Show that if 
Nilpotent Matrices
October 5th, 2009 by Jeremy No comments »Binary Expansions
September 21st, 2009 by Jeremy No comments »Are the binary expansions of all rational numbers eventually periodic? Answer with proof.
Never Invertible?
September 17th, 2009 by Jeremy No comments »The product of two rectangular matrices sized mxn and nxm respectively with m
Bug on a Triangle!
September 15th, 2009 by Jeremy No comments »A bug moves along segments on a triangle. From any particular vertex, he has a 
Hint: there is a slightly easier (albeit less rigorous) heuristic approach over the traditional one.
Taken from an AIME exam
Interesting clock question
September 8th, 2009 by Jeremy No comments »Just when you thought you saw all of them!
A man leaves his house between 4 pm and 5 pm. He returns between 5 pm and 6 pm only to discover that the hour hand and the minute hand have exactly interchanged places! Deduce the time the man left his house.
*Source: India National Olympiad 1986
Modular Arithmetic #1
July 21st, 2009 by Jeremy No comments »Ex 3.2.1
Prove that any subset of 
Solution
There are nine congruence classes modulo 9. By the pidgeonhole principle seven of the fifty-five chosen are in the same congruence class. Label them 
Source:
Putnam Training Day
June 10th, 2009 by Jeremy No comments »I will be training for the Putnam this upcoming year and will be posting an assortment of problems and my personal solutions here on this webpage. Each post will have the following format: Example, Problem, Solution.
Strategy:
Exploit Symmetry
Source:
Problem Solving Through Problems
Example:
Evaluate 
Example Solution:
Exploit the symmetry of the expression about the point 
From symmetry, the expression evaluates to one half the area of the rectangle that encloses the function over the domain of the integral.
Problem and my solution coming later today.
Source:
