Found this problem at The MAA Mathematical Sciences Digital Library.
The site demonstrates solutions to this problem using strategies including data analysis, technology-driven geometric sketches, algebraic analysis and calculus. I think it would be very interesting to present the problem to students in each of your gr.10 - 12 classes and then showcase the different methods they used to explore the problem. I think students would see the value in different representations/methods from peers in higher/lower grades.
How about school-wide math-talk?
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