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

Number problems at primary level that require careful consideration.

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

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

Can you work out some different ways to balance this equation?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

What two-digit numbers can you make with these two dice? What can't you make?

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?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

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

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.

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

What happens when you round these numbers to the nearest whole number?

Can you replace the letters with numbers? Is there only one solution in each case?

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

Can you find the chosen number from the grid using the clues?

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Have a go at balancing this equation. Can you find different ways of doing it?

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

What happens when you round these three-digit numbers to the nearest 100?

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

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

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?

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?

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

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

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.

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

A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

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?

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

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

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

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

Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?