Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
How many trains can you make which are the same length as Matt's, using rods that are identical?
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?
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?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Use the clues to colour each square.
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?
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 greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
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?
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?
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
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
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
Design an arrangement of display boards in the school hall which fits the requirements of different people.
What happens when you try and fit the triomino pieces into these
Can you cover the camel with these pieces?
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 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 put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
If you have three circular objects, you could arrange them so that
they are separate, touching, overlapping or inside each other. Can
you investigate all the different possibilities?
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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?
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?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
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.
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Find out what a "fault-free" rectangle is and try to make some of
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Can you find all the different ways of lining up these Cuisenaire
How many different rhythms can you make by putting two drums on the
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?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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 the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?
Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column
What is the least number of moves you can take to rearrange the
bears so that no bear is next to a bear of the same colour?