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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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.
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?
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?
This challenge is about finding the difference between numbers which have the same tens digit.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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.
Find all the numbers that can be made by adding the dots on two dice.
Can you fill in the empty boxes in the grid with the right shape
Can you find all the different triangles on these peg boards, and
find their angles?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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?
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 find all the different ways of lining up these Cuisenaire
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?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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 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?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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?
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
Can you rearrange the biscuits on the plates so that the three
biscuits on each plate are all different and there is no plate with
two biscuits the same as two biscuits on another plate?
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?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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?
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.
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?