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?

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

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?

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?

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

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?

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

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

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

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?

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?

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

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

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?

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

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?

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?

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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.

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

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

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

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?

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?

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?

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

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

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

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

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

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

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

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?

How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?

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

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

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?"

Can you complete this jigsaw of the multiplication square?

Can you explain the strategy for winning this game with any target?

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? 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?

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

A number N is divisible by 10, 90, 98 and 882 but it is NOT divisible by 50 or 270 or 686 or 1764. It is also known that N is a factor of 9261000. What is N?

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. . . .

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

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

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

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