Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
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?
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?
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
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?
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!
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.
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
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?
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.
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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!
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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.
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?
Dotty Six is a simple dice game that you can adapt in many ways.
Can you follow the rule to decode the messages?
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?
If you have only four weights, where could you place them in order
to balance this equaliser?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
If the answer's 2010, what could the question be?
How would you count the number of fingers in these pictures?
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?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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?
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
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 arrange 5 different digits (from 0 - 9) in the cross in the
Imagine a pyramid which is built in square layers of small cubes.
If we number the cubes from the top, starting with 1, can you
picture which cubes are directly below this first cube?
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?
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?
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?
Investigate what happens when you add house numbers along a street
in different ways.
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?
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
In this section from a calendar, put a square box around the 1st,
2nd, 8th and 9th. Add all the pairs of numbers. What do you notice
about the answers?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
Choose four of the numbers from 1 to 9 to put in the squares so
that the differences between joined squares are odd.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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?
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.