# Zome Theorems

## Theorem 1

*In any connected Zome structure, all of the balls will have the
same orientation in space.*

### Proof Sketch

A proof by induction on the number of balls is pretty easy to see.
It hinges on the following key observations: 1) The two balls on
either end of a single stick have the same orientation. 2) In a
connected structure, each ball is connected to some other ball, and
then to another ball, and so on.

## Theorem 2

*There are never enough Zome pieces.*

### Proof

The proof of this theorem is by excessive experimentation. The
more you experiment with Zome, the more you'll find yourself running
out of pieces before you can finish a particular shape.

## Theorem 3

*There is no such thing as "the last dandelion in your yard".
*

### Proof

By observation, of course. This has nothing to do with Zome, but
I'm a homeowner and it's dandelion season and I just had to vent
*somewhere*.

Tom Magliery

tom@magliery.com