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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!

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

MP3 Work together!

This is collaborative problem solving in which students discuss their strategies to solve a problem and identify missteps in a failed solution. MathPickle recommends pairing up students for all its puzzles.

MP6 Be precise!

This is where our 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!

One of the things that the human brain does very well is identify pattern. We sometimes do this too well and identify patterns that don't really exist.


Please use MathPickle in your classrooms. If you have improvements to make, please contact us. We'll give you credit 😉

Gordon Hamilton

(MMath, PhD)


Lora Saarnio