Use these four dominoes to make a square that has the same number of dots on each side.
Use the 'double-3 down' dominoes to make a square so that each side has eight dots.
Using the numbers 1, 2, 3, 4 and 5 once and only once, and the
operations x and ÷ once and only once, what is the smallest
whole number you can make?
Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit
numbers such that their total is close to 1500?
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.
All the girls would like a puzzle each for Christmas and all the
boys would like a book each. Solve the riddle to find out how many
puzzles and books Santa left.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
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.
Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.
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?
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?
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?
This challenge is to make up YOUR OWN alphanumeric. Each letter
represents a digit and where the same letter appears more than once
it must represent the same digit each time.
There are lots of different methods to find out what the shapes are worth - how many can you find?
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
Fill in the numbers to make the sum of each row, column and
diagonal equal to 34. For an extra challenge try the huge American
Flag magic square.
Cassandra, David and Lachlan are brothers and sisters. They range
in age between 1 year and 14 years. Can you figure out their exact
ages from the clues?
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 of balls?
Use the information to work out how many gifts there are in each
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.
Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
Can you guess the colours of the 10 marbles in the bag? Can you
develop an effective strategy for reaching 1000 points in the least
number of rounds?
You have two sets of the digits 0 – 9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?
Exploring balance and centres of mass can be great fun. The
resulting structures can seem impossible. Here are some images to
encourage you to experiment with non-breakable objects of your own.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.
The graph represents a salesman’s area of activity with the
shops that the salesman must visit each day. What route around the
shops has the minimum total distance?
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?
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?
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?
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
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
56 406 is the product of two consecutive numbers. What are these
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
In this problem you have to place four by four magic squares on the
faces of a cube so that along each edge of the cube the numbers
Sam sets up displays of cat food in his shop in triangular stacks.
If Felix buys some, then how can Sam arrange the remaining cans in
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
Can you number the vertices, edges and faces of a tetrahedron so
that the number on each edge is the mean of the numbers on the
adjacent vertices and the mean of the numbers on the adjacent
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.
Using only six straight cuts, find a way to make as many pieces of
pizza as possible. (The pieces can be different sizes and shapes).
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?