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

A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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?

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

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?

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

A few extra challenges set by some young NRICH members.

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

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

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

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

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

Try out the lottery that is played in a far-away land. What is the chance of winning?

Four friends must cross a bridge. How can they all cross it in just 17 minutes?

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?

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

Can you use the information to find out which cards I have used?

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

This challenge extends the Plants investigation so now four or more children are involved.

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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?

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?

Use the differences to find the solution to this Sudoku.

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

Can you use your powers of logic and deduction to work out the missing information in these sporty situations?

Four small numbers give the clue to the contents of the four surrounding cells.

In this matching game, you have to decide how long different events take.

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.

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

Find out about Magic Squares in this article written for students. Why are they magic?!

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

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.

This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?