How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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?
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
A challenging activity focusing on finding all possible ways of stacking 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?
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?
What is the best way to shunt these carriages so that each train
can continue its journey?
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?
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?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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?
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 from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
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?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
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.
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 numbers 1 to 8 into the circles so that the four
calculations are correct?
How many different symmetrical shapes can you make by shading triangles or squares?
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....?
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.
An activity making various patterns with 2 x 1 rectangular tiles.
Can you find all the different ways of lining up these Cuisenaire
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Use the interactivity to play two of the bells in a pattern. How do
you know when it is your turn to ring, and how do you know which
bell to ring?
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?
Can you coach your rowing eight to win?
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
A Sudoku with clues as ratios.
Investigate the different ways you could split up these rooms so
that you have double the number.
This article for teachers describes several games, found on the
site, all of which have a related structure that can be used to
develop the skills of strategic planning.
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?
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
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
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
The letters of the word ABACUS have been arranged in the shape of a
triangle. How many different ways can you find to read the word
ABACUS from this triangular pattern?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?