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Networks/Graph Theory. Mathematical reasoning & proof. Making and proving conjectures. Algorithms. Combinatorics. Mathematical induction. Codes and cryptography. Patterned numbers. Working systematically. Binomial Theorem.There are 127 results
Broad Topics > Using, Applying and Reasoning about Mathematics > Working systematically
Magic W
Age 14 to 16 Challenge Level:
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.
Olympic Magic
Age 14 to 16 Challenge Level:
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?
Magic Caterpillars
Age 14 to 18 Challenge Level:
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
Rainstorm Sudoku
Age 14 to 16 Challenge Level:
Use the clues about the shaded areas to help solve this sudoku
Games Related to Nim
Age 5 to 16
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.
Twin Corresponding Sudokus II
Age 11 to 16 Challenge Level:
Two sudokus in one. Challenge yourself to make the necessary connections.
Integrated Sums Sudoku
Age 11 to 16 Challenge Level:
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. . . .
An Introduction to Magic Squares
Age 7 to 16
Find out about Magic Squares in this article written for students. Why are they magic?!
Colour in the Square
Age 7 to 16 Challenge Level:
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?
Constellation Sudoku
Age 14 to 18 Challenge Level:
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.
Shopping Basket
Age 11 to 16 Challenge Level:
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
Quadruple Sudoku
Age 11 to 16 Challenge Level:
Four small numbers give the clue to the contents of the four surrounding cells.
Difference Sudoku
Age 14 to 16 Challenge Level:
Use the differences to find the solution to this Sudoku.
Seasonal Twin Sudokus
Age 11 to 16 Challenge Level:
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Magnetic Personality
Age 7 to 16 Challenge Level:
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
Corresponding Sudokus
Age 11 to 18
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
The Best Card Trick?
Age 11 to 16 Challenge Level:
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?
LOGO Challenge - Pentagram Pylons
Age 11 to 18 Challenge Level:
Pentagram Pylons - can you elegantly recreate them? Or, the European flag in LOGO - what poses the greater problem?
LOGO Challenge - Sequences and Pentagrams
Age 11 to 18 Challenge Level:
Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?
Latin Squares
Age 11 to 18
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.
Smith and Jones
Age 14 to 16 Challenge Level:
Mr Smith and Mr Jones are two maths teachers. By asking questions, the answers to which may be right or wrong, Mr Jones is able to find the number of the house Mr Smith lives in... Or not!
Diagonal Product Sudoku
Age 11 to 16 Challenge Level:
Given the products of diagonally opposite cells - can you complete this Sudoku?
Twin Line-swapping Sudoku
Age 14 to 16 Challenge Level:
A pair of Sudoku puzzles that together lead to a complete solution.
Wallpaper Sudoku
Age 11 to 16 Challenge Level:
A Sudoku that uses transformations as supporting clues.
The Great Weights Puzzle
Age 14 to 16 Challenge Level:
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?
Pole Star Sudoku
Age 14 to 18 Challenge Level:
A Sudoku based on clues that give the differences between adjacent cells.
One Out One Under
Age 14 to 16 Challenge Level:
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?
Difference Dynamics
Age 14 to 18 Challenge Level:
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?
Latin Lilies
Age 7 to 16 Challenge Level:
Have a go at this game which has been inspired by the Big Internet Math-Off 2019. Can you gain more columns of lily pads than your opponent?
Olympic Logic
Age 11 to 16 Challenge Level:
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
Twin Chute-swapping Sudoku
Age 14 to 18 Challenge Level:
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?
Twin Corresponding Sudoku
Age 11 to 18 Challenge Level:
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
I've Submitted a Solution - What Next?
Age 5 to 18
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
Warmsnug Double Glazing
Age 14 to 16 Challenge Level:
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
Advent Calendar 2011 - Secondary
Age 11 to 18 Challenge Level:
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
The Naked Pair in Sudoku
Age 7 to 16
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
A Long Time at the Till
Age 14 to 18 Challenge Level:
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?
Instant Insanity
Age 11 to 18 Challenge Level:
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.
Simultaneous Equations Sudoku
Age 11 to 16 Challenge Level:
Solve the equations to identify the clue numbers in this Sudoku problem.
Alphabetti Sudoku
Age 11 to 16 Challenge Level:
This Sudoku requires you to do some working backwards before working forwards.
Rectangle Outline Sudoku
Age 11 to 16 Challenge Level:
Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.
Twin Corresponding Sudoku III
Age 11 to 16 Challenge Level:
Two sudokus in one. Challenge yourself to make the necessary connections.
Colour Islands Sudoku 2
Age 11 to 18 Challenge Level:
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.
NRICH is part of the family of activities in the Millennium Mathematics Project.