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?

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

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?

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

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

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

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

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

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?

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?

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?

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

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

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

There are a number of coins on a table. One quarter of the coins show heads. If I turn over 2 coins, then one third show heads. How many coins are there altogether?

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

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

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?

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 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?

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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?

Explore the relationship between simple linear functions and their graphs.

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?

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?

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

I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?

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

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?

Are these statements always true, sometimes true or never true?

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.

The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?

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

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

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

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

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?

Number problems at primary level to work on with others.

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

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

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

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

Number problems at primary level that may require determination.

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.

How many different sets of numbers with at least four members can you find in the numbers in this box?

Can you find what the last two digits of the number $4^{1999}$ are?

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