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?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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
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 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.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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 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!
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
There are three buckets each of which holds a maximum of 5 litres.
Use the clues to work out how much liquid there is in each bucket.
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
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.
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Use the information to work out how many gifts there are in each
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?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Rocco ran in a 200 m race for his class. Use the information to
find out how many runners there were in the race and what Rocco's
finishing position was.
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?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
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?
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Mr. Sunshine tells the children they will have 2 hours of homework.
After several calculations, Harry says he hasn't got time to do
this homework. Can you see where his reasoning is wrong?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
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?
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
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?
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?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
What is happening at each box in these machines?
Put a number at the top of the machine and collect a number at the
bottom. What do you get? Which numbers get back to themselves?
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
This task combines spatial awareness with addition and multiplication.
This challenge combines addition, multiplication, perseverance and even proof.
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.
This challenge encourages you to explore dividing a three-digit number by a single-digit number.