Kazu Sagashi Puzzles from Naoki Inaba

Recently, I was scrolling through pictures I had taken on my phone, and I realized that I never got around to blogging about the Kazu Sagashi Puzzles I used with my students back in April.

I was introduced to this logic puzzle in 2016 when I discovered the amazing puzzles of Naoki Inaba. Inaba is best known for his area maze puzzles which have become quite popular.

Discovering these puzzles led me to his website (which is entirely in Japanese, by the way) and a treasure trove of other puzzles with great applications in the math classroom. I ended up creating an entire page on my blog highlighting his amazing puzzles.

Since then, I have translated several of these puzzles into English to use with my students. As a result, I have shared the files here on my blog. You may remember my posts on Angle Mazes and Zukei Puzzles. Recently, I went looking for a new puzzle to use with my students, and I settled on the Kazu Sagashi puzzle to translate.

Though, I prefer to think of these as Apple and Orange puzzles. I like that these puzzles take on several different variations as you progress through the different levels. When I used these with my students, I only gave them the first four levels. Each of these levels has a very similar set of instructions.

These kazu sagashi puzzles are in no way my own creation. All credit goes to Naoki Inaba. I have simply retyped the original puzzles to make them easier to use in an English-speaking classroom.

Let’s take a look at the different kazu sagashi puzzle variations.

In Level 1, students are presented with a set of squares. Some squares contain an apple. Other squares do not. The goal is to identify a 2 x 2 square which holds the specified number of apples. The first puzzle has a 1 beside it. This means the goal is to find a 2 x 2 square that only contains a single apple. Do you see it?

Let’s progress to Level 2.

It’s the same set-up as before, but this time we are looking for a 3 x 3 square.

With Level 3, we’re back to 2 x 2 squares with the added twist that some of the individual squares now contain more than one apple.

Level 4 continues the trend of multiple apples with a larger, 3 x 3 square.

I’ve only used these four levels with students. My Algebra 2 classes had a bit of difficulty wrapping their minds around the instructions to get started, but my Pre-Calculus classes jumped right into solving the puzzles without any help or clarification from me. The students really enjoyed the puzzles. A few days after we did these, a student asked if we could do more of those apple puzzles instead of the lesson I had planned for the day!

We had quite a few days of interrupted instruction in April where I only ended up seeing half of my classes due to standardized testing in the morning, and I found these were the perfect task to give students to keep their minds working on a day that might have been wasted otherwise. These did not take anywhere near the entire class period. But, that was okay because many of my students used the extra time to retake quizzes, complete missing work, or work on assignments for another class.

If you’ve been wondering why I like to refer to these as Apple and Orange Puzzles when so far the puzzles have only contained apples, you are about to find out!

Level 5 tasks you with finding a 2 x 2 square which meets a specified requirement instead of a specific number of apples as before. In the first problem for this level, you need to find a 2 x 2 square that contains an equal number of apples and oranges. For the second problem, the square needs to contain more oranges than apples.

Level 6 continues this new trend but with 3 x 3 squares.

Level 7 changes things up once again by specifying what the difference between the number of apples and oranges must be.