Can you work out some different ways to balance this equation?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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. . . .
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Have a go at balancing this equation. Can you find different ways of doing it?
Number problems at primary level that require careful consideration.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Can you replace the letters with numbers? Is there only one
solution in each case?
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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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 the numbers and symbols to make this number sentence correct. How many different ways can you find?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
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?
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?
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?
An investigation that gives you the opportunity to make and justify
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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?"
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!
Given the products of adjacent cells, can you complete this Sudoku?
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?
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!
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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.
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?
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
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Can you find all the ways to get 15 at the top of this triangle of 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?
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?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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.
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?
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?
This task follows on from Build it Up and takes the ideas into three dimensions!
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
What happens when you round these three-digit numbers to the nearest 100?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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?