October 2019
Problem of the Month

The Spider and the Fly

A hungry spider is sitting on the floor in the corner of a rectangular room.

She sees a tasty fly on the ceiling in the far corner.   The room is a meters long, b meters wide, and c meters high.

What is the shortest route from the spider to the fly if the spider must always crawl along a wall?
Show your work!

Solution to the Problem:

The answer could also have been sqrt(a^2 + (b + c)^2) or sqrt(b^2 + (a + c)^2) since we don't know the relationship between a, b, and c.

The easiest way to see this is to "unfold" the sides of the room and draw a line segment between the spider and the fly.   Below is a diagram of the front face and the end face when it is unfolded.   The dashed line shows the path of the spider.



Now use the Pythagorean Theorem to solve for the distance.
(distance)² = (a + b)² + c²
Then take the square root of each side to obtain the answer.

Correctly solved by:

1. Kelly Stubblefield	Mobile, Alabama
2. Ivy Joseph	Pune, Maharashtra, India
3. James Alarie	Flint, Michigan
4. Leah Snyder ***	Nashville, Tennessee
5. Mia Tucker	Mountain View High School, Mountain View, Wyoming
6. Haylee Rudy	Mountain View High School, Mountain View, Wyoming
7. Soonho You (유순호)	JeonJu, South Korea
8. Tyler Petersen	Mountain View High School, Mountain View, Wyoming
9. Haily Stephens	Mountain View High School, Mountain View, Wyoming
10. Drew Harris	Delta High School, Delta, Colorado
11. Brijesh Dave	Mumbai City, Maharashtra, India

*** extra credit for sending multiple solutions for the problem.

Send any comments or questions to: David Pleacher