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.
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?
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?
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
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?
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
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?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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?
Use the clues to colour each square.
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?
Can you use the information to find out which cards I have used?
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
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 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
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?
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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Can you find out in which order the children are standing in this line?
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?
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?
Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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.
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. . . .
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'.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
My coat has three buttons. How many ways can you find to do up all the buttons?
This challenge extends the Plants investigation so now four or more children are involved.
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
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.
El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?
There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
What happens when you try and fit the triomino pieces into these two grids?
Can you cover the camel with these pieces?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Find your way through the grid starting at 2 and following these operations. What number do you end on?
This challenge is about finding the difference between numbers which have the same tens digit.
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?
In this matching game, you have to decide how long different events take.
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.