In this article, the NRICH team describe the process of selecting solutions for publication on the site.

This article for primary teachers suggests ways in which to help children become better at working systematically.

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.

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

Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.

A Sudoku with clues given as sums of entries.

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.

This sudoku requires you to have "double vision" - two Sudoku's for the price of one

Two sudokus in one. Challenge yourself to make the necessary connections.

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

A Sudoku that uses transformations as supporting clues.

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

This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.

Two sudokus in one. Challenge yourself to make the necessary connections.

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

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

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.

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

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

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

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.

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.

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?

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

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

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.

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?

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.

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?

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

You need to find the values of the stars before you can apply normal Sudoku rules.

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

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

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

A few extra challenges set by some young NRICH members.

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.

Can you find all the different triangles on these peg boards, and find their angles?

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

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

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

An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.

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.