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

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

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?

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

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?

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?

Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?

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

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?

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

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

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

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

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?

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?

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

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

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 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?

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.

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?

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?

Got It game for an adult and child. How can you play so that you know you will always win?

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

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?

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

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

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?

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

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

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

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

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.

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

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?

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

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

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

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?

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .

Number problems at primary level that may require determination.

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

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

Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?

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?

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

An investigation that gives you the opportunity to make and justify predictions.