What’s Your Problem?

December 1, 2014 at 6:54 am Leave a comment

Problems in the MathCounts School Handbook are presented “shotgun style,” that is, a geometry problem precedes a logic puzzle and follows a probability question. (I worked for MathCounts for seven years and then served as a writer and chair of their Question Writing Committee, so I’m not unbiased.)

By comparison, textbooks often present 50 exercises on the same topic, each one only minimally different from the previous one. That tips the hand to students, methinks, and makes them realize, “Oh, I just need to do the same thing.” I prefer the MathCounts approach, where students have to dig into their bag of tricks to find a viable solution strategy.

With that in mind, here are a few problems I’ve encountered recently, each one not like the others.

Problem 1. The simple polygon is made from 73 squares, connected at their sides. What is the perimeter of the figure?

Thing Puzzle

A simple polygon made from 73 unit squares.

Problem 2. What is the expected number of times that a six-sided die must be rolled to get each number 1–6?

Problem 3. A wall is to be constructed from 2 x 1 bricks (that is, bricks that are twice as long in one direction as the other). A strong wall must have no fault lines; that is, it should have no horizontal or vertical lines that cut entirely through a configuration, dividing it into two pieces. What is the minimum size of a wall with no fault lines? The figure below shows a 3 × 4 wall that has both horizontal and vertical fault lines.

Fault Line - 3 x 4 Wall

A 3 × 4 wall with a fault line.

Please share great problems you’ve recently encountered in the Comments.


No answers, but here are some hints.

Problem 1. Look for a pattern.

Problem 2. Check out this simulation for the Cereal Box problem.

Problem 3. The smallest arrangement without a fault line is larger than 3 × 4 and smaller than 10 × 10.

Entry filed under: Uncategorized. Tags: , , , , , .

Thanksgiving Math Quiz Birbiglia, Baby Boomers, and Computers

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Trackback this post  |  Subscribe to the comments via RSS Feed


About MJ4MF

The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.

MJ4MF (offline version)

Math Jokes 4 Mathy Folks is available from Amazon, Borders, Barnes & Noble, NCTM, Robert D. Reed Publishers, and other purveyors of exceptional literature.

Past Posts

December 2014
M T W T F S S
« Nov   Jan »
1234567
891011121314
15161718192021
22232425262728
293031  

Enter your email address to subscribe to the MJ4MF blog and receive new posts via email.

Join 243 other followers

Visitor Locations

free counters

%d bloggers like this: