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Area Maze Puzzles from Naoki Inaba

Area Maze Puzzles from prolific Japanese puzzle creator Naoki Inaba have become quite popular in the United States. This hasn’t always been the case.

Area Maze Puzzles by Naoki Inaba.

I first learned about these puzzles from a tweet from Lisa Bejarano. At the time of her tweet, you could only really get your hands on a large number of area maze puzzles by ordering them from Japan.

Area Maze Puzzle

Area Maze puzzles, also known as menseki meiro puzzles, are an original creation of Naoki Inaba. Inaba is a Japanese puzzle author who has created over 400 different types of puzzles.

If you’re a die-hard logic puzzle lover, I highly recommend purchasing a copy of Inaba’s book: The Original Area Mazes.

He has since followed this up with both a second volume of area maze puzzles and a volume geared toward kids.

So, what is an area maze puzzle?

I really like the example puzzles provided in this article from The Guardian by Alex Bellos. In fact, Alex Bellos actually wrote the introduction to Inaba’s The Original Area Mazes book.

The goal of the puzzle is quite simple: figure out the value of the question mark.  One caveat: you are NOT allowed to use fractions in your solution. All of these puzzles can be solved using ONLY whole numbers.

To solve the puzzle above, you’re going to need to think outside of the boxes provided. Alex Bellos offers up this hint in his Guardian article. If we form another rectangle as shown below, we can easily find its area. After all, we know its length and width. We can also realize that the rectangle on the left and the two rectangles on the right both have the same area. If they have the same area and the same height, they must also have the same width. Isn’t that an incredibly satisfying feeling?

Want more puzzles to solve? I know I do! Here are some sources of free area maze puzzles to keep you busy while you wait on a copy of Inaba’s full book of puzzles to arrive at your doorstep.

Sources of Free Area Maze Puzzles (Menseki Meiro Puzzles)

The article in The Guardian by Alex Bellos that I referenced above has a total of 5 puzzles embedded in the article.

There is also a blog post from the New York Times that features the puzzle.  This blog post 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!

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.

The Waterloo Region District School Board has a page of puzzles and riddles for elementary students to tackle. They feature several area maze puzzles as well as questions and prompts to use with students as they are tackling these puzzles.

Five Thirty Eight features two of Inaba’s area maze puzzles on their website for you to try your hand at.

If you have a free account on TES, there is a free printable of area maze puzzles to use with your students.

Transum (an all around lovely site for math teachers with tons of free resources) has four levels of area maze puzzles for students to work through. They are even self-checking!

Area Maze Puzzle from Transum

Rose Lorenz has put some of the area maze puzzles into Desmos Activity Builder to make them easier to use with students.

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.  

Looking for more amazing logic puzzles from Naoki Inaba to use in your classroom or to solve yourself? Check out these other puzzle posts:

Step Puzzles

Kazu Sagashi Puzzles

Angle Mazes

Zukei Puzzles

Interested in just more puzzles in general? I’ve got a whole page on my blog dedicated to all things puzzles.

Puzzle Solutions

I intentionally do not share solutions to the puzzles I feature on my website because I strive to provide learning experiences for my students that are not google-able. I would like other teachers to be able to use these puzzles in their classrooms as well without the solutions being easily found on the Internet.

However, I do recognize that us teachers are busy people and sometimes need to quickly reference an answer key to see if a student has solved a puzzle correctly or to see if they have interpreted the instructions properly.

If you are a teacher who is using these puzzles in your classroom, please send me an email at sarah@mathequalslove.net with information about what you teach and where you teach. I will be happy to forward an answer key to you.

Anonymous

Monday 5th of November 2018

"Thanks debbie"

AC89

Friday 20th of October 2017

Using these today! So excited - keep forgetting about them and then keep resdicovering them through endless reading of your blog - which is one of my favourite things! Thanks for these :)

Unknown

Monday 15th of August 2016

I bought the book after seeing Lisa's post-and I loved reading your posts on it! Thanks for the links to the previews-it's so cool that the language doesn't matter in math. I also love Sarah Millard Lanahan's idea for PD!! I teach adults at night and can't wait to use these with them as well as my middle schoolers. Keep blogging-I love what you're doing!!! @debboden

Sarah Carter (@mathequalslove)

Wednesday 17th of August 2016

Thanks Debbie!

Unknown

Wednesday 10th of August 2016

I'm totally going to start using these at the beginning of the PD I deliver to my math teachers! It'll be a great warm up and something for them to do while we're waiting for the stragglers.

Sarah Carter (@mathequalslove)

Wednesday 17th of August 2016

Great idea!

Anonymous

Saturday 6th of August 2016

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.

Sarah Carter (@mathequalslove)

Saturday 6th of August 2016

Please blog about how it goes!