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.
A pair of Sudoku puzzles that together lead to a complete solution.
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?
Use the differences to find the solution to this Sudoku.
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.
This Sudoku, based on differences. Using the one clue number can you find the solution?
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?
Four small numbers give the clue to the contents of the four
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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.
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
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?
Can you coach your rowing eight to win?
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?
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 Sudoku with a twist.
Find out about Magic Squares in this article written for students. Why are they magic?!
A Sudoku with clues as ratios.
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?
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.
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
Given the products of adjacent cells, can you complete this Sudoku?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
You need to find the values of the stars before you can apply normal Sudoku rules.
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.
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
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?
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Two sudokus in one. Challenge yourself to make the necessary
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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Use the clues about the shaded areas to help solve this sudoku
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
How many different symmetrical shapes can you make by shading triangles or squares?
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?
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 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?
An introduction to bond angle geometry.
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.