A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?
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?
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 challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
This challenge extends the Plants investigation so now four or more children are involved.
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?
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
This Sudoku, based on differences. Using the one clue number can you find the solution?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
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 the information to find out which cards I have used?
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?
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?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
A challenging activity focusing on finding all possible ways of stacking rods.
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.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Four small numbers give the clue to the contents of the four surrounding cells.
A few extra challenges set by some young NRICH members.
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
Find out about Magic Squares in this article written for students. Why are they magic?!
Use the clues about the symmetrical properties of these letters to place them on the grid.
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
This activity investigates how you might make squares and pentominoes from Polydron.
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Given the products of adjacent cells, can you complete this Sudoku?
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
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?
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
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?
You need to find the values of the stars before you can apply normal Sudoku rules.
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?
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.
Follow the clues to find the mystery number.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?