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

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

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

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

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?

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

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 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?

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

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

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

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

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

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

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

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

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

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?

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. . . .

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

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

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?

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

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

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?

A few extra challenges set by some young NRICH members.

Use the differences to find the solution to this Sudoku.

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

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.

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

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?

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?

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?

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

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?

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?

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

Different combinations of the weights available allow you to make different totals. Which totals can you make?

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .

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. . . .