Play this game and see if you can figure out the computer's chosen number.
Factors and Multiples game for an adult and child. How can you make sure you win this game?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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.
Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?
Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
What is the smallest number of answers you need to reveal in order to work out the missing headers?
A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
Can you find any two-digit numbers that satisfy all of these statements?
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.
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?
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 fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
Can you find a way to identify times tables after they have been shifted up or down?
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?
These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
If you have only four weights, where could you place them in order to balance this equaliser?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Given the products of adjacent cells, can you complete this Sudoku?
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
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?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
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.
Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
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?
I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
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?
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?
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.
List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?
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?"
Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.