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

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?

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

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

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?

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....?

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

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

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?

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?

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

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?

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?

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?

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?

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?

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

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

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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?

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.

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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?

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

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?

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

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 task follows on from Build it Up and takes the ideas into three dimensions!

This dice train has been made using specific rules. How many different trains can you make?

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

Can you find all the ways to get 15 at the top of this triangle of numbers?

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

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!

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.

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!

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

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?

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?

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

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

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

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?

Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?