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

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?

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.

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

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

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?

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?

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?

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?

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?

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

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

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?

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

Follow this recipe for sieving numbers and see what interesting patterns emerge.

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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

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

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

A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.

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

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

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

Number problems at primary level that may require resilience.

These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?

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.

Given the products of diagonally opposite cells - can you complete this Sudoku?

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

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.

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

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

How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?

When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

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?

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

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...

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

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 order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the times table too?

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?

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

Number problems at primary level to work on with others.

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