Imagine you were given the chance to win some money... and imagine
you had nothing to lose...
Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
If the answer's 2010, what could the question be?
After training hard, these two children have improved their
results. Can you work out the length or height of their first
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.
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?
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
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?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
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.
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?
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?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
This number has 903 digits. What is the sum of all 903 digits?
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.
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
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
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
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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.
What is happening at each box in these machines?
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
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?
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
Use the information to work out how many gifts there are in each
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.
The triangles in these sets are similar - can you work out the
lengths of the sides which have question marks?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?
What is the sum of all the three digit whole numbers?
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
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?
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?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.