### Counting Counters

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

### Cuisenaire Squares

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

### Doplication

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

# Simple Train Journeys

##### Age 5 to 11Challenge Level

Well, here's a train route. The train starts at the top and makes a number of visits to the stations.
Now let's suppose that the train is going to make visits to three stations (they do not have to be different stations - each station can be visited several times!).
So the first station would be Dorby - this will always be the case! (Why?)
Then the train can go on to Ender. When at Ender it could return and visit Dorby again OR it could go on to Floorin.
So two different journeys:
Dorby - Ender - Floorin
Dorby - Ender - Dorby

Your challenge is to find all the different journeys for visiting four stations.

You could then go on to find all the different journeys for visiting more stations - try five.