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 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
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?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
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?
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?
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 many trains can you make which are the same length as Matt's, using rods that are identical?
How many different triangles can you make on a circular pegboard that has nine pegs?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
How many different rhythms can you make by putting two drums on the
What happens when you try and fit the triomino pieces into these
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
Can you cover the camel with these pieces?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
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....?
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
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
When newspaper pages get separated at home we have to try to sort
them out and get things in the correct order. How many ways can we
arrange these pages so that the numbering may be different?
Can you find all the different ways of lining up these Cuisenaire
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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 triangles can you make on the 3 by 3 pegboard?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
Investigate the different ways you could split up these rooms so
that you have double the number.
An activity making various patterns with 2 x 1 rectangular tiles.
Can you find all the different triangles on these peg boards, and
find their angles?
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 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?
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.
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?