Show there are exactly 12 magic labellings of the Magic W using the numbers 1 to 9. Prove that for every labelling with a magic total T there is a corresponding labelling with a magic total 30-T.
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
Label this plum tree graph to make it totally magic!
Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?
This Sudoku problem consists of a pair of linked standard Suduko puzzles each with some starting digits
Pentagram Pylons - can you elegantly recreate them? Or, the European flag in LOGO - what poses the greater problem?
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
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?
Can you swap the black knights with the white knights in the minimum number of moves?
This is about a fiendishly difficult jigsaw and how to solve it using a computer program.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
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 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 Sudoku based on clues that give the differences between 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.
Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.
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?
in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
The challenge is to find the values of the variables if you are to solve this Sudoku.
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2
Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?
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?
An introduction to the binomial coefficient, and exploration of some of the formulae it satisfies.
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.
Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.
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?
What is the smallest perfect square that ends with the four digits 9009?
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?
Find out about Magic Squares in this article written for students. Why are they magic?!
Use the differences to find the solution to this Sudoku.
Four small numbers give the clue to the contents of the four surrounding cells.
A Sudoku with clues as ratios.
Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?
This Sudoku, based on differences. Using the one clue number can you find the solution?
A function pyramid is a structure where each entry in the pyramid is determined by the two entries below it. Can you figure out how the pyramid is generated?
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.
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?
This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
A pair of Sudoku puzzles that together lead to a complete solution.
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
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.