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?

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

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

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

Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths I. . . .

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

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

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?

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?

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?

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

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

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?

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?

Number problems at primary level that may require determination.

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'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?

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

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?

This article for teachers describes how number arrays can be a useful reprentation 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?

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

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

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?

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

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. . . .

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?

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?

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

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

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

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

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?

Number problems at primary level to work on with others.

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

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

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

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

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?

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?

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

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

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

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.

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.

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