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.

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 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!

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.