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?
What is the best way to shunt these carriages so that each train
can continue its journey?
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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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?
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
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
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?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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?
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?
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?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
These practical challenges are all about making a 'tray' and covering it with paper.
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
How many models can you find which obey these rules?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Investigate the different ways you could split up these rooms so
that you have double the number.
In how many ways can you stack these rods, following the rules?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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
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?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
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.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
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?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
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!
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Can you substitute numbers for the letters in these sums?
This dice train has been made using specific rules. How many different trains can you make?
Can you find all the ways to get 15 at the top of this triangle of numbers?
This task follows on from Build it Up and takes the ideas into three dimensions!
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?
Ben has five coins in his pocket. How much money might he have?
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?