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.
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?
A student in a maths class was trying to get some information from
her teacher. She was given some clues and then the teacher ended by
saying, "Well, how old are they?"
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
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.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.
Use the differences to find the solution to this Sudoku.
Four small numbers give the clue to the contents of the four
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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.
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.
This Sudoku, based on differences. Using the one clue number can you find the solution?
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Label this plum tree graph to make it totally magic!
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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?
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.
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 man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
A Sudoku with a twist.
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Given the products of adjacent cells, can you complete this Sudoku?
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
A Sudoku with clues as ratios.
You need to find the values of the stars before you can apply normal Sudoku rules.
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
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?
Charlie and Abi 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?
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.
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?
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
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 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.