100 Day Summer Challenge

100 problems in 100 days. #100problems

Day 0

A preview: Can you solve this?

Logic

Which pocket will the ball end up in?

Assume that the ball is shot at a 45 degree angle directly from corner \(\text{B}\) of the table and that it will only land in a pocket if the center of the ball meets the corner of the pocket exactly. Model the ball as a point mass on a frictionless table.

This puzzle can be solved by carefully considering the path of the ball bounce-by-bounce, but there's also a beautiful shortcut that combines geometry and algebra to calculate the solution in <1 minute!

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