Working systematically

This train line has two tracks which cross at different points. Can you find all the routes that end at Cheston?

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

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?

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

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.

Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column