**Prime Number Catacombs**

##### (William Paulsen, 2000)

This is absolutely one of my favourite pedagogic discoveries from recreational mathematics. It is engaging, evocative and curiosity inducing. I now prefer to start students groups off at different numbers. They must try to meet. Good starting numbers are: 2, 11, 17, 31, 37, and 79.

Here is a pdf file – the last three sheets are suitable for printing. The first are suitable for presentation.

PS. Warning: This problem requires students to learn binary! Most curricula have this appearing years after students learn about prime numbers.

Nothing must be advanced in a positive manner. The mind of the ** pupil** is to be the principal operator; it must instruct, convince, and confute

*itself**;*and when it arrives at some important truth or result, it must be through its own powers. It ought not even to perceive that it has been guided thither.

**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?