Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
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?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
Fill in the numbers to make the sum of each row, column and
diagonal equal to 34. For an extra challenge try the huge American
Flag magic square.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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. . . .
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?
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
There were 22 legs creeping across the web. How many flies? How many spiders?
Woof is a big dog. Yap is a little dog.
Emma has 16 dog biscuits to give to the two dogs.
She gave Woof 4 more biscuits than Yap.
How many biscuits did each dog get?
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 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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
This challenge is about finding the difference between numbers which have the same tens digit.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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
This task follows on from Build it Up and takes the ideas into three dimensions!
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?
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?
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!
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 challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Can you find all the ways to get 15 at the top of this triangle of numbers?
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Well now, what would happen if we lost all the nines in our number
system? Have a go at writing the numbers out in this way and have a
look at the multiplications table.
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Annie cut this numbered cake into 3 pieces with 3 cuts so that the
numbers on each piece added to the same total. Where were the cuts
and what fraction of the whole cake was each piece?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Find out what a Deca Tree is and then work out how many leaves
there will be after the woodcutter has cut off a trunk, a branch, a
twig and a leaf.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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.
Number problems at primary level that may require determination.
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
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?
Cassandra, David and Lachlan are brothers and sisters. They range
in age between 1 year and 14 years. Can you figure out their exact
ages from the clues?
Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?
A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?