You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Can you explain the strategy for winning this game with any target?
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. . . .
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?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
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.
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.
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...
How many noughts are at the end of these giant numbers?
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.
Is there an efficient way to work out how many factors a large number has?
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" .
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Got It game for an adult and child. How can you play so that you know you will always win?
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?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. 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?
Given the products of adjacent cells, can you complete this Sudoku?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
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.
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?
Can you find any perfect numbers? Read this article to find out more...
Find the highest power of 11 that will divide into 1000! exactly.
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?
Make a line of green and a line of yellow rods so that the lines differ in length by one (a white rod)
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 I. . . .
Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.
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?
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
Given the products of diagonally opposite cells - can you complete this Sudoku?
Can you find any two-digit numbers that satisfy all of these statements?
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
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!?
Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.
Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.
The nth term of a sequence is given by the formula n^3 + 11n . Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. . . .
Prove that if the integer n is divisible by 4 then it can be written as the difference of two squares.
Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?
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?
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
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?"
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.
In how many ways can the number 1 000 000 be expressed as the product of three positive integers?
What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A
How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?
What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?