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.
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?
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
A Sudoku with clues given as sums of entries.
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.
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.
Find out about Magic Squares in this article written for students. Why are they magic?!
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
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?
Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.
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.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
What happens when you try and fit the triomino pieces into these two grids?
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?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Can you cover the camel with these pieces?
Can you find all the different triangles on these peg boards, and find their angles?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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.
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
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?
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.
This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.
In this matching game, you have to decide how long different events take.
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Try this matching game which will help you recognise different ways of saying the same time interval.
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?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
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.
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
Find out what a "fault-free" rectangle is and try to make some of your own.
Can you find all the different ways of lining up these Cuisenaire rods?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
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.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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?
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?
How many trains can you make which are the same length as Matt's, using rods that are identical?
A challenging activity focusing on finding all possible ways of stacking rods.
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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?
I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?