How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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?
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
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?
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?
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?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Use the clues to colour each square.
Can you cover the camel with these pieces?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
What is the least number of moves you can take to rearrange the
bears so that no bear is next to a bear of the same colour?
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?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
What happens when you try and fit the triomino pieces into these
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
Systematically explore the range of symmetric designs that can be
created by shading parts of the motif below. Use normal square
lattice paper to record your results.
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.
Use the clues about the symmetrical properties of these letters to
place them on the grid.
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?
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?
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.
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?
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?
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?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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
A challenging activity focusing on finding all possible ways of stacking rods.
In how many ways can you stack these rods, following the rules?
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?
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 rhythms can you make by putting two drums on the
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.
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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.
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?
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
In the planet system of Octa the planets are arranged in the shape
of an octahedron. How many different routes could be taken to get
from Planet A to Planet Zargon?
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
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?
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?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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?