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?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
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?"
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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?
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.
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. . . .
Four small numbers give the clue to the contents of the four
A pair of Sudoku puzzles that together lead to a complete solution.
Given the products of adjacent cells, can you complete this Sudoku?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
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.
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?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
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.
This Sudoku, based on differences. Using the one clue number can you find the solution?
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
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.
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?
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. . . .
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.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Use the differences to find the solution to this Sudoku.
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?
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
This Sudoku combines all four arithmetic operations.
Given the products of diagonally opposite cells - can you complete this Sudoku?
The clues for this Sudoku are the product of the numbers in adjacent squares.
A Sudoku with clues as ratios.
A Sudoku that uses transformations as supporting clues.
Two sudokus in one. Challenge yourself to make the necessary
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's
there is one digit, between the two 2's there are two digits, and
between the two 3's there are three digits.
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?
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?
A Sudoku with clues given as sums of entries.
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?
A pair of Sudokus with lots in common. In fact they are the same problem but rearranged. Can you find how they relate to solve them both?
This sudoku requires you to have "double vision" - two Sudoku's for
the price of one
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.