This article for primary teachers suggests ways in which to help children become better at working systematically.
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 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?
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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?
Find out what a "fault-free" rectangle is and try to make some of
This challenge is about finding the difference between numbers which have the same tens digit.
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.
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.
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.
In this town, houses are built with one room for each person. There
are some families of seven people living in the town. In how many
different ways can they build their houses?
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?
What happens when you try and fit the triomino pieces into these
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 ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
My coat has three buttons. How many ways can you find to do up all
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
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?
Find out about Magic Squares in this article written for students. Why are they magic?!
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
This challenge extends the Plants investigation so now four or more children are involved.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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?
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?
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
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?
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?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
How many trains can you make which are the same length as Matt's, using rods that are identical?
Can you fill in the empty boxes in the grid with the right shape
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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?
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?