How many different rhythms can you make by putting two drums on the
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
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?
Use the clues to colour each square.
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
How many different triangles can you make on a circular pegboard that has nine pegs?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
An activity making various patterns with 2 x 1 rectangular tiles.
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?
What is the best way to shunt these carriages so that each train
can continue its journey?
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 triangles can you draw on the dotty grid which each have one dot in the middle?
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?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
How many trains can you make which are the same length as Matt's, using rods that are identical?
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
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....?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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?
These practical challenges are all about making a 'tray' and covering it with paper.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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?
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 find all the different ways of lining up these Cuisenaire
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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.
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?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
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?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.