ne 0, and p(2)=−7,p(3)=−11p(2) = -7, p(3) = -11, find p(10)p(10).
algebra
2008 PUMaC Combinatorics A9 / B10

Source:

10/4/2019
How many spanning trees does the following graph (with 66 vertices and 99 edges) have? (A spanning tree is a subset of edges that spans all of the vertices of the original graph, but does not contain any cycles.) https://cdn.artofproblemsolving.com/attachments/0/4/0e53e0fbb141b66a7b1c08696be2c5dfe68067.png
combinatorics