Math = Love: Area Maze Puzzles

## Wednesday, August 3, 2016

### Area Maze Puzzles

A few weeks ago, I saw a tweet from Lisa Bejarano that sparked hours of google searching and oohing and aahing and saving every single puzzle I could get my hands on.

The puzzles are known as "area maze" or "menseki meiro" puzzles.  They are an original creation of Naoki Inaba.  A quick google search leads to an article from The Guardian by Alex Bellos.

Here's what one of the puzzles looks like:

 Source: https://www.theguardian.com/science/2015/aug/03/alex-belllos-monday-puzzle-question-area-maze-smarter-than-japanese-schoolchild
The goal of the puzzle is to figure out the value of the question mark.  One caveat: you are NOT allowed to use fractions in your solution.  If you're stumped, scroll to the bottom of this post for a hint.  You'll probably want to slap your forehead after seeing the hint if you're anything like me.  Remember - you shouldn't have to use fractions at any point in time!

If you're now thinking that you'd like to try some of these puzzles with your students (as I was by this point), I'm going to point you to some free and paid resources that will let you do so.

Sources of Free Puzzles:
• The article in The Guardian has a total of 5 puzzles embedded in the article (4 in addition to the one above).
• There is also a blogpost from the New York Times that features the puzzle.  This blogpost links to two pdfs of puzzles that you can download here and here.  And, for the record, these puzzles get quite large and complex.  Don't believe me?  Just click on that last link!  The bottom of the New York Times Post also includes a 3D Version!

 Source: http://wordplay.blogs.nytimes.com/2015/08/17/naoki-2/?_r=0
• Someone has created a website called AreaMaze.com that features digital versions of these puzzles.  They start out easy and get progressively harder.
• There are also Area Maze apps for Apple and Android.  I, however, haven't tried either of these out.
• Naoki Inaba, the creator of the Area Maze puzzles, has also posted four free puzzles as a PDF on his website.  The text is in Japanese, but this won't keep you from working the puzzles.
I love how these puzzles show how universal of a language math is!  Even if the puzzles are published in different languages, we can still use and understand them.  How cool is that?!?

Sources of Paid Puzzles:

If these puzzles aren't enough to satisfy you, you can purchase entire books of these puzzles from Amazon:

I think these would make good warm-up puzzles in the classroom.  They'd also be great to stick in a unit on area or volume!  Or, you could use them as a sort of brain break.  Stick one of these in your slides to give your students a quick challenge and break from whatever topic you are working on.  In the course of my research on these logic puzzles, I ran across quite a few more new-to-me logic puzzles with math-y ties.  But, this post is already getting long, so I'll put those in another post.

And, to be honest, I plan on printing a set of these out and solving them myself!

1. I was also excited and did a little bit of research after seeing Lisa's post. I have tried out the Android app and it's a little clunky, but there are lots of available puzzles. I am planning to use them as warm-ups. (Maze Monday?)

2. I just spent an hour on the iPhone app solving these puzzles. I am completely hooked. The puzzles focus on logic, proportional relationships and most of all number sense. I definitely see them having a place in my classroom.

1. I downloaded the app and spent some significant time on it, too!

3. I think I'm going to use this as a first day of school activity for Geometry. I think I'll also bring them back as we start to do 2-column proofs to remind them about perseverance, and how we might have to alter our thinking to reach the end goal of proving something.