game
Celebrate 25 years of NRICH
To celebrate NRICH's 25th birthday, why not play this special version of our classic game, Got It? Can you devise a strategy so that you will always win?
article
Can you find a perfect number?
Can you find any perfect numbers? Read this article to find out more...
problem
Favourite
Dozens
Age
7 to 14
Challenge level
Can you select the missing digit(s) to find the largest multiple?
problem
A first product Sudoku
Age
7 to 14
Challenge level
Given the products of adjacent cells, can you complete this Sudoku?
problem
Favourite
Statement snap
Age
7 to 14
Challenge level
You'll need to know your number properties to win a game of Statement Snap...
problem
Neighbourly addition
Age
7 to 14
Challenge level
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
game
Favourite
Factors and multiples game
A game in which players take it in turns to choose a number. Can you block your opponent?
game
Favourite
The remainders game
Play this game and see if you can figure out the computer's chosen number.
problem
3 by 3 Mathdokus
Age
7 to 14
Challenge level
Can you use the clues to complete these 3 by 3 Mathematical Sudokus?
game
Factors and multiples game for two
Factors and Multiples game for an adult and child. How can you make sure you win this game?
problem
Favourite
4 by 4 Mathdokus
Age
7 to 14
Challenge level
Can you use the clues to complete these 4 by 4 Mathematical Sudokus?
problem
Favourite
5 by 5 Mathdokus
Age
7 to 16
Challenge level
Can you use the clues to complete these 5 by 5 Mathematical Sudokus?
problem
6 by 6 Mathdokus
Age
7 to 16
Challenge level
Can you use the clues to complete these 6 by 6 Mathematical Sudokus?
problem
Favourite
Missing multipliers
Age
7 to 14
Challenge level
What is the smallest number of answers you need to reveal in order to work out the missing headers?
problem
Favourite
Three neighbours
Age
7 to 14
Challenge level
Take three consecutive numbers and add them together. What do you notice?
problem
Favourite
Factor lines
Age
7 to 14
Challenge level
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
problem
Favourite
Got it
Age
7 to 14
Challenge level
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
problem
Favourite
Remainders
Age
7 to 14
Challenge level
I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?
game
Got it for two
Got It game for an adult and child. How can you play so that you know you will always win?
problem
Favourite
Counting cogs
Age
7 to 14
Challenge level
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
article
Divisibility tests
This article explains various divisibility rules and why they work. An article to read with pencil and paper handy.
problem
Transposition cipher
Age
11 to 16
Challenge level
Can you work out what size grid you need to read our secret message?
problem
Favourite
Summing consecutive numbers
Age
11 to 14
Challenge level
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
problem
Favourite
Factors and multiples puzzle
Age
11 to 14
Challenge level
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
problem
Favourite
Multiple surprises
Age
11 to 16
Challenge level
Sequences of multiples keep cropping up...
problem
Nine in a line
Age
11 to 14
Challenge level
The sum of 9 consecutive positive whole numbers is 2007. What is the largest of these numbers?
problem
Favourite
Gabriel's problem
Age
11 to 14
Challenge level
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
problem
Favourite
Number families
Age
11 to 14
Challenge level
How many different number families can you find?
problem
Flow chart
Age
11 to 14
Challenge level
The flow chart requires two numbers, M and N. Select several values
for M and try to establish what the flow chart does.
problem
Satisfying statements
Age
11 to 14
Challenge level
Can you find any two-digit numbers that satisfy all of these statements?
problem
LCM Sudoku II
Age
11 to 18
Challenge level
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
problem
Favourite
Multiples Sudoku
Age
11 to 14
Challenge level
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
problem
Favourite
How much can we spend?
