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
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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....?
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?
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 a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
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?
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?
Can you cover the camel with these pieces?
Use the clues to colour each square.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
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?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
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?
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. . . .
An activity making various patterns with 2 x 1 rectangular tiles.
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.
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
How many trains can you make which are the same length as Matt's, using rods that are identical?
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 different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Try this matching game which will help you recognise different ways of saying the same time interval.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Can you find all the different ways of lining up these Cuisenaire
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
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?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Find out what a "fault-free" rectangle is and try to make some of
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
In this maze of hexagons, you start in the centre at 0. The next
hexagon must be a multiple of 2 and the next a multiple of 5. What
are the possible paths you could take?
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
These practical challenges are all about making a 'tray' and covering it with paper.
How many different triangles can you make on a circular pegboard that has nine pegs?