The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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.
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?
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.
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?
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
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.
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
Find out what a "fault-free" rectangle is and try to make some of
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 information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
Start with three pairs of socks. Now mix them up so that no
mismatched pair is the same as another mismatched pair. Is there
more than one way to do it?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
A Sudoku with clues given as sums of entries.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
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.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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?
Find out about Magic Squares in this article written for students. Why are they magic?!
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
This challenge is about finding the difference between numbers which have the same tens digit.
Seven friends went to a fun fair with lots of scary rides. They
decided to pair up for rides until each friend had ridden once with
each of the others. What was the total number rides?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
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. . . .
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?
This challenge extends the Plants investigation so now four or more children are involved.
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?
In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way
to share the sweets between the three children so they each get the
kind they like. Is there more than one way to do it?
Can you find all the different triangles on these peg boards, and
find their angles?
In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?
Find all the numbers that can be made by adding the dots on two dice.
Imagine that the puzzle pieces of a jigsaw are roughly a
rectangular shape and all the same size. How many different puzzle
pieces could there be?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
My coat has three buttons. How many ways can you find to do up all
Two children made up a game as they walked along the garden paths.
Can you find out their scores? Can you find some paths of your own?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
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?
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 fill in the empty boxes in the grid with the right shape