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?
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
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.
Got It game for an adult and child. How can you play so that you know you will always win?
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...
Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Given the products of adjacent cells, can you complete this Sudoku?
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.
You'll need to know your number properties to win a game of Statement Snap...
Play this game and see if you can figure out the computer's chosen number.
Can you explain the strategy for winning this game with any target?
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
The clues for this Sudoku are the product of the numbers in adjacent squares.
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.
Can you make lines of Cuisenaire rods that differ by 1?
A collection of resources to support work on Factors and Multiples at Secondary level.
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?
Is there an efficient way to work out how many factors a large number has?
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. . . .
Can you work out what step size to take to ensure you visit all the dots on the circle?
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.
How many zeros are there at the end of the number which is the product of first hundred positive integers?
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?
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?
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?
I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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?
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" .
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...
Factors and Multiples game for an adult and child. How can you make sure you win this game?
Find the highest power of 11 that will divide into 1000! exactly.
How many different number families can you find?
Find the number which has 8 divisors, such that the product of the divisors is 331776.
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
Follow this recipe for sieving numbers and see what interesting patterns emerge.
What is the smallest number of answers you need to reveal in order to work out the missing headers?
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...
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
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?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
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?