Age
11 to 14
Challenge level
A country has decided to have just two different coins, 3z and 5z
coins. Which totals can be made? Is there a largest total that
cannot be made? How do you know?
problem
Favourite
Shifting times tables
Age
11 to 14
Challenge level
Can you find a way to identify times tables after they have been shifted up or down?
problem
Favourite
Charlie's delightful machine
Age
11 to 16
Challenge level
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
problem
Product 100
Age
11 to 14
Challenge level
The product of four different positive integers is 100. What is the sum of these four integers?
list
Factors and Multiples - Secondary resources
Age
11 to 16
Challenge level
A collection of resources to support work on Factors and Multiples at Secondary level.
problem
Adding all nine
Age
11 to 14
Challenge level
Make a set of numbers that use all the digits from 1 to 9, once and
once only. Add them up. The result is divisible by 9. Add each of
the digits in the new number. What is their sum? Now try some other
possibilities for yourself!
problem
Factor trio
Age
11 to 14
Challenge level
Which of the numbers shown is the product of exactly 3 distinct prime factors?
problem
Favourite
American billions
Age
11 to 14
Challenge level
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...
problem
Favourite
What numbers can we make?
Age
11 to 14
Challenge level
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
problem
Favourite
Have you got it?
Age
11 to 14
Challenge level
Can you explain the strategy for winning this game with any target?
problem
Favourite
Diagonal product Sudoku
Age
11 to 16
Challenge level
Given the products of diagonally opposite cells - can you complete this Sudoku?
problem
Favourite
Sieve of Eratosthenes
Age
11 to 14
Challenge level
Follow this recipe for sieving numbers and see what interesting patterns emerge.
problem
Prime order
Age
11 to 14
Challenge level
Weekly Problem 24 - 2006
How many of the rearrangements of the digits 1, 3 and 5 give prime numbers?
How many of the rearrangements of the digits 1, 3 and 5 give prime numbers?
problem
Favourite
Counting factors
Age
11 to 14
Challenge level
Is there an efficient way to work out how many factors a large number has?
problem
Power crazy
Age
11 to 14
Challenge level
What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?
problem
Find from factors
Age
11 to 14
Challenge level
Weekly Problem 35 - 2006
A number has exactly eight factors, two of which are 21 and 35. What is the number?
A number has exactly eight factors, two of which are 21 and 35. What is the number?
problem
Divisively so
Age
11 to 14
Challenge level
How many numbers less than 1000 are NOT divisible by either: a) 2
or 5; or b) 2, 5 or 7?
problem
Repeaters
Age
11 to 14
Challenge level
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
problem
Favourite
What numbers can we make now?
Age
11 to 14
Challenge level
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
problem
Oh! Hidden inside?
Age
11 to 14
Challenge level
Find the number which has 8 divisors, such that the product of the divisors is 331776.
problem
Remainder
Age
11 to 14
Challenge level
What is the remainder when 2^2002 is divided by 7? What happens
with different powers of 2?
problem
Favourite
Alison's quilt
Age
11 to 14
Challenge level
Nine squares are fitted together to form a rectangle. Can you find its dimensions?
problem
AB search
Age
11 to 14
Challenge level
The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?
problem
Star product Sudoku
Age
11 to 16
Challenge level
The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.
problem
Favourite
Robotic rotations
Age
11 to 16
Challenge level
How did the the rotation robot make these patterns?
problem
Digat
Age
11 to 14
Challenge level
What is the value of the digit A in the sum below: [3(230 + A)]^2 =
49280A
problem
Thirty six exactly
Age
11 to 14
Challenge level
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
problem
Favourite
Power mad!
Age
11 to 14
Challenge level
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
problem
What does it all add up to?
Age
11 to 18
Challenge level
If you take four consecutive numbers and add them together, the answer will always be even. What else do you notice?
problem
Favourite
Take three from five
Age
11 to 16
Challenge level
Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?
problem
Drawing Celtic knots
Age
11 to 14
Challenge level
Here is a chance to create some Celtic knots and explore the mathematics behind them.
problem
How old are the children?
Age
11 to 14
Challenge level
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?"
problem
Four coloured lights
Age
11 to 14
Challenge level
Imagine a machine with four coloured lights which respond to different rules. Can you find the smallest possible number which will make all four colours light up?
problem
Favourite
Funny factorisation
Age
11 to 16
Challenge level
Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
problem
Millennium leap
Age
11 to 14
Challenge level
How many leap years will there be between 2001 and 3001?
problem
Favourite
Stars
Age
11 to 14
Challenge level
Can you work out what step size to take to ensure you visit all the dots on the circle?
problem
Adjacent factors
Age
11 to 14
Challenge level
Two numbers can be placed adjacent if one of them divides the other. Using only $1,...,10$, can you write the longest such list?
problem
Back of the queue
Age
11 to 14
Challenge level
Weekly Problem 48 - 2013
What is the remainder when the number 743589×301647 is divided by 5?
