What is the largest number you can make using the three digits 2, 3
and 4 in any way you like, using any operations you like? You can
only use each digit once.
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
This addition sum uses all ten digits 0, 1, 2...9 exactly once.
Find the sum and show that the one you give is the only
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?
When I type a sequence of letters my calculator gives the product
of all the numbers in the corresponding memories. What numbers
should I store so that when I type 'ONE' it returns 1, and when I
type. . . .
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?
What is the sum of all the digits in all the integers from one to
Find the sum of all three-digit numbers each of whose digits is
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
A combination mechanism for a safe comprises thirty-two tumblers
numbered from one to thirty-two in such a way that the numbers in
each wheel total 132... Could you open the safe?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Whenever two chameleons of different colours meet they change
colour to the third colour. Describe the shortest sequence of
meetings in which all the chameleons change to green if you start
with 12. . . .
What is the sum of all the three digit whole numbers?
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?
There are over sixty different ways of making 24 by adding,
subtracting, multiplying and dividing all four numbers 4, 6, 6 and
8 (using each number only once). How many can you find?
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
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
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 your logical reasoning to work out how many cows and how many
sheep there are in each field.
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?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
I throw three dice and get 5, 3 and 2. Add the scores on the three
dice. What do you get? Now multiply the scores. What do you notice?
Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit
numbers such that their total is close to 1500?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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 do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Here is a chance to play a version of the classic Countdown Game.
Replace each letter with a digit to make this addition correct.
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your oponent.
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?
Got It game for an adult and child. How can you play so that you know you will always win?
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?
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten
numbers from the bags above so that their total is 37.
Find a great variety of ways of asking questions which make 8.
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to 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?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
If you have only four weights, where could you place them in order
to balance this equaliser?
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?