This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?

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?

A little mouse called Delia lives in a hole in the bottom of a tree.....How many days will it be before Delia has to take the same route again?

We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?

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.

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?

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

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.

Find all the numbers that can be made by adding the dots on two dice.

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Can you make square numbers by adding two prime numbers together?

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.

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?

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

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 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?

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?

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

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.

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

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

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?

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?

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?

What could the half time scores have been in these Olympic hockey matches?

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

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

The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

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

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?

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.

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

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?

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?

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

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

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?

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

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?

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?

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?

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?