### Instant Insanity

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

### Pattern of Islands

In how many distinct ways can six islands be joined by bridges so that each island can be reached from every other island...

### Only Connect

The graph represents a salesman’s area of activity with the shops that the salesman must visit each day. What route around the shops has the minimum total distance?

# Tourism

##### Stage: 3 Challenge Level:

If you can copy a network

• without lifting your pen off the paper

• without drawing any line twice

then it is traversable.

Decide which of these diagrams are traversable.

If you end up where you started when you draw a traversable diagram it is called a traversing circuit .

If you don't end up where you started when you draw a traversable diagram it is called a traversing path.

Can you give a set of criteria for determining whether a diagram is traversable by a path or a circuit or neither?