For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

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.

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.

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?

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 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.

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

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

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.

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?

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

A game that tests your understanding of remainders.

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

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. . . .

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

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

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.

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

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?

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

Given the products of adjacent cells, can you complete this Sudoku?

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

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?"

Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?

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. . . .

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

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

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.

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

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?

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?

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 collection of resources to support work on Factors and Multiples at Secondary level.

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

115^2 = (110 x 120) + 25, that is 13225 895^2 = (890 x 900) + 25, that is 801025 Can you explain what is happening and generalise?

Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.

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

Factorial one hundred (written 100!) has 24 noughts when written in full and that 1000! has 249 noughts? Convince yourself that the above is true. Perhaps your methodology will help you find the. . . .

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" .

How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?

Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...

What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?

Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?

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

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