How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
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?
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 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.
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?
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?
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?
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 interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Use the clues to colour each square.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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 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?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
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?
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 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
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?
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?
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.
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?
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 cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these
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 work out how to balance this equaliser? You can put more
than one weight on a hook.
An activity making various patterns with 2 x 1 rectangular tiles.
How many different rhythms can you make by putting two drums on the
In how many ways can you stack these rods, following the rules?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
These practical challenges are all about making a 'tray' and covering it with paper.
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
In this town, houses are built with one room for each person. There
are some families of seven people living in the town. In how many
different ways can they build their houses?
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
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?
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the
clues to work out which name goes with each face.
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!