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

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?

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

Number problems at primary level to work on with others.

Number problems at primary level that may require resilience.

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

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

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?

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

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?

One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there?

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.

Can you make square numbers by adding two prime numbers together?

What is the smallest number of answers you need to reveal in order to work out the missing headers?

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?

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.

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

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

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?

Can you find different ways of creating paths using these paving slabs?

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 is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

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?

6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!?

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

Play this game and see if you can figure out the computer's chosen number.

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

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?

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

The clues for this Sudoku are the product of the numbers in adjacent squares.

Find the number which has 8 divisors, such that the product of the divisors is 331776.

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.

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.

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

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

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

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?

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

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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

Nine squares are fitted together to form a rectangle. Can you find its dimensions?

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.

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?