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

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?

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.

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?

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?

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?

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?

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

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.

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?

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

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?

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?

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

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?

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

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

Factors and Multiples game for an adult and child. How can you make sure you win this game?

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

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

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.

Can you complete this jigsaw of the multiplication square?

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

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

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?

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?

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

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?

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.

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

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

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

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

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!?

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

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?

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

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

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

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