Design an arrangement of display boards in the school hall which fits the requirements of different people.
What is the best way to shunt these carriages so that each train
can continue its journey?
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?
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
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?
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?
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?
Use the clues to colour each square.
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?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
Can you cover the camel with these pieces?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
What happens when you try and fit the triomino pieces into these
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?
These practical challenges are all about making a 'tray' and covering it with paper.
This problem focuses on Dienes' Logiblocs. What is the same and
what is different about these pairs of shapes? Can you describe the
shapes in the picture?
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 find all the different ways of lining up these Cuisenaire
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?
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 work out how to balance this equaliser? You can put more
than one weight on a hook.
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
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?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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?
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?
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.
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 many triangles can you make on the 3 by 3 pegboard?
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?
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?
El Crico the cricket has to cross a square patio to get home. He
can jump the length of one tile, two tiles and three tiles. Can you
find a path that would get El Crico home in three jumps?
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?
Chandra, Jane, Terry and Harry ordered their lunches from the
sandwich shop. Use the information below to find out who ordered
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?
If we had 16 light bars which digital numbers could we make? How
will you know you've found 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.
Investigate the different ways you could split up these rooms so
that you have double the number.
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....?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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?