### Delia's Routes

A little mouse called Delia lives in a hole in the bottom of a tree.....How many days will it be before Delia has to take the same route again?

### Redblue

Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?

### Diagonal Trace

You can trace over all of the diagonals of a pentagon without lifting your pencil and without going over any more than once. Can the same thing be done with a hexagon or with a heptagon?

# Rail Network

### Why do this problem?

This problem encourages children to work systematically and use trial and improvement. You could print off this sheet for learners to work on.

### Key questions

Can you find a way to the middle?
Which stations did you visit more than once?
Can you find another way?
Can you find a way which only visits each station once?

### Possible extension

Pupils could try Paw Prints as a follow-up to this problem.

### Possible support

This sheet will allow children to record their different routes.