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?

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?

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.

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?

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

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?

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

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?

Number problems at primary level that may require determination.

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?

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

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

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

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

Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. . . .

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.

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.

Number problems at primary level to work on with others.

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

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

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

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

Explore the relationship between simple linear functions and their graphs.

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?

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

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?

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

A car's milometer reads 4631 miles and the trip meter has 173.3 on it. How many more miles must the car travel before the two numbers contain the same digits in the same order?

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

Four strategy dice games to consolidate pupils' understanding of rounding.

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

Number problems at primary level that require careful consideration.

Number problems for inquiring primary learners.

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?

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?

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

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

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?

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

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

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

We are used to writing numbers in base ten, using 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Eg. 75 means 7 tens and five units. This article explains how numbers can be written in any number base.

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?

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