Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.
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?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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?
A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
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
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?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
What is the greatest volume you can get for a rectangular (cuboid)
parcel if the maximum combined length and girth are 2 metres?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
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?
Use the information to work out how many gifts there are in each
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
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?
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.
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?
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?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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.
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
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 make the green spot travel through the tube by moving the
yellow spot? Could you draw a tube that both spots would follow?
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?
Can you use the information to find out which cards I have used?
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.
Three teams have each played two matches. The table gives the total
number points and goals scored for and against each team. Fill in
the table and find the scores in the three matches.
A car's milometer reads 4631 miles and the trip meter has 173.3 on
it. How many more miles must the car travel before the two numbers
contain the same digits in the same order?
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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.
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
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?
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
56 406 is the product of two consecutive numbers. What are these
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
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.
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?
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.
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 out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.