Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

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 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.

A Sudoku with clues given as sums of entries.

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

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

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?

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

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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?

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.

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

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.

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.

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

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

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.

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.

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?

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

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

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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.

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.

Try out the lottery that is played in a far-away land. What is the chance of winning?

We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

How many models can you find which obey these rules?

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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

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

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

My coat has three buttons. How many ways can you find to do up all the buttons?

A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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?

Can you fill in the empty boxes in the grid with the right shape and colour?

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

Can you find all the different ways of lining up these Cuisenaire rods?

How many trains can you make which are the same length as Matt's, using rods that are identical?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

Can you work out how to balance this equaliser? You can put more than one weight on a hook.