How many shelves measuring 8 inches by 12 inches can be cut from a 36-inch-by-56-inch piece of plywood so that there is no waste?

Answer 1

21, if you have a laser beam.

You can cut the plywood into three equal pieces length-wise, giving you three 12 by 56 planks. Each of those can be cut into seven parts, resulting in 21 shelves. (Since you have to use a circular saw, table saw, or belt saw - or even a hand saw - the corner shelves will lose half the width of the saw on two sides, the outer shelves of the middle plank and the inner shelves of the two outside planks will lose will lose three halves of the width of the saw, and the inner pieces if the middle plank will lose four halves of the width of the saw.)

Probably good enough for government work.

Nice question.