Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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.
Find out about Magic Squares in this article written for students. Why are they magic?!
Four small numbers give the clue to the contents of the four surrounding cells.
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.
You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?
Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.
Imagine a stack of numbered cards with one on top. Discard the top, put the next card to the bottom and repeat continuously. Can you predict the last card?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
This Sudoku, based on differences. Using the one clue number can you find the solution?
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.
Use the differences to find the solution to this Sudoku.
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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?
Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
A pair of Sudoku puzzles that together lead to a complete solution.
in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?
You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest?
It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?
Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?
Two sudokus in one. Challenge yourself to make the necessary connections.
This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .
A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.
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. . . .
The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?
A Sudoku with a twist.
A Sudoku with clues as ratios.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.
Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
An introduction to bond angle geometry.
Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?
How many different symmetrical shapes can you make by shading triangles or squares?
Charlie and Lynne put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
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.
A challenging activity focusing on finding all possible ways of stacking rods.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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.
This challenge extends the Plants investigation so now four or more children are involved.
If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?