**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!

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.