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?"

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.

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?

Can you complete this jigsaw of the multiplication square?

A game that tests your understanding of remainders.

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?

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...

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

If you have only four weights, where could you place them in order to balance this equaliser?

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

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?

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?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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.

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

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

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.

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

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

Got It game for an adult and child. How can you play so that you know you will always win?

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?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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?

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?

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

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

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

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

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

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?

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

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?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

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

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.

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

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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

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.

What is the smallest number of answers you need to reveal in order to work out the missing headers?

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?

Can you find a way to identify times tables after they have been shifted up?

Have a go at balancing this equation. Can you find different ways of doing it?