Number Ball Puzzles by Naoki Inaba

Today I want to share a new puzzle I’ve been playing with for the last few days: Naoki Inaba‘s Number Ball Puzzles.

The other day, I set out to try to bring some semblance of order to my puzzles folder on my laptop. This is the place on my computer where I keep PDFs of all the different types of logic puzzles I have come across over my years of browsing the internet. I started collecting these puzzles in college, and I still get excited when I run across a new type of puzzle that I have never seen before.

In this folder, I found a collection of puzzles that I had downloaded from Naoki Inaba’s amazing website (that happens to be written in Japanese). I had planned to run these puzzles through google translate, but I apparently got distracted and promptly forgot about my intended task. I had put a few of these puzzles in a folder named “To Try.” Since we’ve been stuck at home due the ice/snowpocalypse, I decided to print out a set of these puzzles and give them a try.

The first new type of Naoki Inaba puzzle I tried is called Number Ball (ナンバーボール). In this puzzle, you are presented with a square grid. Some of the squares contain numbers in circles. Other squares contain empty circles or x’s.

Here’s my translation of the original Japanese rules: Each row and column must contain balls with one of each of the numbers in the given range. Squares containing a circle must be used. Squares containing an x may not be used.

Inaba provides an example of a puzzle and its solution to help ensure that you understand the rules before beginning.

I was really hoping that I had discovered a new type of puzzle to use in my classroom with my math students. Then, I tried to solve the puzzles myself. I found them much harder than I expected. On my first day of puzzling, I managed to solve exactly ONE of the number ball puzzles. Of the five puzzles provided by Inaba, I could only work out a solution to the SMALLEST puzzle.

The next night after the toddler was put to bed, I pulled my clipboard of puzzles back out. This time, I was able to solve the next three puzzles. But, the last and largest puzzle proved to be a huge stumper. I tried several methods of solving it and ended up doing a lot of erasing and starting over in hopes that I would find some sort of clue that I had overlooked.

Tonight, I decided to have one more go at solving these number ball puzzles. I thought that maybe I had overlooked some strategy in solving the smaller puzzles that I needed to solve the largest puzzle.

I printed off a fresh set of number ball puzzles. Then, I set about to resolve the puzzles I had previously solved the previous two nights. I did make one slight change. I started by solving the small example puzzle that Inaba had originally provided a worked solution for. I made my way through each of the previously solved puzzles. My experience made the puzzle solving much smoother, but I still found them to be quite tricky at times.

Then, I tackled the largest puzzle. Halfway through solving it, I had an epiphany that ended up helping me break through my puzzle solving roadblock.

I really enjoyed solving these puzzles, but I think there are many other puzzles by Naoki Inaba that are more suitable for use in the secondary classroom. Still, I am sharing my English translation of these puzzles here on my blog in case you want to try your hand at solving these yourselves. I found them a very satisfying puzzle to solve. I think you will, too.

Instead of including a worked example like Inaba did in his PDF of the puzzles, I have placed the example puzzle as the first puzzle to be solved.

If you do want to try these with kids, I think the first two puzzles are quite accessible to students. The third and subsequent puzzles will likely give your students much frustration. Though, maybe they will discover a solving method that I somehow overlooked? I have a feeling my students will take their normal approach to solving such puzzles and bypass the logical thinking step to jump straight into writing random numbers into boxes…

I would like to emphasize that you should try these puzzles out yourself BEFORE using them with students! These puzzles are difficult, but they are not impossible. Productive struggle is a good thing. You need to know your students and how much struggle is productive and how much struggle is overwhelming/crippling.