Pizza Problems

What Are Pizza Problem?

Pizza problems are an opportunity for Whitman College students to compete using their mathematical skills and knowledge of the campus/community. Each semester there are four problems posted (two at the beginning of the semester, and two part way through). Each posting contains one speed problem (the first to solve it wins the prize) and one "quality" problem which students have until the end of the alloted time to submit their solution ("best" solution wins, with "best" being defined in the problem).

Accessibility:

These problems are typically designed to force you out of a classroom to engage in a variety of ways with the local campus and community. Some of these modes of engagement may not be accessible to every person. If the problems as posted are not accessible to you please reach out to me at gabbardm@whitman.edu for alternative versions of the problems which cover the same topics in a way accessible to you. Math is for everybody, and these problems are too!

Fall Pizza Problems:

These are the first two pizza problems of the Fall 2026 semester. If you have any questions please do not hesitate to reach out via email at gabbardm@whitman.edu or by dropping by Olin 216.

Problem 1:

Overview:

Find and take a picture with all 7 different Frieze patterns somewhere in Walla Walla. The first person to send all 7 photos to gabbardm@whitman.edu is the winner.

In-Depth Rules:

Your submission must contain 7 photos along with a short written component. The 7 photos must satisfy the following requirements:

The photos must be taken in Walla Walla, after September 1st.
You must be clearly visible in the photo.
Each of the 7 photos must contain a different Frieze pattern (see Frieze Pattern Information section of this page for an overview of Frieze patterns). The Frieze patterns do not have to be (and won't be) infinite, but must repeat at least 4 times. It is acceptable for the Frieze pattern to be "poorly framed" in the picture, just as long as it is clear from the picture that viewed from some perspective it is truly the Frieze pattern you are claiming it is.
The Frieze patterns must be outside and "in their natural habitat". This means they cannot be drawn in chalk by you/a friend, in a textbook you brought outside, on a phone screen, etc.

In the short written component you must identify which pattern is which, using the naming conventions in the Frieze pattern Information section, and explain where on campus/town the picture was taken. As long as you correctly identify the pattern and give a description of the location which could guide me to the location, your written component is complete!

Announcing Winner:

As soon as a winner is confirmed they will be notified and this webpage will be updated. Submissions after this point are welcome (math is fun!), but will not be eligible for a prize.

Problem 2:

Overview:

Take a picture with the most Frieze patterns in the background.

In-Depth Rules:

You must take a single picture with multiple mathematically distinct Frieze patterns in the background. You will submit a single photo and a short written component. The photo must satisfy the following:

The photo must be taken in Walla Walla, after September 1st.
You must be clearly visible in the photo.
The Frieze patterns do not have to be (and won't be) infinite, but must repeat at least 4 times. It is acceptable for some of the Frieze patterns to be "poorly framed" in the picture, just as long as it is clear from the picture that viewed from some perspective they are truly the Frieze patterns you are claiming they are.
The Frieze patterns must be outside and "in their natural habitat". This means they cannot be drawn in chalk by you/a friend, in a textbook you brought outside, on a phone screen, etc.

In the short written component you must identify which patterns are present in your photo, using the naming conventions in the Frieze pattern Information section, and explain where on campus/town the picture was taken. Your score will be the total number of distinct symmetries present and correctly identified, repeated patterns do not earn points. Therefore, the maximum score is 7. Frieze patterns present but incorrectly identified will not earn points.

Submission Deadline:

Submissions will be accepted until October 23rd, with the winner being announced the following Monday.

Frieze Pattern Information:

Frieze patterns are patterns that repeat infinitely on an infinitely long strip. Specifically, they are any pattern on the strip which has a translational symmetry. This means that the pattern must be the exact same if you shift the strip one step to the left or right. These patterns show up in art and architecture from around the world and are often extremely ornate. Stripping away the colors and ornamentation, mathematicians have classified Frieze patterns by their specific types of symmetry. The different symmetries a Frieze pattern can have are horizontal reflection (mirroring left and right), vertical reflection (mirroring up and down), rotation, glide reflection, or some combination of these. Mathematicians have proven that there are exactly 7 possible combinations of these symmetries that can appear, and have labeled them as follows:

In this image, the shaded yellow box in each strip is called the fundamental domain of the pattern. This fundamental domain is repeated over and over, either by reflecting over green/red lines, rotating around red points, or doing a more obscure move of gliding and reflecting (see the second Frieze pattern).

For more information about these patterns, mathematically and historically, I recommend the following resources:

Wikipedia! A good overview of the 7 different patterns.
Video overview. This video goes through what Frieze patterns are, what the 7 symmetries are and how we know there are exactly 7. It is short and worth a watch!
Frieze Designs in Indigenous Art. This article introduces Frieze patterns and highlights their prevalence in various forms of textiles created by indigenous people in North America.

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