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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?
An environment which simulates working with Cuisenaire rods.
What is the smallest number of answers you need to reveal in order to work out the missing headers?
Can you use the clues to complete these 3 by 3 Mathematical Sudokus?
Can you use the clues to complete these 4 by 4 Mathematical Sudokus?
You'll need to know your number properties to win a game of Statement Snap...
Factors and Multiples game for an adult and child. How can you make sure you win this game?
Can you find any perfect numbers? Read this article to find out more...
Given the products of adjacent cells, can you complete this Sudoku?
Play this game and see if you can figure out the computer's chosen number.
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
Take three consecutive numbers and add them together. What do you notice?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Got It game for an adult and child. How can you play so that you know you will always win?
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.
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?
A game in which players take it in turns to choose a number. Can you block your opponent?
Can you use the clues to complete these 5 by 5 Mathematical Sudokus?
Can you use the clues to complete these 6 by 6 Mathematical Sudokus?
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...
The product of four different positive integers is 100. What is the sum of these four integers?
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?
Weekly Problem 24 - 2006
How many of the rearrangements of the digits 1, 3 and 5 give prime numbers?
The sum of 9 consecutive positive whole numbers is 2007. What is the largest of these numbers?
Can you find a way to identify times tables after they have been shifted up or down?
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?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Can you find any two-digit numbers that satisfy all of these statements?
Follow this recipe for sieving numbers and see what interesting patterns emerge.
The flow chart requires two numbers, M and N. Select several values for M and try to establish what the flow chart does.
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!
Can you explain the strategy for winning this game with any target?
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
Which of the numbers shown is the product of exactly 3 distinct prime factors?
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
Weekly Problem 48 - 2013
What is the remainder when the number 743589×301647 is divided by 5?
Is there an efficient way to work out how many factors a large number has?
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?
Nine squares are fitted together to form a rectangle. Can you find its dimensions?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?
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?
Two numbers can be placed adjacent if one of them divides the other. Using only $1,...,10$, can you write the longest such list?
How many leap years will there be between 2001 and 3001?
Here is a chance to create some Celtic knots and explore the mathematics behind them.
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.
Weekly Problem 35 - 2006
A number has exactly eight factors, two of which are 21 and 35. What is the number?
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.
The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Three people run up stairs at different rates. If they each start from a different point - who will win, come second and come last?
What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A
Can you work out what step size to take to ensure you visit all the dots on the circle?
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?
Find the number which has 8 divisors, such that the product of the divisors is 331776.
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?"
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?
What could be the scores from five throws of this dice?
What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?
Can you place the nine cards onto a 3x3 grid such that every row, column and diagonal has a product of 1?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
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?
How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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.
Weekly Problem 22 - 2008
The following sequence continues indefinitely... Which of these integers is a multiple of 81?
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?
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" .
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
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?
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.
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?
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...
Find the highest power of 11 that will divide into 1000! exactly.
6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!?
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?
This article explains various divisibility rules and why they work. An article to read with pencil and paper handy.
Can you work out what size grid you need to read our secret message?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Given the products of diagonally opposite cells - can you complete this Sudoku?
A collection of resources to support work on Factors and Multiples at Secondary 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.
Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
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?
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.
Substitution and Transposition all in one! How fiendish can these codes get?
Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.