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" .

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?

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

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?

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

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

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?

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.

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

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

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

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?

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.

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?

How many six digit numbers are there which DO NOT contain a 5?

Number problems at primary level that may require determination.

Number problems at primary level to work on with others.

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

This activity involves rounding four-digit numbers to the nearest thousand.

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.

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

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?

Explore the relationship between simple linear functions and their graphs.

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?

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.

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

The number 3723(in base 10) is written as 123 in another base. What is that base?

Each child in Class 3 took four numbers out of the bag. Who had made the highest even number?

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

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

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

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. . . .

Number problems for inquiring primary learners.

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

This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.

Number problems at primary level that require careful consideration.

A school song book contains 700 songs. The numbers of the songs are displayed by combining special small single-digit boards. What is the minimum number of small boards that is needed?

Take the numbers 1, 2, 3, 4 and 5 and imagine them written down in every possible order to give 5 digit numbers. Find the sum of the resulting numbers.

There are two forms of counting on Vuvv - Zios count in base 3 and Zepts count in base 7. One day four of these creatures, two Zios and two Zepts, sat on the summit of a hill to count the legs of. . . .

Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?

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

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...

This article for the young and old talks about the origins of our number system and the important role zero has to play in it.

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

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