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

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

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.

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

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.

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

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

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

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?

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

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

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

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

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?

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?

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.

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

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?

How many different triangles can you make on a circular pegboard that has nine pegs?

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?

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

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?

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?

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

How many models can you find which obey these rules?

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

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

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

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. . . .

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

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

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.

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?

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.

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

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?

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.

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

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

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

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

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?

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.

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?

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

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?

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

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.