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?

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

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

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

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?

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.

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?

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

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

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?

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

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

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....?

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

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

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

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.

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?

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

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

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

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

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?

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?

How many different rhythms can you make by putting two drums on the wheel?

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

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

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

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?

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 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.

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?

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

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

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?

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?

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?

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

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?

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

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?

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

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?

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