Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
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?
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 happens when you try and fit the triomino pieces into these
Can you cover the camel with these pieces?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Use the clues to colour each square.
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
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?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
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?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Can you find all the different ways of lining up these Cuisenaire
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?
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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.
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?
What is the best way to shunt these carriages so that each train
can continue its journey?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
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?
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?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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 put the numbers 1 to 8 into the circles so that the four
calculations are correct?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
These practical challenges are all about making a 'tray' and covering it with paper.
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?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Place this "worm" on the 100 square and find the total of the four
squares it covers. Keeping its head in the same place, what other
totals can you make?
An activity making various patterns with 2 x 1 rectangular tiles.
How many different rhythms can you make by putting two drums on the
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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back