This package contains a collection of problems from the NRICH
website that could be suitable for students who have a good
understanding of Factors and Multiples and who feel ready to take
on some. . . .
A student in a maths class was trying to get some information from
her teacher. She was given some clues and then the teacher ended by
saying, "Well, how old are they?"
Given the products of adjacent cells, can you complete this Sudoku?
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?
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
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 take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
The clues for this Sudoku are the product of the numbers in adjacent squares.
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?
A mathematician goes into a supermarket and buys four items. Using
a calculator she multiplies the cost instead of adding them. How
can her answer be the same as the total at the till?
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you work out some different ways to balance this equation?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
Alice and Brian are snails who live on a wall and can only travel
along the cracks. Alice wants to go to see Brian. How far is the
shortest route along the cracks? Is there more than one way to go?
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
A Sudoku that uses transformations as supporting clues.
My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?
In this matching game, you have to decide how long different events take.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
The pages of my calendar have got mixed up. Can you sort them out?
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
George and Jim want to buy a chocolate bar. George needs 2p more
and Jim need 50p more to buy it. How much is the chocolate bar?
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
The Vikings communicated in writing by making simple scratches on
wood or stones called runes. Can you work out how their code works
using the table of the alphabet?
Systematically explore the range of symmetric designs that can be
created by shading parts of the motif below. Use normal square
lattice paper to record your results.
How many rectangles can you find in this shape? Which ones are
differently sized and which are 'similar'?
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?
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
You cannot choose a selection of ice cream flavours that includes
totally what someone has already chosen. Have a go and find all the
different ways in which seven children can have ice cream.