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?

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.

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.

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

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

Use the clues about the symmetrical properties of these letters to place them on the grid.

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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

A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.

This challenge extends the Plants investigation so now four or more children are involved.

A challenging activity focusing on finding all possible ways of stacking rods.

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?

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

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

How many solutions can you find to this sum? Each of the different letters stands for a different number.

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

Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.

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?

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

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?

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?

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

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

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?

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

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

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?

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

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?

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

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?

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

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

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

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?

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

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?

These practical challenges are all about making a 'tray' and covering it with paper.

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

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?

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

Have a go at balancing this equation. Can you find different ways of doing it?

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

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