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

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

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?

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?

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

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

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

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

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

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

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.

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

A challenging activity focusing on finding all possible ways of stacking rods.

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?

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

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.

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

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 find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

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

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.

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

A few extra challenges set by some young NRICH members.

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.

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

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.

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

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

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?

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

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

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

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

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?

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

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

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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

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

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

Two sudokus in one. Challenge yourself to make the necessary connections.

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?