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

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

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

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

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

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

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?

Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.

How many models can you find which obey these rules?

What is the best way to shunt these carriages so that each train can continue its journey?

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

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

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

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

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?

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

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

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

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

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

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.

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

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 work out how to balance this equaliser? You can put more than one weight on a hook.

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

Investigate the different ways you could split up these rooms so that you have double the number.

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

An activity making various patterns with 2 x 1 rectangular tiles.

In how many ways can you stack these rods, following the rules?

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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