A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

Find the values of the nine letters in the sum: FOOT + BALL = GAME

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

You need to find the values of the stars before you can apply normal Sudoku rules.

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?"

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

A few extra challenges set by some young NRICH members.

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

How will you go about finding all the jigsaw pieces that have one peg and one hole?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

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?

The clues for this Sudoku are the product of the numbers in adjacent squares.

Given the products of diagonally opposite cells - can you complete this Sudoku?

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

Investigate the different ways you could split up these rooms so that you have double the number.

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

This Sudoku, based on differences. Using the one clue number can you find the solution?

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?

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

Can you make square numbers by adding two prime numbers together?

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?