Find out about Magic Squares in this article written for students. Why are they magic?!
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
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.
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.
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
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.
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
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?
Try this matching game which will help you recognise different ways of saying the same time interval.
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
How many different shapes can you make by putting four right-
angled isosceles triangles together?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
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?
My coat has three buttons. How many ways can you find to do up all
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Investigate the different ways you could split up these rooms so
that you have double the number.
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
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
In this maze of hexagons, you start in the centre at 0. The next
hexagon must be a multiple of 2 and the next a multiple of 5. What
are the possible paths you could take?
Find out what a "fault-free" rectangle is and try to make some of
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
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?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Explore the different snakes that can be made using 5 cubes.
Chandra, Jane, Terry and Harry ordered their lunches from the
sandwich shop. Use the information below to find out who ordered
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?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
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?
An investigation that gives you the opportunity to make and justify
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.
This task follows on from Build it Up and takes the ideas into three dimensions!
Can you find all the ways to get 15 at the top of this triangle of numbers?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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?
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?
How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
The brown frog and green frog want to swap places without getting
wet. They can hop onto a lily pad next to them, or hop over each
other. How could they do it?
Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?
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?
What two-digit numbers can you make with these two dice? What can't you make?