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

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

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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....?

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

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

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

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

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

Can you find all the different ways of lining up these Cuisenaire rods?

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

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

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

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

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

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

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?

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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 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?

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

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

An activity making various patterns with 2 x 1 rectangular tiles.

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?

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

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?

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

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?

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

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

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

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

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

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

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?

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?

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?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

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?

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?

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 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!

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?

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