Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
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?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
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.
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
Can you replace the letters with numbers? Is there only one solution in each case?
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.
On a calculator, make 15 by using only the 2 key and any of the
four operations keys. How many ways can you find to do it?
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
This challenge is a game for two players. Choose two numbers from the grid and multiply or divide, then mark your answer on the number line. Can you get four in a row before your partner?
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
Number problems at primary level that require careful consideration.
This number has 903 digits. What is the sum of all 903 digits?
Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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?
On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Take the number 6 469 693 230 and divide it by the first ten prime
numbers and you'll find the most beautiful, most magic of all
numbers. What is it?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
If you had any number of ordinary dice, what are the possible ways
of making their totals 6? What would the product of the dice be
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?
In this investigation, you are challenged to make mobile phone
numbers which are easy to remember. What happens if you make a
sequence adding 2 each time?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Number problems at primary level that may require determination.