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.
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.
This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.
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.
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Can you find all the different triangles on these peg boards, and find their angles?
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
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.
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 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?
Can you substitute numbers for the letters in these sums?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
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?
Can you replace the letters with numbers? Is there only one solution in each case?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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.
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.
Find out what a "fault-free" rectangle is and try to make some of your own.
Try out the lottery that is played in a far-away land. What is the chance of winning?
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?
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?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Can you find all the different ways of lining up these Cuisenaire rods?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
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?
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?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Can you find the chosen number from the grid using the clues?
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?
A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
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.
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?
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?
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.
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
How many trains can you make which are the same length as Matt's, using rods that are identical?