How many models can you find which obey these rules?
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?
Can you cover the camel with these pieces?
Use the clues to colour each square.
What is the best way to shunt these carriages so that each train
can continue its journey?
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
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.
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.
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?
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?
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.
What happens when you try and fit the triomino pieces into these
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
How many different rhythms can you make by putting two drums on the
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
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 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?
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?
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?
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?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
My coat has three buttons. How many ways can you find to do up all
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....?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
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?
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?
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?
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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
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.
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
How many different triangles can you make on a circular pegboard
that has nine pegs?
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?
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?
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?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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
Here are four cubes joined together. How many other arrangements of
four cubes can you find? Can you draw them on dotty paper?
How many triangles can you make on the 3 by 3 pegboard?
The Red Express Train usually has five red carriages. How many ways
can you find to add two blue carriages?
Explore the different snakes that can be made using 5 cubes.
Take three differently coloured blocks - maybe red, yellow and
blue. Make a tower using one of each colour. How many different
towers can you make?
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?
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?