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?

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" .

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.

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

Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?

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

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

Can you replace the letters with numbers? Is there only one solution in each case?

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?

What is the sum of all the digits in all the integers from one to one million?

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

There are nasty versions of this dice game but we'll start with the nice ones...

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your oponent.

Find the values of the nine letters in the sum: FOOT + BALL = GAME

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

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

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

This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.

Explore the relationship between simple linear functions and their graphs.

You have two sets of the digits 0 – 9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?

When asked how old she was, the teacher replied: My age in years is not prime but odd and when reversed and added to my age you have a perfect square...

Dicey Operations for an adult and child. Can you get close to 1000 than your partner?

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?

There are six numbers written in five different scripts. Can you sort out which is which?

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

Amazing as it may seem the three fives remaining in the following `skeleton' are sufficient to reconstruct the entire long division sum.

Consider all two digit numbers (10, 11, . . . ,99). In writing down all these numbers, which digits occur least often, and which occur most often ? What about three digit numbers, four digit numbers. . . .

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

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?

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.

Consider all of the five digit numbers which we can form using only the digits 2, 4, 6 and 8. If these numbers are arranged in ascending order, what is the 512th number?

Take any four digit number. Move the first digit to the 'back of the queue' and move the rest along. Now add your two numbers. What properties do your answers always have?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

The number 27 is special because it is three times the sum of its digits 27 = 3 (2 + 7). Find some two digit numbers that are SEVEN times the sum of their digits (seven-up numbers)?

What happens when you round these three-digit numbers to the nearest 100?