Solution¶
Four 3-4-5 slices can be made from each 5-inch square, accounting for $96\%$ of its area and leaving a 1-inch square from the center.
The Riddler Cheese Company is producing what are called “craft triples” — triangular slices of cheese whose side lengths are Pythagorean triples, when measured in inches.
However, the company’s slicing machine recently malfunctioned and produced a stock of square slices with side lengths of 5 inches. To salvage this situation, what is the greatest number of whole Pythagorean slices that can be made from each 5-inch square? (Note: You can only cut pieces out of the square. No melting or gluing pieces together!)
Extra credit: What is the smallest square of cheese such that 100 percent of the square can be partitioned into craft triples?
Four 3-4-5 slices can be made from each 5-inch square, accounting for $96\%$ of its area and leaving a 1-inch square from the center.
$100\%$ of a 12-inch square can be partitioned into craft triples that are 3-4-5, 6-8-10, or 9-12-15. One such arrangement is shown below.
