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?

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

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

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

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?

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.

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

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

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

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

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

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

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?

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

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

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?

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.

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. . . .

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.

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

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

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.

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?

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

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

Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?

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?

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

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?

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.

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

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

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

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

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

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?

These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?

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

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?

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

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?

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?

What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A

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