A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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?
Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
Given the products of diagonally opposite cells - can you complete this Sudoku?
A little mouse called Delia lives in a hole in the bottom of a tree.....How many days will it be before Delia has to take the same route again?
Follow the clues to find the mystery number.
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.
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
This Sudoku, based on differences. Using the one clue number can you find the solution?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
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.
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?
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?
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.
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?
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?
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.
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?
Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.
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.
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
A Sudoku with a twist.
On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?
A Sudoku with clues as ratios.
Investigate the different ways you could split up these rooms so that you have double the number.
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
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?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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?