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?
Start with four numbers at the corners of a square and put the
total of two corners in the middle of that side. Keep going... Can
you estimate what the size of the last four numbers will be?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Find the next number in this pattern: 3, 7, 19, 55 ...
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
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.
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?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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?
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?
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.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
If the answer's 2010, what could the question be?
How would you count the number of fingers in these pictures?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
At the beginning of May Tom put his tomato plant outside. On the
same day he sowed a bean in another pot. When will the two be the
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!
Investigate what happens when you add house numbers along a street
in different ways.
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
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?
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?
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?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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
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?
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?
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?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
These sixteen children are standing in four lines of four, one
behind the other. They are each holding a card with a number on it.
Can you work out the missing numbers?
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!
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Can you arrange 5 different digits (from 0 - 9) in the cross in 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?
Dotty Six is a simple dice game that you can adapt in many ways.
This challenge is about finding the difference between numbers which have the same tens digit.
Can you follow the rule to decode the messages?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
Dotty Six game for an adult and child. Will you be the first to have three sixes in a straight line?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?
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?