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?
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?
Can you use the information to find out which cards I have used?
Your challenge is to find the longest way through the network
following this rule. You can start and finish anywhere, and with
any shape, as long as you follow the correct order.
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.
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
The discs for this game are kept in a flat square box with a square
hole for each disc. Use the information to find out how many discs
of each colour there are in the box.
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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.
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's
there is one digit, between the two 2's there are two digits, and
between the two 3's there are three digits.
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Use these four dominoes to make a square that has the same number of dots on each side.
I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?
There were 22 legs creeping across the web. How many flies? How many spiders?
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
If these balls are put on a line with each ball touching the one in
front and the one behind, which arrangement makes the shortest line
There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?
Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Can you make the green spot travel through the tube by moving the
yellow spot? Could you draw a tube that both spots would follow?
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
Arrange the shapes in a line so that you change either colour or
shape in the next piece along. Can you find several ways to start
with a blue triangle and end with a red circle?
Can you draw a continuous line through 16 numbers on this grid so
that the total of the numbers you pass through is as high as
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Find another number that is one short of a square number and when
you double it and add 1, the result is also a square number.
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Rocco ran in a 200 m race for his class. Use the information to
find out how many runners there were in the race and what Rocco's
finishing position was.
Can you make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person