Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
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.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
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?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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.
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?
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.
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 put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?
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. . . .
My coat has three buttons. How many ways can you find to do up all the buttons?
Try out the lottery that is played in a far-away land. What is the chance of winning?
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?
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?
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?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.
How many trains can you make which are the same length as Matt's, using rods that are identical?
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?
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.
Can you find out in which order the children are standing in this line?
Use the clues to colour each square.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?
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 greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Can you find all the different ways of lining up these Cuisenaire rods?
Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
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?
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
Try this matching game which will help you recognise different ways of saying the same time interval.
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?