Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
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 make dice stairs using the rules stated? How do you know you have all the possible stairs?
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?
A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.
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 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.
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.
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?
Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
What is the greatest volume you can get for a rectangular (cuboid)
parcel if the maximum combined length and girth are 2 metres?
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?
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?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Can you use the information to find out which cards I have used?
Use these four dominoes to make a square that has the same number of dots on each side.
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?
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 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
Use the information to work out how many gifts there are in each
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?
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
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.
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.
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
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
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
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.
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.
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.
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.
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?