Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
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?
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?
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
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 values of the nine letters in the sum: FOOT + BALL = GAME
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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?
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.
A pair of Sudoku puzzles that together lead to a complete solution.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
Given the products of adjacent cells, can you complete this Sudoku?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
This Sudoku, based on differences. Using the one clue number can you find the solution?
Special clue numbers related to the difference between numbers in
two adjacent cells and values of the stars in the "constellation"
make this a doubly interesting problem.
Four small numbers give the clue to the contents of the four
Given the products of diagonally opposite cells - can you complete this Sudoku?
Use the differences to find the solution to this Sudoku.
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
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 mathematician goes into a supermarket and buys four items. Using
a calculator she multiplies the cost instead of adding them. How
can her answer be the same as the total at the till?
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.
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do 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.
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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 use your powers of logic and deduction to work out the missing information in these sporty situations?
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?
Use the interactivity to play two of the bells in a pattern. How do
you know when it is your turn to ring, and how do you know which
bell to ring?
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?
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
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?
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
You need to find the values of the stars before you can apply normal Sudoku rules.
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
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?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
Two sudokus in one. Challenge yourself to make the necessary