Area Maze puzzles, also known as Menseki Meiro, were created by Japanese puzzle master Naoki Inaba (see also sankaku puzzles). He has published several books of area mazes including The Original Area Mazes and The Original Area Mazes, Volume 2. Each book has 100 area mazes.
To solve an area maze, you must use your knowledge of area to find the missing information in a diagram involving rectangles. The only caveat is that you are not allowed to use fractions or decimals. Every area maze puzzle can be solved using only whole numbers!
For example, can you use the information provided in this diagram to figure out what number is represented by the question mark?
Try it for yourself before you look at how I solved it below.
Here’s how I did this one:
My Reasoning: I am looking for the area of the shaded rectangle, because that is where I see the quesiton mark. I used the 4 cm and the 3 cm to determine that the length of the larger rectangle was 7 cm. Since the area of the larger rectangle is 42 sq. cm and one side length is 7cm, then I knew the other side length was 6 cm. I knew the combined heights of both rectangles measures 10 cm. If the hight of the larger rectangle is 6 cm, than that leaves 4cm for the height of the smaller rectangle. Then I multiplied 4 cm by 4 cm to get an area of 16 sq cm.
There are 4 levels of challenge for area mazes, so they are great for students at every level. Here are a few examples from Mr Inaba’s website:
Mr. Inaba has even created 3D area mazes, like the one below, which focus on the surface area of the diagrams.
Here are some resources for learning more about area mazes. Each one has a few free area mazes to investigate:
- Can you solve it? Are you smarter than a Japanese schoolchild? (The Guardian’s Alex Bellos Monday Puzzle)
- Naoki Inaba’s Area Maze Puzzle (New York Times NumberPlay)
- Area Maze Puzzles (Sarah Carter’s Math Blog, Math Equals Love)
- A Google Books preview of Naoki Inaba’s book The Original Area Mazes
You can also download a free Area Maze iPhone app
Mr. Inaba’s books The Original Area Mazes and The Original Area Mazes, Volume 2 are available at most bookstores, and you can often find used copies for sale as well.
