Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

Design an arrangement of display boards in the school hall which fits the requirements of different people.

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

What is the best way to shunt these carriages so that each train can continue its journey?

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

How will you go about finding all the jigsaw pieces that have one peg and one hole?

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

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

How many different triangles can you make on a circular pegboard that has nine pegs?

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

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

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

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

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

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

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

If you had 36 cubes, what different cuboids could you make?

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

Try this matching game which will help you recognise different ways of saying the same time interval.

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

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

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

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

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 possible answers?

Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.

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

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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 are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

In this matching game, you have to decide how long different events take.

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?

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

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