A Simple Mat(h) Problem

Interesting math problems have always seemed to jump out of the woodwork at me. Here’s a simple geometry problem inspired by mat cutting. However, you don’t need a mat cutter or mat cutting experience to solve this problem.

Starting with a regular 40″ by 60″ foam board, a 23″ (by 40″) slice had already been removed for another project (shown as the large black-hashed area on the left edge of the illustration). In the blue dashed lines of the illustration, I drew simple plans to cut out four standard 16″ by 20″ pieces. Then I discovered that there were problems along the top edge requiring me to remove a one-inch strip (shown with red hash marks). That left a piece of foam board 39″ high by 37″ wide.

The question is, “How many 16″ by 20″ pieces can I still get out of this remaining foam board?”. One would make the cuts on their mat cutter with a razor-like blade, so you don’t have to worry about a kerf (the extra material removed by the width of the saw blade).

The seven best answers will receive $7 off any print and another $7 off if you choose to frame (or gallery-wrap) the image. I will publish some responses, but not immediately. So that nobody dies from the suspense, we will put a two-month deadline on this offer. Prizes may be redeemed any time afterward.  Good luck!