What is the best way to shunt these carriages so that each train
can continue its journey?
Can you shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
10 space travellers are waiting to board their spaceships. There
are two rows of seats in the waiting room. Using the rules, where
are they all sitting? Can you find all the possible ways?
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?
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.
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
Starting with four different triangles, imagine you have an
unlimited number of each type. How many different tetrahedra can
you make? Convince us you have found them all.
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?
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.
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?
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?
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?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
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 are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
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?
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
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 of fitting five hexagons
together? How will you know you have found all the ways?
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.
Find out what a "fault-free" rectangle is and try to make some of
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
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.
These practical challenges are all about making a 'tray' and covering it with paper.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
Can you find all the different ways of lining up these Cuisenaire
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
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?
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
An activity making various patterns with 2 x 1 rectangular tiles.
How many different triangles can you make on a circular pegboard that has nine pegs?
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 dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?