Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

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

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Use these head, body and leg pieces to make Robot Monsters which are different heights.

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

Find your way through the grid starting at 2 and following these operations. What number do you end on?

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?

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

You have 5 darts and your target score is 44. How many different ways could you score 44?

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

Using the statements, can you work out how many of each type of rabbit there are in these pens?

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

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

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

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?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

My coat has three buttons. How many ways can you find to do up all the buttons?

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

What happens when you try and fit the triomino pieces into these two grids?

Investigate the different ways you could split up these rooms so that you have double the number.

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

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?