Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
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!
If the answer's 2010, what could the question be?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears,
yellow jelly bees and jelly belly beans. In how many different ways
could she make a jolly jelly feast with 32 legs?
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.
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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.
This project challenges you to work out the number of cubes hidden
under a cloth. What questions would you like to ask?
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?
If you have only four weights, where could you place them in order
to balance this equaliser?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
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.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the 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?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
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.
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
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?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
An environment which simulates working with Cuisenaire rods.
Tim had nine cards each with a different number from 1 to 9 on it.
How could he have put them into three piles so that the total in
each pile was 15?
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?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
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?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?