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

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

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.

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

A few extra challenges set by some young NRICH members.

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

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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?

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

A Sudoku that uses transformations as supporting clues.

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

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.

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?

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

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.

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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

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?

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he 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 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.

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?

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

This challenge extends the Plants investigation so now four or more children are involved.

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?

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

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

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

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.

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.

In this matching game, you have to decide how long different events take.

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

A challenging activity focusing on finding all possible ways of stacking rods.

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

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

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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....?