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!
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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!
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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.
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
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?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Can you replace the letters with numbers? Is there only one
solution in each case?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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?
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.
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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
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?
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?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
Can you order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
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?
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
The Scot, John Napier, invented these strips about 400 years ago to
help calculate multiplication and division. Can you work out how to
use Napier's bones to find the answer to these multiplications?
Claire thinks she has the most sports cards in her album. "I have
12 pages with 2 cards on each page", says Claire. Ross counts his
cards. "No! I have 3 cards on each of my pages and there are. . . .
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
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?
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?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
There were 22 legs creeping across the web. How many flies? How many spiders?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
At the beginning of May Tom put his tomato plant outside. On the
same day he sowed a bean in another pot. When will the two be the
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
What happens when you add the digits of a number then multiply the
result by 2 and you keep doing this? You could try for different
numbers and different rules.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you work out some different ways to balance this equation?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Have a go at balancing this equation. Can you find different ways of doing it?
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
If the answer's 2010, what could the question be?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
This article for teachers describes how modelling number properties
involving multiplication using an array of objects not only allows
children to represent their thinking with concrete materials,. . . .
Use the information to work out how many gifts there are in each
This number has 903 digits. What is the sum of all 903 digits?