Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

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.

This challenge involves calculating the number of candles needed on birthday cakes. It is an opportunity to explore numbers and discover new things.

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

Can you find the chosen number from the grid using the clues?

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

How many trains can you make which are the same length as Matt's, using rods that are identical?

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

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

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

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?

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

Find out what a "fault-free" rectangle is and try to make some of your own.

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

Try out the lottery that is played in a far-away land. What is the chance of winning?

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?

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

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

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

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

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

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?

If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

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

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

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

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!

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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?

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

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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