Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
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?
Use the clues to colour each square.
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?
Can you cover the camel with these pieces?
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 rhythms can you make by putting two drums on the
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
What happens when you try and fit the triomino pieces into these
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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....?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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 find all the different ways of lining up these Cuisenaire
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?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
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?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
An activity making various patterns with 2 x 1 rectangular tiles.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
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?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
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?
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
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?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
What is the best way to shunt these carriages so that each train
can continue its journey?
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?
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 many different triangles can you draw on the dotty grid which each have one dot in the middle?
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
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 triangles can you make on a circular pegboard that has nine pegs?
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
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?
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
These practical challenges are all about making a 'tray' and covering it with paper.
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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.