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.
The letters of the word ABACUS have been arranged in the shape of a
triangle. How many different ways can you find to read the word
ABACUS from this triangular pattern?
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.
Four small numbers give the clue to the contents of the four
Use the differences to find the solution to this Sudoku.
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. . . .
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?
A few extra challenges set by some young NRICH members.
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?
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.
This Sudoku, based on differences. Using the one clue number can you find the solution?
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
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?
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?
This challenge extends the Plants investigation so now four or more children are involved.
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
A pair of Sudoku puzzles that together lead to a complete solution.
Four friends must cross a bridge. How can they all cross it in just
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.
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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 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. . . .
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?
Can you coach your rowing eight to win?
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
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?
A Sudoku with a twist.
A Sudoku with clues as ratios.
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.
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. . . .
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?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
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.
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
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?
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.
A challenging activity focusing on finding all possible ways of stacking rods.
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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?
Use the clues about the shaded areas to help solve this sudoku