Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Given the products of diagonally opposite cells - can you complete this Sudoku?
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.
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.
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 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.
The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?
A collection of resources to support work on Factors and Multiples at Secondary level.
This article takes the reader through divisibility tests and how they work. An article to read with pencil and paper to hand.
What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?
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?
Make a line of green and a line of yellow rods so that the lines differ in length by one (a white rod)
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
Can you explain the strategy for winning this game with any target?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Can you work out what size grid you need to read our secret message?
Substitution and Transposition all in one! How fiendish can these codes get?
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. . . .
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
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?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
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?
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.
How many zeros are there at the end of the number which is the product of first hundred positive integers?
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.
Is there an efficient way to work out how many factors a large number has?
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?
A game that tests your understanding of remainders.
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. . . .
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?
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?
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.
The clues for this Sudoku are the product of the numbers in adjacent squares.
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...
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.
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
Given any 3 digit number you can use the given digits and name another number which is divisible by 37 (e.g. given 628 you say 628371 is divisible by 37 because you know that 6+3 = 2+7 = 8+1 = 9). . . .
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.
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?
What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?
Find the number which has 8 divisors, such that the product of the divisors is 331776.
Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?