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

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

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

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

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?

A game that tests your understanding of remainders.

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

Look at three 'next door neighbours' amongst the counting numbers. Add them together. 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.

56 406 is the product of two consecutive numbers. What are these two numbers?

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?

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

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.

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?

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?

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?

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

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

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

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

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?

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

Can you find the chosen number from the grid using the clues?

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

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

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

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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.

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

Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the times table too?

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

Look at the squares in this problem. What does the next square look like? I draw a square with 81 little squares inside it. How long and how wide is my square?

Can you work out some different ways to balance this equation?

Have a go at balancing this equation. Can you find different ways of doing it?

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

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?

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

Use the interactivity to sort these numbers into sets. Can you give each set a name?

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?