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?
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?
What is the sum of all the three digit whole numbers?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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.
This number has 903 digits. What is the sum of all 903 digits?
Are these domino games fair? Can you explain why or why not?
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?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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).
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?
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.
Explore Alex's number plumber. What questions would you like to
ask? Don't forget to keep visiting NRICH projects site for the
latest developments and questions.
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 substitute numbers for the letters in these sums?
Find a great variety of ways of asking questions which make 8.
Use the 'double-3 down' dominoes to make a square so that each side
has eight dots.
Can you use the information to find out which cards I have used?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
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?
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?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
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?
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
These two group activities use mathematical reasoning - one is
numerical, one geometric.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
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!
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?
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?
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?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
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?
What is happening at each box in these machines?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
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.
There were 22 legs creeping across the web. How many flies? How many spiders?
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.