Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?
If each of these three shapes has a value, can you find the totals
of the combinations? Perhaps you can use the shapes to make the
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
Who said that adding couldn't be fun?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears,
yellow jelly bees and jelly belly beans. In how many different ways
could she make a jolly jelly feast with 32 legs?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
Find the sum of all three-digit numbers each of whose digits is
Number problems at primary level that require careful consideration.
Can you make square numbers by adding two prime numbers together?
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 1-5 in the V shape so that both 'arms' have the same total?
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
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
Ben has five coins in his pocket. How much money might he have?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
These two group activities use mathematical reasoning - one is
numerical, one geometric.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
Tim had nine cards each with a different number from 1 to 9 on it.
How could he have put them into three piles so that the total in
each pile was 15?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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!
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?
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.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Place this "worm" on the 100 square and find the total of the four
squares it covers. Keeping its head in the same place, what other
totals can you make?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
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!
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
This dice train has been made using specific rules. How many different trains can you make?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Can you substitute numbers for the letters in these sums?
How could you arrange at least two dice in a stack so that the total of the visible spots is 18?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
This task follows on from Build it Up and takes the ideas into three dimensions!