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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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 put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
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 eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight 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
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
A Sudoku with clues as ratios or fractions.
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....?
What is the best way to shunt these carriages so that each train
can continue its journey?
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.
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?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
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?
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?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
A Sudoku with clues as ratios.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
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?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Can you find all the different triangles on these peg boards, and
find their angles?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Can you recreate these designs? What are the basic units? What
movement is required between each unit? Some elegant use of
procedures will help - variables not essential.
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.
A mathematician goes into a supermarket and buys four items. Using
a calculator she multiplies the cost instead of adding them. How
can her answer be the same as the total at the till?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Find out what a "fault-free" rectangle is and try to make some of
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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?
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?
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
In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way
to share the sweets between the three children so they each get the
kind they like. Is there more than one way to do it?
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?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?