In a previous post, I shared instructions, tutorials, and links for introducing two types of Japanese number logic puzzles to your students: Kakuro and Futoshiki. Here are two additional types that are also less well known, along with tutorials and free resources you can use in your classroom.
Hashiwokakero or Hashi o kakero means “building bridges” in Japanese, and is usually known as “Hashi” or “Bridges.” In this puzzle, you are presented with numbers that must be connected with lines, or bridges. Between any two numbers, either ONE line (bridge) or TWO lines (bridges) can be drawn. However, the number of lines drawn from any number must equal that number.
Before creating a tutorial, I decided to check to see if there was a good one out there. Why reinvent the wheel? I was happy to find the video below, created by algebra teacher Mike DeVor, who does an excellent job explaining how to logically solve this kind of puzzle.
You can find interactive online “Bridges” puzzles, and also printable versions at KrazyDad, Jim Bumgardner’s puzzle site. He generously shares these puzzles free of charge, asking only for donations by those who wish to show their thanks!
Another type of Japanese number logic puzzle is Hitori, which means ” alone,” as in “leave me alone!” The goal in solving this puzzle is similar to Sudoku, but rather than writing digits in the cells, the numbers are already in place, and you must eliminate them so that no number appears more than once in a column or row. There are a few other rules involved as well. Eliminated (shaded) numbers may not be adjacent, vertically or horizontally, and remaining (unshaded) numbers cannot be “cut off” and isolated from the rest of the puzzle.
I created this tutorial to introduce Hitori to students. You can also view the video here.
You can find daily online Hitori puzzles as well as other types of puzzles and brainteasers on the BrainBashers website and printable ones here. If you print them out, I recommend putting them in sheet protectors and solving with dry erase markers! This allows students to reuse puzzles and they can be kept in a classroom logic center (see “Kid-Created Logic Puzzles”).
If you need a rationale for doing these types of puzzles with your students, this NCTM article by Assistant Professor Jeffrey Wanko elaborates on his work with math students. He believes working these types of logical puzzles can improve deductive reasoning and help students both organize and better articulate their thinking as they solve problems.
Please leave a comment and share your experience with using these types of puzzles in your classroom. Also, if you are aware of other online resources that provide puzzle sets, let us know! As always, I encourage you to subscribe if you’d like to receive regular updates of new resources listed.