Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's there is one digit, between the two 2's there are two digits, and between the two 3's there are three digits.
This article for primary teachers suggests ways in which to help children become better at working systematically.
A Sudoku with clues given as sums of entries.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
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.
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.
A little mouse called Delia lives in a hole in the bottom of a tree.....How many days will it be before Delia has to take the same route again?
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.
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
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?
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?
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?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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?
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
Can you cover the camel with these pieces?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
Find your way through the grid starting at 2 and following these operations. What number do you end on?
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?
A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?
Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?
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. . . .
How many different triangles can you make on a circular pegboard that has nine pegs?
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.
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?
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?
Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.
How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?
Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?
Find out about Magic Squares in this article written for students. Why are they magic?!
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
What happens when you try and fit the triomino pieces into these two grids?
In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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?
George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?