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?

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

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

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

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?

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?

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?"

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

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

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

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

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

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

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

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?

Can you find any two-digit numbers that satisfy all of these statements?

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

Can you complete this jigsaw of the multiplication square?

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

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

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

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

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.

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

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

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

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

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

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.

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

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?

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?

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

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?

Factors and Multiples game for an adult and child. How can you make sure you win this game?

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?

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

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?

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. . . .

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

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

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

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?

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

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?