ΒΆ 2007 USAMO Day 2 Problems and Solutions
Problem Set Workbook
Access the downloadable workbook for 2007 USAMO Day 2 problems here.
Discussion Forum
Engage in discussion about the 2007 USAMO Day 2 math contest by visiting [Random Math USAMO Day 2 2007 Forum](https://forums.randommath.com/c/tournaments/MAA/2007-usamo-day 2)
Individual Problems and Solutions
For problems and detailed solutions to each of the 2007 USAMO Day 2 problems, please refer below:
Problem 4: An animal with cells is a connected figure consisting of equal-sized square cells. The figure below shows an -cell animal.
A dinosaur is an animal with at least cells. It is said to be primitive if its cells cannot be partitioned into two or more dinosaurs. Find with proof the maximum number of cells in a primitive dinosaur.
Solution:
Problem 5: Prove that for every nonnegative integer , the number is the product of at least (not necessarily distinct) primes.
Solution:
Problem 6: Let be an acute triangle with , and being its incircle, circumcircle, and circumradius, respectively. Circle is tangent internally to at and tangent externally to . Circle is tangent internally to at and tangent internally to . Let and denote the centers of and , respectively. Define points analogously. Prove that
with equality if and only if triangle is equilateral.
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions