December 8–January 4, 2009
This will be the last challenge puzzle for this year; we'll resume next year at the beginning of next quarter. Feel free to submit a solution to any part of this puzzle any time from now until January 4.
Problem
Jason has a 4 foot by 8 foot rectangular piece of plywood that he would like to make into the top of a circular table.
- What is the largest table that he can make by cutting out two identical semicircles (and throwing the remaining wood away)? Hint: it's possible to make a table with radius bigger than 8/3.
- Instead of cutting out semicircles, suppose Jason can cut two identical pieces of any shape to make a circular table. What's the largest table he can make? (And how should he do it?)
- Finally, suppose there's no restriction on the shape of the pieces. What's the largest table possible with two pieces of any shape?
To clarify the last two parts, here are some ideas for how the pieces might be cut:
Solution
List of solvers
T.R. Mukundan, Congpa You, Lloyd Sakazaki, Greg Rudzinksi (outside).
Lloyd Sakazaki wins the prize!