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.
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?
A challenging activity focusing on finding all possible ways of stacking rods.
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.
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
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.
This challenge extends the Plants investigation so now four or more children are involved.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
Try out the lottery that is played in a far-away land. What is the chance of winning?
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Can you use the information to find out which cards I have used?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.
Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
Can you find all the different ways of lining up these Cuisenaire rods?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
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....?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
Use the clues to colour each square.
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Follow the clues to find the mystery number.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?
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 is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
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?
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 triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?