Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Can you find all the different ways of lining up these Cuisenaire
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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.
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Can you cover the camel with these pieces?
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?
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?
What happens when you try and fit the triomino pieces into these
Use the clues to colour each square.
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.
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?
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 smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
Investigate the different ways you could split up these rooms so
that you have double the number.
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?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
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?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
Put 10 counters in a row. Find a way to arrange the counters into
five pairs, evenly spaced in a row, in just 5 moves, using the
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?
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
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
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?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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 triangles can you make on the 3 by 3 pegboard?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
How many models can you find which obey these rules?
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?
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?
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
In how many ways can you stack these rods, following the rules?
These practical challenges are all about making a 'tray' and covering it with paper.
Design an arrangement of display boards in the school hall which fits the requirements of different people.
In this matching game, you have to decide how long different events take.