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?
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?
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.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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?
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.
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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?
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.
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
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
Can you use the information to find out which cards I have used?
A 3 digit number is multiplied by a 2 digit number and the
calculation is written out as shown with a digit in place of each
of the *'s. Complete the whole multiplication sum.
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 make a 3x3 cube with these shapes made from small cubes?
A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.
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 10 in the circles so that each number is the
difference between the two numbers just below it.
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?
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 draw a continuous line through 16 numbers on this grid so
that the total of the numbers you pass through is as high as
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?
Is it possible to draw a 5-pointed star without taking your pencil
off the paper? Is it possible to draw a 6-pointed star in the same
way without taking your pen off?
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?
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).
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
56 406 is the product of two consecutive numbers. What are these
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.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
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 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?
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?
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.
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?
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?
Use the information to work out how many gifts there are in each
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 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.
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
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