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. You don’t need a mat cutter or mat cutting experience to solve this problem, however.

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, but then discovered that there were problems along the top edge requiring me to remove a one-inch strip (shown with red hash marks), leaving a piece of foam board 39″ high by 37″ wide.

Illustration for Mat(h) problemThe 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 obviously 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 afterwards.  Good luck!

Author: Bruce

Although I grew up in Garden Grove, California, I have lived here in South Miami longer than I've lived anywhere else in the world. I've been married to my wonderful wife, Nancy, longer than I was ever without her. We were both teachers. Nancy recently retired after 40 years. I have also spent time as an officer in the Coast Guard, a commercial property appraiser, and an electrical engineering student. Now I'm technical support for Bee Happy Graphics. That means I handle this blog, our web page, and all E-mail, I do all post-processing and printing of the images, I cut mats and glass and frames. If you have a technical question, I would be the one trying to answer it.

2 thoughts on “A Simple Mat(h) Problem”

  1. Bruce,

    I would say that the number of mats left is four.

    Jim Farrington

    After further prodding, Jim added the following information:

    The solution as I see it is to change the orientation of the mats, i.e., from an all vertical layout to one of two verticals and two horizontals. I have attached a rough drawing to graphically back up my solution.


    Jim Farrington's solution

  2. Excellent, Jim. Thanks! You don’t have to wait for me to finish designing a certificate before you claim your reward. And even though this is the off-season for Florida Art Festivals, it’s still not a good idea to wait until the day of some deadline to contact us about your print.

    For those of you who would like more information (including other possible solutions and maybe even some trigonometry), go to Comments on Mat(h) Solution.

    I’ve already come up with two more math problems, one based on mat cutting (again) and one from printing, but I’m not sure how soon I will be introducing them. Stay tuned.

Your "two cents worth" is welcome (but I don't give change).

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