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

A Sudoku with clues given as sums of entries.

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

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

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.

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?

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

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?

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.

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?

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?

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

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

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

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

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

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 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.

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?

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.

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.

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

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.

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.

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?

What happens when you try and fit the triomino pieces into these two grids?

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

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?

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

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

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.

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.

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

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

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

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 different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

Find out about Magic Squares in this article written for students. Why are they magic?!

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

Find out what a "fault-free" rectangle is and try to make some of your own.

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?

How many models can you find which obey these rules?

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

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

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

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

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?