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?

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

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

Number problems at primary level that may require resilience.

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?

Number problems at primary level to work on with others.

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?

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

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?

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

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.

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

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

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

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

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?

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.

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?

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

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

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?

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

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

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?

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

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

Can you work out what size grid you need to read our secret message?

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...

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

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?

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

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?

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

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

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

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

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

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?

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

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.

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

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

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?

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.

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?

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?

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

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.