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

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?

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?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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

Given the products of diagonally opposite cells - can you complete this Sudoku?

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

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.

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

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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

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.

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.

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

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?

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

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

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?

Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?

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?

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.

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.

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

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?

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?

This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

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?

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?

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. . . .

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.

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.

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

Investigate the different ways you could split up these rooms so that you have double the number.

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.

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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.

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

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?