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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. . . .
Given the products of adjacent cells, can you complete this Sudoku?
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" .
How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Can you find a way to identify times tables after they have been shifted up?
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the 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.
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?"
Given the products of diagonally opposite cells - can you complete this Sudoku?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
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?
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?
How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?
Can you find any perfect numbers? Read this article to find out more...
Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?
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.
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 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?
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?
The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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.
Find the highest power of 11 that will divide into 1000! exactly.
Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?
What is the smallest number of answers you need to reveal in order to work out the missing headers?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Follow this recipe for sieving numbers and see what interesting patterns emerge.
Can you work out what size grid you need to read our secret message?
Find the frequency distribution for ordinary English, and use it to help you crack the code.
Substitution and Transposition all in one! How fiendish can these codes get?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any 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.
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. . . .
Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths. . . .
A game that tests your understanding of remainders.
How many zeros are there at the end of the number which is the product of first hundred positive integers?
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?
Find the number which has 8 divisors, such that the product of the divisors is 331776.
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
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.
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.