Math = Love: Volume 1: Japanese Logic Puzzles for the Secondary Math Classroom

Thursday, August 4, 2016

Volume 1: Japanese Logic Puzzles for the Secondary Math Classroom

I left a teaser at the end of yesterday's blog post which probably wasn't the nicest thing to do.  Sorry!  :)

To catch you up, I posted about some awesome area and volume puzzles created by Naoki Inaba.  You can read that post here.  While researching those puzzles and looking for possible online sources for them, I found some on Mr. Inaba's website.  This led me to start wondering, "What kind of other puzzles has he created?"

So, ever-curious me, decided to visit the rest of the website.  Of course, it's all written in Japanese.  But, with enough random-clicking, I was able to stumble across some more math-y logic puzzles that I can't wait to incorporate in my math classroom.  The instructions are in Japanese, but the math of the puzzle is universal.

So, let's play a game.  Here are the rules:

1.  I'll post a picture of a puzzle and the solution.  The instructions are in Japanese.
2.  Determine the goal of the puzzle.
3.  Figure out how you could use it in your math classroom.
4.  Scroll down and see if your thoughts match mine!  

Sound fun?  Let's Begin!

These are all original puzzles created by Naoki Inaba and posted for free on his website.  There are quite a few that I see math-y applications of, so I'll be splitting them into multiple posts over the next few days.

Puzzle 1:

Inaba calls these K-Maze Puzzles.

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From my puzzle-studying, I've determined that these are angle puzzles.  S stands for Start.  G stands for Goal.  Draw a path from S to G so that the path passes through each circle with the angle measure specified by the puzzle.

[Full Disclosure: I don't know any Japanese unless you count the summer our Vacation Bible School was Japan themed.  If I've made a mistaken assumption, please correct me in the comments!]

Google Translate translates this as "Angle Maze."  The PDF file of these puzzles contains an example of a wrong solution.  So, I'm also assuming that you can only travel through each circle once.

This PDF contains 38 of these puzzles which get progressively harder.  Here are the solutions.

If you like this sort of angle puzzle, Inaba also has a different version where you're not told where to start or end.  Instead, you're just told exactly which points you MUST go through.  You can find four of those puzzles here.

I think these would be a great warm-up for a geometry class!

Puzzle 2:

Inaba calls these Sankaku Puzzles.

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These are area puzzles.  See that number 3 next to those characters?  That tells you to make a triangle that goes through a subset of those points with an area of 3.

I think the associated instructional images in the PDF file for these puzzles are beautiful.  I'm not going to insert them here because I really do want you to go and check them out!

Google Translate translates this puzzle title as "Looking Triangle."  Not quite sure what that's about...

The PDF file provides you with 42 of these to keep you (or your students) busy.  There are also solutions so you can check your work along the way.  Since the directions are in a foreign language, I try to check my work with the solutions A LOT just to make sure I haven't made any wrong assumptions about the rules of the puzzle.

These would be great for practicing/reviewing finding the area of a triangle.  

Puzzle 3:

Inaba calls this puzzle "Kazu."

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 I have to admit, these puzzles are a bit trickier for me to decode.  See that 2 below the puzzle?  That tells you that you need to create a square that holds exactly 2 apples.  I thought they were pumpkins at first, but Google Translate told me otherwise.  As for the title of this puzzle, Google Translate says it's "Looking for Kaz."  

You also need to know that your square must be 3 x 3.  How are you supposed to know that?  If you look closely at the text above the puzzles, you'll see the number 3 appear twice.

The PDF file for this puzzle contains 42 different puzzles, but I've only figured out how to solve the first 24.  Starting with puzzle 25, there are apples and oranges in the puzzles.  And the numbers go away.  If someone figures out how to do the later puzzles, please let us know in the comments below!  If you want to check your assumptions, here are the solutions.

I think these puzzles would make a great warm-up.  They would also be great to put inside a dry erase pocket (affiliate link) and give to students who finish early and need something to keep their brains stimulated.

Okay.  That's enough for Volume 1.  Come back tomorrow for three more puzzles!


  1. I think I've got Puzzle 3: Kazu. Each puzzle that contains apples and oranges is asking a different question. For example, find the 2x2 (or 3x3) box containing more/less/the same number of apples and oranges. Using Google translate, it is easy enough to figure out if the question is asking for the same number or less. From what I can gather, Google is translating the word meaning "more" into the English word "cover." So questions 25-30 are asking for the 2x2 box containing:
    25. same number of apples and oranges
    26. more oranges than apples
    27. fewer oranges than apples
    28. more apples than oranges
    29. fewer apples than oranges
    30. same number of apples and oranges

    Questions 31-36 are asking the same questions in the same order for the 3x3 box.

    Questions 37-42 are asking for the difference in the number of apples and oranges in each box. So if the difference is 1, the box either contains one more apple than oranges or one less apple than oranges.
    37. the difference in apples and oranges is 1
    38. the difference is 2
    39. the difference is 0
    40. the difference is 1
    41. the difference is 2
    42. the difference is 0

    Hope this helps!
    - Julie

  2. The name of the second one is "Triangle Search" and the third is "Count Search" (where "count" is a noun), from my moderate Japanese ability. It's actually the same word for "search" both times but it's written phonetically in the count search for some reason.