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.

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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?

If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

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.

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

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?

Try this matching game which will help you recognise different ways of saying the same time interval.

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

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

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

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.

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

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

My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?

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?

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?

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.

How many different triangles can you make on a circular pegboard that has nine pegs?

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

Can you find out in which order the children are standing in this line?

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

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

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

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

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

What could the half time scores have been in these Olympic hockey matches?

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

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

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

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

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

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

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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?

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

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

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

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.

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

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