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?"
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
Given the products of adjacent cells, can you complete this Sudoku?
An investigation that gives you the opportunity to make and justify
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. . . .
Do you notice anything about the solutions when you add and/or
subtract consecutive negative 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?
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?
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?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
This dice train has been made using specific rules. How many different trains can you make?
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?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you find all the ways to get 15 at the top of this triangle of numbers?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
If you had any number of ordinary dice, what are the possible ways
of making their totals 6? What would the product of the dice be
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?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Can you work out some different ways to balance this equation?
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
This task follows on from Build it Up and takes the ideas into three dimensions!
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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
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?
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.
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?
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.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
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?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.