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Welcome to Math Problem of the Day, a blog run by past and current students of Thomas Jefferson High School in Alexandria, Virginia. Each day, one of us will post an original problem for discussion. We invite you to join in and contribute to our investigation of what will hopefully be interesting and thought-provoking problems.

Problems of the day will generally be at the difficulty level of high school mathematics competitions such as the AIME or USAMO. Topics covered will include Algebra, Geometry, Combinatorics, and Number Theory.

Problems will typically be solvable without the use of a calculator or computer. If the computations involved in your approach are too complicated or extensive to do by hand, there’s probably a nicer solution to be found.

We will try to make all problems of the day original (unless otherwise noted). If you find that a problem of the day is not original, please notify us.

To view all problems posted to date, visit the main page. The potd page displays a condensed list of the most recent problems of the day, while the bonus page will host any extra problems we post.