Problem-Solving Under Pressure

Near the end of a long morning building a small table, I encountered the following simple geometry problem:  I needed to cut four small rectangles from a square of self-adhesive rubber to serve as the feet of the table’s legs.  So I cut the square into four equal strips, lopped off the end of eachand had my feet.

All well and good, but I missed the superior solution that any decent problem solver should have seen immediately:

This solution would have left me with one long rectangular remainder, as opposed to four small square remainders.

After working on the table for a while, I was mentally and physically drained, and I think this affected my ability to see the better solution.  I guess it makes sense that being tired [and frustrated!] would negatively impact one’s ability to solve problems.

It’s interesting to think about how our physical, mental, and emotional states can affect our problem-solving abilities.  And I think this suggests that problem-solving stamina is something we might want to work on.

Categories: ChallengeGeometry

patrick honner

Math teacher in Brooklyn, New York

Scott Matthews · August 22, 2010 at 12:56 am

Maybe I’m not quite understanding, but couldn’t you just cut off one full strip (a quarter of the total area), then take that strip and cut that into four small squares? Does the pattern that’s left of the remaining 3/4 of the square really matter? Please clarify.

MrHonner · August 22, 2010 at 8:07 am

It wasn’t the small squares I needed, it was the small rectangles.

Aha! Thank you!

Hilary · August 26, 2010 at 2:04 pm

I had the same question! Aha.

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