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Given the products of diagonally opposite cells - can you complete this Sudoku?
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.
The clues for this Sudoku are the product of the numbers in adjacent squares.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
Can you find a way to identify times tables after they have been shifted up?
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...
A game that tests your understanding of remainders.
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?
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?"
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?
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.
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.
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. . . .
Find the frequency distribution for ordinary English, and use it to help you crack the code.
Given the products of adjacent cells, can you complete this Sudoku?
A game in which players take it in turns to choose a number. Can you block your opponent?
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?
I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?
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. . . .
What is the smallest number with exactly 14 divisors?
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?
How many zeros are there at the end of the number which is the product of first hundred positive integers?
The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
Find the highest power of 11 that will divide into 1000! exactly.
Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?
Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?
Make a line of green and a line of yellow rods so that the lines differ in length by one (a white rod)
Data is sent in chunks of two different sizes - a yellow chunk has 5 characters and a blue chunk has 9 characters. A data slot of size 31 cannot be exactly filled with a combination of yellow and. . . .
Can you find any perfect numbers? Read this article to find out more...
How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?
A collection of resources to support work on Factors and Multiples at Secondary level.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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?
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?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
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.
This article takes the reader through divisibility tests and how they work. An article to read with pencil and paper to hand.
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
Find the number which has 8 divisors, such that the product of the divisors is 331776.
What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?
Can you find what the last two digits of the number $4^{1999}$ are?
I put eggs into a basket in groups of 7 and noticed that I could easily have divided them into piles of 2, 3, 4, 5 or 6 and always have one left over. How many eggs were in the basket?
What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A
Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?
A challenge that requires you to apply your knowledge of the properties of numbers. Can you fill all the squares on the board?
Substitution and Transposition all in one! How fiendish can these codes get?
Factorial one hundred (written 100!) has 24 noughts when written in full and that 1000! has 249 noughts? Convince yourself that the above is true. Perhaps your methodology will help you find the. . . .