In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

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?

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?

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

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?

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?

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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

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

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?

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

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

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

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?

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

What happens when you round these three-digit numbers to the nearest 100?

What two-digit numbers can you make with these two dice? What can't you make?

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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?

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

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?

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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?

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

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!

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?

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?

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

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?

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?

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

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?

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 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?

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

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?

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

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.

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

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!

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