What is the remainder when the number 743589×301647 is divided by 5?
problem
Rolling along the trail
Age
11 to 14
Challenge level
What could be the scores from five throws of this dice?
problem
Magical products
Age
11 to 14
Challenge level
Can you place the nine cards onto a 3x3 grid such that every row, column and diagonal has a product of 1?
problem
Even so
Age
11 to 14
Challenge level
Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?
problem
Stair climb
Age
11 to 14
Challenge level
Three people run up stairs at different rates. If they each start from a different point - who will win, come second and come last?
problem
Cogs
Age
11 to 14
Challenge level
A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the cogwheel A as the wheels rotate.
problem
Favourite
Product Sudoku
Age
11 to 16
Challenge level
The clues for this Sudoku are the product of the numbers in adjacent squares.
problem
Great Granddad
Age
11 to 14
Challenge level
Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born?
problem
Substitution transposed
Age
11 to 16
Challenge level
Substitution and Transposition all in one! How fiendish can these codes get?
problem
X marks the spot
Age
11 to 14
Challenge level
When the number x 1 x x x is multiplied by 417 this gives the
answer 9 x x x 0 5 7. Find the missing digits, each of which is
represented by an "x" .
problem
Favourite
Big powers
Age
11 to 16
Challenge level
Three people chose this as a favourite problem. It is the sort of
problem that needs thinking time - but once the connection is made
it gives access to many similar ideas.
problem
Expanding zeros
Age
11 to 14
Challenge level
Weekly Problem 22 - 2008
The following sequence continues indefinitely... Which of these integers is a multiple of 81?
The following sequence continues indefinitely... Which of these integers is a multiple of 81?
problem
Mathematical swimmer
Age
11 to 14
Challenge level
Can you work out how many lengths I swim each day?
problem
Favourite
Shopping basket
Age
11 to 16
Challenge level
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
problem
Gaxinta
Age
11 to 14
Challenge level
A number N is divisible by 10, 90, 98 and 882 but it is NOT
divisible by 50 or 270 or 686 or 1764. It is also known that N is a
factor of 9261000. What is N?
problem
Just repeat
Age
11 to 14
Challenge level
Think of any three-digit number. Repeat the digits. The 6-digit
number that you end up with is divisible by 91. Is this a
coincidence?
problem
Inclusion exclusion
Age
11 to 14
Challenge level
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
problem
Three times seven
Age
11 to 14
Challenge level
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
problem
Special sums and products
Age
11 to 14
Challenge level
Find some examples of pairs of numbers such that their sum is a
factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and
16 is a factor of 48.
problem
Times right
Age
11 to 16
Challenge level
Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?
problem
Two much
Age
11 to 14
Challenge level
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
problem
Factoring factorials
Age
11 to 14
Challenge level
Find the highest power of 11 that will divide into 1000! exactly.
problem
Favourite
Ben's game
Age
11 to 16
Challenge level
Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?
problem
Favourite
Cuboids
Age
11 to 14
Challenge level
Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
problem
Adding in rows
Age
11 to 14
Challenge level
List any 3 numbers. It is always possible to find a subset of
adjacent numbers that add up to a multiple of 3. Can you explain
why and prove it?
problem
Favourite
One to eight
Age
11 to 14
Challenge level
Complete the following expressions so that each one gives a four
digit number as the product of two two digit numbers and uses the
digits 1 to 8 once and only once.
problem
Hot pursuit
Age
11 to 14
Challenge level
I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same...
problem
Eminit
Age
11 to 14
Challenge level
The number 8888...88M9999...99 is divisible by 7 and it starts with
the digit 8 repeated 50 times and ends with the digit 9 repeated 50
times. What is the value of the digit M?