Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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
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.
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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.
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?
Use the clues to colour each square.
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.
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
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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Can you cover the camel with these pieces?
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?
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
How many models can you find which obey these rules?
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?
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?
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 work out how to balance this equaliser? You can put more
than one weight on a hook.
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 happens when you try and fit the triomino pieces into these
What is the best way to shunt these carriages so that each train
can continue its journey?
Here are four cubes joined together. How many other arrangements of
four cubes can you find? Can you draw them on dotty paper?
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 many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
A game for 2 people. Take turns placing a counter on the star. You
win when you have completed a line of 3 in your colour.
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
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.
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?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
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?
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
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
How many trains can you make which are the same length as Matt's, using rods that are identical?
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?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
These practical challenges are all about making a 'tray' and covering it with paper.
My coat has three buttons. How many ways can you find to do up all
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
How many different triangles can you make on a circular pegboard that has nine pegs?
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....?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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?