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?

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

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

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?

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?

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

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!

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?

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?

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?

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?

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

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

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

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

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

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.

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?

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.

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

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!

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?

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

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

Can you use the information to find out which cards I have used?

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

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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 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?

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.

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?

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

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?

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?

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

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

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

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?

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.

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?

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?