Make a line of green and a line of yellow rods so that the lines differ in length by one (a white rod)

Follow this recipe for sieving numbers and see what interesting patterns emerge.

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. . . .

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!?

In how many ways can the number 1 000 000 be expressed as the product of three positive integers?

This article takes the reader through divisibility tests and how they work. An article to read with pencil and paper to hand.

Find the highest power of 11 that will divide into 1000! exactly.

How many zeros are there at the end of the number which is the product of first hundred positive integers?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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.

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

Given the products of diagonally opposite cells - can you complete this Sudoku?

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?

How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?

Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.

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.

A game in which players take it in turns to choose a number. Can you block your opponent?

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

Substitution and Transposition all in one! How fiendish can these codes get?

Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?

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.

What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?

Can you work out what size grid you need to read our secret message?

A number N is divisible by 10, 90, 98 and 882 but it is NOT divisible by 50 or 270 or 686 or 1764. It is also known that N is a factor of 9261000. What is N?

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

Find the frequency distribution for ordinary English, and use it to help you crack the code.

Can you find a way to identify times tables after they have been shifted up?

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. . . .

Can you find any perfect numbers? Read this article to find out more...

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?

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?

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

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...

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 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.

A game that tests your understanding of remainders.

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.

Have you seen this way of doing multiplication ?

What is the smallest number of answers you need to reveal in order to work out the missing headers?

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.

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

The clues for this Sudoku are the product of the numbers in adjacent squares.

Explore the relationship between simple linear functions and their graphs.

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

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?

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?