Station C
A Sneak Peek at a Weird Machine

There is an island of weird machines for us to explore later, but why not have a sneak peek at a weird machine right now?

Let’s go!

Question 1

This is a $2 \leftarrow 3$ machine.
It follows the rule that whenever there are three dots in a box, they explode away to be replaced with two dots, one box to their left.

Here are ten dots loaded into a $2 \leftarrow 3$ machine.
What code for ten does the machine give?

Question 2

Work out the $2 \leftarrow 3$ codes for the numbers one up to twenty (or higher if you like) and record them on a piece of paper.
I have some questions about these codes next.

What patterns do you see in these codes?
Does it make sense that the final digits of the codes cycle $1, 2, 0, 1, 2, 0, ...$ ?
After a while do all the codes begin with a $2$ ? Begin with $21$ ? Begin with … ?
We’ll definitely come back to this weird machine later on!