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Problems of the Week

A Brief Explanation

The Problems of the Week (PotW) are moderately difficult problems that I've found in math books, mathematical competitions, or created myself. The difficulty of the problems ranges greatly, depending on what I feel like giving you. A few problems are close to the level of simple brainteasers, but some others (Such as The Locus of X...) are at a much higher level, coming from competitions such as the International Mathematical Olympiad (IMO). No Problems of the Week involve calculus.

If you have a great problem that you want to submit, just send it in here. Likewise, if you have an brilliant solution that you want the rest of the smarty pants here to see, send it to me here.

Citation Reference

Here is a list of the abbreviations used most often in the citations:

AoPS: and Beyond --- refers to the second volume in the Art of Problem Solving series.
AHSME --- the American High School Mathematical Examination, which has been renamed the AMC 12.
AIME --- refers to the American Invitational Mathematics Examination.
USAMO --- refers to the United States of American Mathematical Olympiad.
IMO --- refers to the International Mathematical Olympiad, probably the most prestigious and rigorous competitions in high school mathematics.

Problem of the Week 6/6/10: Horizontal and Vertical
Problem of the Week 1/27/09: Red and Blue
Problem of the Week 10/29/07: Geometry Series #4
Problem of the Week 10/22/07: Geometry Series #3
Problem of the Week 10/15/07: Geometry Series #2
Problem of the Week 10/8/07: Geometry Series #1
Problem of the Week 10/1/07: Hjelmslev's Theorem
Problem of the Week 9/10/07: All Handshakes Ever Shaken
Problem of the Week 9/3/07: Quadrangle Problem
Problem of the Week 8/27/07: The Number 111111111
Problem of the Week 8/21/07: Alice and Bob
Problem of the Week 8/13/07: Angles in a Triangle
Problem of the Week 8/6/07: A Convex Hexagon
Problem of the Week 7/30/07: The 1990's
Problem of the Week 7/23/07: An 'Edgy' Cube
Problem of the Week 7/17/07: 5 Points in a Plane
Problem of the Week 7/8/07: Zero!
Problem of the Week 7/2/07: An Arithmetic Progression
Problem of the Week 6/25/07: N Lines Divide a Plane
Problem of the Week 6/18/07: Gilligan's Island Problem
Problem of the Week 6/11/07: Problem in Base 2
Problem of the Week 6/4/07: Lined Up in a Row...
Problem of the Week 5/28/07: Sides, Products, and Triangles
Problem of the Week 5/21/07: N^th Roots of 1
Problem of the Week 5/14/07: Pi, Phi, and e (An easy one!)
Problem of the Week 5/7/07: Primitive Pythagorean Triangles
Problem of the Week 4/30/07: Harder Diophantine Equation
Problem of the Week 4/23/07: End Digits of Squares
Problem of the Week 4/16/07: Intermediate Diophantine Equation
Problem of the Week 4/9/07: A Game of Six
Problem of the Week 4/2/07: The Measure of A
Problem of the Week 3/26/07: Two Spheres in a Room...
Problem of the Week 3/19/07: Airport Traffic
Problem of the Week 3/12/07: A Confused Banquet
Problem of the Week 3/5/07: 50 Cards...
Problem of the Week 2/26/07: Verticies of a Graph
Problem of the Week 2/19/07: How Many Integers....
Problem of the Week 2/12/07: The Divine Proportion
Problem of the Week 2/5/07: Special Subsets
Problem of the Week 1/29/07: Work-days and Rest-days
Problem of the Week 1/22/07: The Locus of X... (Very Difficult!)
Problem of the Week 1/15/07: Midpoints of A Quadrilateral
Problem of the Week 1/8/07: How Many...?
Problem of the Week 1/1/07: Determinants
Problem of the Week 12/24/06: 'Persistent' Numbers

Much more to come soon.