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Mimizu means earthworm in Japanese. Your goal is to digest leaves and other stuff that is in your compost bin. Number hints are given as well as black barriers which cannot be crossed.

After stepping through these slides click here to download printable mimizu puzzles.

You must eat all the leaf. This didn't work.

This is better because we ate through the whole leaf, but unfortunately there are other rules...

No Barrier Rule:

There must be no barrier between two numbers which share a common prime factor. 10 and 14 share a common prime factor of 2, so there should be no barrier between them. Our path is wrong.

Yes Barrier Rule:

There must be a barrier between two non-consecutive numbers which lack a common prime factor. 2 and 11  do not share a common prime factor, so there must be a barrier between them. Our path is wrong for a second reason.


Consecutive numbers never have a barrier between them.

Even though this path is wrong, there are some things which work. 9 and 15 have a common prime factor of 3. There must not be a barrier between them and indeed there is not. Good.


(MathPickle, 2012)

Download Mimizu puzzles to try to solve in front of whole classroom here.

Download Mimizu puzzle-sheets here.

Download puzzles created by other students and a design-your-own template here.

Download larger template to design your own puzzles here.

Email me for extra puzzles.

The video above right is from a long time ago – before Mimizu were given the interesting leaf shapes. If your class experiments with Mimizu and develops their own puzzles – please email them with the solution sheet. I ask for the latter only because the number of errors in student work can be large and a single omission of a line between two Mimizu hexagons can result in thirty minutes of searching for an answer that doesn’t exist. I like to do that kind of thing to my students, but when I give an impossible puzzle it is usually on purpose and I’m there to make sure frustration levels are kept to reasonable 😉

Standards for Mathematical Practice

MathPickle puzzle and game designs engage a wide spectrum of student abilities while targeting the following Standards for Mathematical Practice:

MP1 Toughen up!

Students develop grit and resiliency in the face of nasty, thorny problems. It is the most sought after skill for our students.

MP2 Think abstractly!

Students take problems and reformat them mathematically. This is helpful because mathematics lets them use powerful operations like addition.

MP3 Work together!

Students discuss their strategies to collaboratively solve a problem and identify missteps in a failed solution. MathPickle recommends pairing up students for all its puzzles.

MP4 Model reality!

Students create a model that mimics the real world. Discoveries made by manipulating the model often hint at something in the real world.

MP5 Know the tools.

Students master the tools at their fingertips - whether it's a pencil or an online app. 

MP6 Be precise!

Students learn to communicate using precise terminology. MathPickle encourages students not only to use the precise terms of others, but to invent and rigorously define their own terms.

MP7 Be observant!

Students learn to identify patterns. This is one of the things that the human brain does very well. We sometimes even identify patterns that don't really exist 😉

MP8 Be lazy!?!

Students learn to seek for shortcuts. Why would you want to add the numbers one through a hundred if you can find an easier way to do it?


Please use MathPickle in your classrooms. If you have improvements to make, please contact me. I'll give you credit and kudos 😉 For a free poster of MathPickle's ideas on elementary math education go here.

Gordon Hamilton

(MMath, PhD)