Home Free Lessons Billiard Ball Problem
Billiard Ball Problem


The Billiard Ball Problem is a beautiful exploration of a situation both natural and novel.
Great for problem solving, with connections to ratio and proportion.

This lesson is the 2nd prize winner of the Rosenthal Prize from the Museum of Mathematics in 2022! Download here.

Also check out this Billiard Ball simulator on Scratch.

Why we love the Billiard Ball Problem

This is a beautiful puzzle, with a deceptively simple and satisfying answer.
As soon as students can draw straight lines at 45 degrees, they have access to the puzzle, but cracking it is much trickier!

Download the full lesson here.

Download the earlier, quicker version here.

New! Follow Up Video from TED-Ed

After you’ve spent at least one lesson on the main problem, a fun followup challenge is to play the first half of this video to pose the Vampire Hunter Riddle. This is a great way to revisit the original task, and push a students to apply their thinking.


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