Working systematically

problem

Bent Out of Shape

Age

14 to 18

Challenge level

2 out of 3

An introduction to bond angle geometry.
problem

Magic Caterpillars

Age

14 to 18

Challenge level

3 out of 3

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
problem

Plate Spotting

Age

7 to 11

Challenge level

3 out of 3

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?
problem

Octa Space

Age

7 to 11

Challenge level

3 out of 3

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?
problem

Knights Moving

Age

16 to 18

Challenge level

3 out of 3

Can you swap the black knights with the white knights in the minimum number of moves?
problem

One Out One Under

Age

14 to 16

Challenge level

3 out of 3

Imagine a stack of numbered cards with one on top. Discard the top, put the next card to the bottom and repeat continuously. Can you predict the last card?
problem

Homes

Age

5 to 7

Challenge level

1 out of 3

Six new homes are being built! They can be detached, semi-detached or terraced houses. How many different combinations of these can you find?
problem

Red Express Train

Age

5 to 7

Challenge level

1 out of 3

The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?
problem

The School Trip

Age

5 to 7

Challenge level

1 out of 3

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?
problem

Fair Exchange

Age

5 to 7

Challenge level

1 out of 3

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?