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.
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?
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
This Sudoku, based on differences. Using the one clue number can you find the solution?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Follow the clues to find the mystery number.
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.
A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
A few extra challenges set by some young NRICH members.
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.
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?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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?
Four small numbers give the clue to the contents of the four surrounding cells.
Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's there is one digit, between the two 2's there are two digits, and between the two 3's there are three digits.
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?
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
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 in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
Penta people, the Pentominoes, always build their houses from five square rooms. I wonder how many different Penta homes you can create?
Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
Can you substitute numbers for the letters in these sums?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column
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?
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 is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
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?
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
How many different triangles can you make on a circular pegboard that has nine pegs?
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.
Two sudokus in one. Challenge yourself to make the necessary connections.