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?

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?

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?

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?

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

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?

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

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

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?

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

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

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?

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?

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

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .

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?

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

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

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

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

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.

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?

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?

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?

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

I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same...

What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?

Number problems at primary level that may require resilience.

I put eggs into a basket in groups of 7 and noticed that I could easily have divided them into piles of 2, 3, 4, 5 or 6 and always have one left over. How many eggs were in the basket?

Can you find any two-digit numbers that satisfy all of these statements?

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

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

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

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

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.

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

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

What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A

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

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

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?"

6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!?

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

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. . . .

Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.

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?

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

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.