Working systematically

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

What could the half time scores have been in these Olympic hockey matches?

Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?

My dice has inky marks on each face. Can you find the route it has taken? What does each face look like?

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.