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

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.

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

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

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?

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.

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

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

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 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?"

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

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

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?

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

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

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

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

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

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 work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.

This article for teachers describes how number arrays can be a useful reprentation for many number concepts.

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

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

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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. . . .

Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.

Is there an efficient way to work out how many factors a large number has?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?

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?

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Find the number which has 8 divisors, such that the product of the divisors is 331776.

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

Got It game for an adult and child. How can you play so that you know you will always win?

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

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?

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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

Are these statements always true, sometimes true or never true?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

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

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...