Beth Malmskog

Math etc.

Month: February, 2012

Reposting This Week’s Puzzle: The Trivium’s Checkerboard

This week’s puzzle can be thought of as a missing page from the Phantom Tollbooth, a book very near and dear to my heart.  Here is the hero of our story, Milo, with his faithful companion, Tock the watchdog:


As our puzzle begins, Milo and Tock (and the illustrious Humbug) are caught in the trap of the Terrible Trivium.  The Trivium is a faceless man who aspires to waste the time of those he catches, by smooth talking them into trivial, endless, time-wasting tasks.  Like emptying a well with an eyedropper. Anyway, Milo and his friends have been wasting time for a  while, and are about to make their getaway, when the Trivium gives them one last task–win a simple game involving dominos and a checkerboard.


I’ll skip the whole story–listen to the linked audio to hear the dialogue!  The task that the Trivium sets Milo on is to cover a modified checkerboard with dominos, without any overlap of dominos or any dominos hanging over the side.  You see, the dominos are rectangles that each exactly cover two squares of the checkerboard.  It is easy to cover a standard 8 by 8 checkerboard with dominos by these rules–simply put 4 dominos end to end in each row.  However, the Trivium has changed the checkerboard.  He’s gotten out his saw and cut the upper left and lower right corner squares off of the board.  His challenge to Milo is to cover this new board by the same rules: each domino covers two squares, no dominos should overlap or hang over the edge.  Milo starts in to work…


Milo tries and tries different rearrangements of the dominos.  Each time, he finds that it doesn’t quite work out.  The Trivium is incredibly pleased with this–he knows that there are millions of arrangements of dominos on a checkerboard like this, and that it will take Milo his entire life to try them all.  However, Milo suddenly stops.  He realizes that he’s been had.  Milo has noticed a very simple fact that makes it clear that he will never be able to cover the board in dominos.  Though the Trivium is furious, he can’t argue with Milo’s simple and impeccable logic, and he is forced to let Milo and his friends leave.  Of course, they go on to finish their quest and rescue the Princesses Rhyme and Reason.  All because of Milo’s amazing observation.

The puzzle–What very simple fact did Milo notice, and how did he know, then, that he could never cover the board?

Send your solution to me at!  The author of the best solution that I receive by the middle of next week will win an incredible Math Mostly/Somewhat Science T-shirt, courtesy of the Wesleyan University Department of Mathematics and Computer Science.  Make sure and tune in to WESU 88.1 FM (in Middletown, or stream live at next week, from 2:30-3:00 on Friday afternoon (Eastern time) to hear the solution to the puzzle.  I’m so excited to read people’s solutions!

[Checkerboard picture source–David Hardman via Wikimedia Commons]

Radio delay! And big news.

Ach!  There has been a technical issue with putting together today’s show, so my first puzzle won’t air until next week.  I’ll repost the puzzle next week.  Still, there will be a science show on WESU today at 2:30, and I’ll be listening to it!

The big news–I have accepted a job at Colorado College starting this fall.  It’s not tenure track, but it is a fairly long term visiting appointment.  I am really excited about it!  It was a tough decision to leave Wesleyan, which is really an incredibly great place to work.  My secret dream is to merge the two schools in to one, which would in my dream be conveniently located in a strange hybrid of San Francisco, Wyoming, New England, and Colorado.  I would also ride a horse to work in this dream.  Since that’s not going to happen anytime soon, I am thrilled to be moving closer to my family and to have the chance to work with the amazing faculty and students at CC.  Plus, Pike’s Peak is actually RIGHT THERE.  Seriously.  It’s stunningly beautiful.

Return to radio!

Exciting news for me!  Math, my constant companion, is reuniting me with radio, my old flame.  That’s pretty dorky, I know.  What I’m trying to say is that, starting now, I will be producing a weekly math puzzle radio segment for WESU.

My segment will be part of “Somewhat Science,” a show put together by Wesleyan students with guidance from Professor Suzanne O’Connell.  These students put together great pieces about global, national, and local issues and advances in science.  I’m adding a 7 minute or so math puzzle, which hopefully involves listeners emailing me with their solutions to my puzzles.  The listener who submits the best solution each week will win a prize.  I’m hoping for math t-shirts.  Maybe some other fabulous prize for this first week, since the t-shirts aren’t set up yet.  As I said, I am just thrilled.

In the spirit of alliteration, I think the segment will be called Mostly Math.  Or Much Like Math.  Or Mucho Math.  You get the idea, I’m sure.  In any case, you can hear it on WESU 88.1 FM Middletown, CT (or stream at  Somewhat Science airs 2:30 and 3:00 PM Eastern time, on Fridays starting February 15.  Not sure exactly when Math Mostly will come on.

To answer a puzzle, send an email to me at mathmostly at gmail dot com.  The best answer as of production time for next show will win an incredible prize, as mentioned earlier.  I will be posting the puzzles here so that people can reference them, though hopefully we will get an actual show website put together in the next couple of weeks.


As for the rest of it, I really don’t know where to begin.  A stress and excitement filled chronicle of these winter months of job interviews and decisions?  An account of the incredible (and apparently really nice) students in my classes?  Ah, I don’t have time now anyway.  Suffice to say it’s been weird.  Will post a puzzle soon, but now I have to go to the radio station!   Hooray!