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.
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?
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?
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
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.
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.
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?
Have a go at this game which has been inspired by the Big Internet Math-Off 2019. Can you gain more columns of lily pads than your opponent?
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
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 article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
What happens when you try and fit the triomino pieces into these two grids?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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?
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?
Try this matching game which will help you recognise different ways of saying the same time interval.
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?
Try out the lottery that is played in a far-away land. What is the chance of winning?
How many trapeziums, of various sizes, are hidden in this picture?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
What is the best way to shunt these carriages so that each train can continue its journey?
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.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
This challenge extends the Plants investigation so now four or more children are involved.
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.
Here are some rods that are different colours. How could I make a yellow rod using white and red 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?
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.
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....?
Can you find all the different triangles on these peg boards, and find their angles?
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 put the numbers 1 to 8 into the circles so that the four calculations are correct?
How many different triangles can you make on a circular pegboard that has nine pegs?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Find out about Magic Squares in this article written for students. Why are they magic?!
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
How long does it take to brush your teeth? Can you find the matching length of time?
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
A Sudoku with clues given as sums of entries.