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.
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
This challenge extends the Plants investigation so now four or more children are involved.
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
In this problem you have to place four by four magic squares on the
faces of a cube so that along each edge of the cube the numbers
How could you arrange at least two dice in a stack so that the total of the visible spots is 18?
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.
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?
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?
Can you substitute numbers for the letters in these sums?
Susie took cherries out of a bowl by following a certain pattern.
How many cherries had there been in the bowl to start with if she
was left with 14 single ones?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to 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 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.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
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.
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?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
Tell your friends that you have a strange calculator that turns
numbers backwards. What secret number do you have to enter to make
141 414 turn around?
The picture shows a lighthouse and many underwater creatures. If
you know the markings on the lighthouse are 1m apart, can you work
out the distances between some of the different creatures?
What is the sum of all the three digit whole numbers?
Investigate the different distances of these car journeys and find out how long they take.
Can you draw a continuous line through 16 numbers on this grid so
that the total of the numbers you pass through is as high as
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?
Use the 'double-3 down' dominoes to make a square so that each side
has eight dots.
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?
This is an adding game for two players.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
If each of these three shapes has a value, can you find the totals
of the combinations? Perhaps you can use the shapes to make the
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?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
Investigate the different distances of these car journeys and find
out how long they take.
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?
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.
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?
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
Three dice are placed in a row. Find a way to turn each one so that
the three numbers on top of the dice total the same as the three
numbers on the front of the dice. Can you find all the ways to. . . .
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?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.