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....?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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
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?
Can you find all the different ways of lining up these Cuisenaire
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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?
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?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
In this matching game, you have to decide how long different events take.
In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?
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 triangles can you make on the 3 by 3 pegboard?
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
Systematically explore the range of symmetric designs that can be
created by shading parts of the motif below. Use normal square
lattice paper to record your results.
How many rectangles can you find in this shape? Which ones are
differently sized and which are 'similar'?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Alice and Brian are snails who live on a wall and can only travel
along the cracks. Alice wants to go to see Brian. How far is the
shortest route along the cracks? Is there more than one way to go?
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
The Vikings communicated in writing by making simple scratches on
wood or stones called runes. Can you work out how their code works
using the table of the alphabet?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
On a digital clock showing 24 hour time, over a whole day, how many
times does a 5 appear? Is it the same number for a 12 hour clock
over a whole day?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
Investigate the different ways you could split up these rooms so
that you have double the number.
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
In the planet system of Octa the planets are arranged in the shape
of an octahedron. How many different routes could be taken to get
from Planet A to Planet Zargon?
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
This challenge is to design different step arrangements, which must
go along a distance of 6 on the steps and must end up at 6 high.
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
You cannot choose a selection of ice cream flavours that includes
totally what someone has already chosen. Have a go and find all the
different ways in which seven children can have ice cream.
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
Can you draw a square in which the perimeter is numerically equal
to the area?