This article for primary teachers suggests ways in which to help children become better at working systematically.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
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.
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.
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?
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.
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?
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.
My coat has three buttons. How many ways can you find to do up all
How many different rhythms can you make by putting two drums on the
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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....?
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. . . .
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?
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?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
Find out what a "fault-free" rectangle is and try to make some of
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?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
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
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
How many different triangles can you make on a circular pegboard that has nine pegs?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
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?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Can you find all the different triangles on these peg boards, and
find their angles?
Can you find all the different ways of lining up these Cuisenaire
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?
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.
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Find all the numbers that can be made by adding the dots on two dice.
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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.
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 trains can you make which are the same length as Matt's, using rods that are identical?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
Can you fill in the empty boxes in the grid with the right shape
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?