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

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.

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?

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?

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

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

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.

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.

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?

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

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 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 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.

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

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

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?

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

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?

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

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.

Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?

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

In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. 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?

In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

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?

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

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.

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

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

Find all the numbers that can be made by adding the dots on two dice.

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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

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

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

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?

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?

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

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

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

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?

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

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

Use these head, body and leg pieces to make Robot Monsters which are different heights.

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

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