Can you substitute numbers for the letters in these sums?
In the multiplication sum, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
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?
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
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.
Can you use the information to find out which cards I have used?
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book 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?
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?
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?
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.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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!
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
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!
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
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?
These eleven shapes each stand for a different number. Can you use
the multiplication sums to work out what they are?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
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?
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?
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?
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?
These two group activities use mathematical reasoning - one is
numerical, one geometric.
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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.
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Can you replace the letters with numbers? Is there only one
solution in each case?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Use your logical-thinking skills to deduce how much Dan's crisps
and ice-cream cost altogether.
This 100 square jigsaw is written in code. It starts with 1 and
ends with 100. Can you build it up?