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?
Can you cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these
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?
Explore the different snakes that can be made using 5 cubes.
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?
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 shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
How many models can you find which obey these rules?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
Use the clues to colour each square.
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
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
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.
Design an arrangement of display boards in the school hall which fits the requirements of different people.
These practical challenges are all about making a 'tray' and covering it with paper.
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
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?
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?
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
Can you find out in which order the children are standing in this
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
My coat has three buttons. How many ways can you find to do up all
Lorenzie was packing his bag for a school trip. He packed four
shirts and three pairs of pants. "I will be able to have a
different outfit each day", he said. How many days will Lorenzie be
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 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.
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?
Can you find all the different ways of lining up these Cuisenaire
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?
When newspaper pages get separated at home we have to try to sort
them out and get things in the correct order. How many ways can we
arrange these pages so that the numbering may be different?
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?
Put 10 counters in a row. Find a way to arrange the counters into
five pairs, evenly spaced in a row, in just 5 moves, using the
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Investigate the different ways you could split up these rooms so
that you have double the number.
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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.
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 different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
When intergalactic Wag Worms are born they look just like a cube.
Each year they grow another cube in any direction. Find all the
shapes that five-year-old Wag Worms can be.
My briefcase has a three-number combination lock, but I have
forgotten the combination. I remember that there's a 3, a 5 and an
8. How many possible combinations are there to try?
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.