A game in which players take it in turns to choose a number. Can you block your opponent?
Follow this recipe for sieving numbers and see what interesting patterns emerge.
How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?
A game that tests your understanding of remainders.
Given the products of adjacent cells, can you complete this Sudoku?
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
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 clues for this Sudoku are the product of the numbers in adjacent squares.
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.
Some 4 digit numbers can be written as the product of a 3 digit number and a 2 digit number using the digits 1 to 9 each once and only once. The number 4396 can be written as just such a product. Can. . . .
What is the smallest number of answers you need to reveal in order to work out the missing headers?
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)
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 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.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Can you explain the strategy for winning this game with any target?
Find the frequency distribution for ordinary English, and use it to help you crack the code.
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?
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
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.
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
Is there an efficient way to work out how many factors a large number has?
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. . . .
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?
The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?
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 three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
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 the highest power of 11 that will divide into 1000! exactly.
Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.
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.
Have you seen this way of doing multiplication ?
Can you find any perfect numbers? Read this article to find out more...
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
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?
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?
What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A
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!?
What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?
How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?
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.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
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.