Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?

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

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

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

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?

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

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 the empty boxes in the grid with the right shape and colour?

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

A challenging activity focusing on finding all possible ways of stacking rods.

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?

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

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?

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

This challenge extends the Plants investigation so now four or more children are involved.

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?

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?

How many different shapes can you make by putting four right- angled isosceles triangles together?

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

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

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

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?

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

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

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

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?

Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?

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

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

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?

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

Can you find out in which order the children are standing in this line?

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.

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

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

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

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

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

Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?

This challenge is about finding the difference between numbers which have the same tens digit.

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

The brown frog and green frog want to swap places without getting wet. They can hop onto a lily pad next to them, or hop over each other. How could they do it?

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

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?

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?