32 problems, 6 games, 65 articles, 33 general resources, 22 from Stage 1, 38 from Stage 2, 62 from Stage 3, 55 from Stage 4, 56 from Stage 5
Product Sudoku
Stage: 3, 4 and 5 Challenge Level: 
The clues for this Sudoku are the product of the numbers in adjacent squares.
Product Sudoku 2
Stage: 3, 4 and 5 Challenge Level:
Given the products of diagonally opposite cells - can you complete this Sudoku?
Vector Walk
Stage: 5 Challenge Level:
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Plaited Origami Polyhedra
Stage: Challenge Level:
These models have appeared around the Centre for Mathematical Sciences. Perhaps you woudl like to try to make some similar models of your own.
Star Find
Stage: 1 Challenge Level:
Can you see which tile is the odd one out in this design? Using the basic tile, can you make a repeating pattern to decorate our wall?
Diagonal Sums Sudoku
Stage: 2, 3 and 4 Challenge Level:
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
Intersection Sums Sudoku
Stage: 2, 3 and 4 Challenge Level:
A Sudoku with clues given as sums of entries.
Integrated Sums Sudoku
Stage: 3 and 4 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. . . .
Integrated Product Sudoku
Stage: 3 and 4 Challenge Level:
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.
More Bridge Building
Stage: 5 Challenge Level:
Which parts of these framework bridges are in tension and which parts are in compression?
All-variables Sudoku
Stage: 3, 4 and 5 Challenge Level:
The challenge is to find the values of the variables if you are to solve this Sudoku.
Basic Rhythms
Stage: 5 Challenge Level:
Explain why this pattern holds in other number systems using bases other than base 10. 987654321 = 8 x 123456789 + 9, 98765432 = 8 x 12345678 + 8, 9876543 = 8 x 1234567 + 7, 987654 = 8 x 123456 +. . . .
LOGO Challenge 5 - Patch
Stage: 3 and 4 Challenge Level:
Using LOGO, can you construct elegant procedures that will draw this family of 'floor coverings'?
Topkapi Palace
Stage: 2 and 3 Challenge Level:
These images are taken from the Topkapi Palace in Istanbul, Turkey. Can you work out the basic unit that makes up each pattern? Can you continue the pattern? Can you see any similarities and. . . .
Vectors - What Are They?
Stage: 5
The article provides a summary of the elementary ideas about vectors usually met in school mathematics, describes what vectors are and how to add, subtract and multiply them by scalars and indicates. . . .
A-level Core Mathematics Curriculum
Stage: 5 Challenge Level:
The mathematical content of A-level and GCSE is described, along with its relevance to science students
Making Maths: Celtic Knot Tiles
Stage: 2, 3 and 4 Challenge Level:
Make some celtic knot patterns using tiling techniques
Prepare for University - Biology
Stage: 5 Challenge Level:
Helpful preparation for university for those intending to study biological sciences.
Advent Sudoku
Stage: 3 Challenge Level:
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
LOGO Challenge 7 - More Stars and Squares
Stage: 3 and 4 Challenge Level:
Can you use LOGO to create a systematic reproduction of a basic design? An introduction to variables in a familiar setting.
Nim-7
Stage: 2 Challenge Level:
Can you work out how to win this game of Nim? Does it matter if you go first or second?
Prepare for University - Physics
Stage: Challenge Level:
Helpful preparation for university for those intending to study physical sciences.
LOGO Challenge - Following On
Stage: 3, 4 and 5 Challenge Level:
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?
Celtic Knotwork Patterns
Stage: 2 and 3
This article for pupils gives an introduction to Celtic knotwork patterns and a feel for how you can draw them.
Geoboards
Stage: 2 Challenge Level:
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
School Dinners
Stage: 3 Short Challenge Level:
Our school dinners offer the same choice each day. I try each option for each course in turn. Today I shall sit down to soup, meat and crumble. How long will it be before I eat the same meal again?
Traffic Lights
Stage: 2 Challenge Level:
The game uses a 3x3 square board. 2 players take turns to play, either placing a red on an empty square, or changing a red to orange, or orange to green. The player who forms 3 of 1 colour in a line. . . .
A First Product Sudoku
Stage: 3 Challenge Level:
Given the products of adjacent cells, can you complete this Sudoku?
Friezes
Stage: 3
Some local pupils lost a geometric opportunity recently as they surveyed the cars in the car park. Did you know that car tyres, and the wheels that they on, are a rich source of geometry?
Product Doubles Sudoku
Stage: 3 and 4 Challenge Level:
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
The NRICH - Transkills Project
Stage: Challenge Level:
Description of the university Transkills project.
First Forward Into Logo 3
Stage: 2, 3 and 4 Challenge Level:
More Logo for beginners. Now learn more about the REPEAT command.
Tessellating Transformations
Stage: 2 Challenge Level:
Can you find out how the 6-triangle shape is transformed in these tessellations? Will the tessellations go on for ever? Why or why not?
Equation Sudoku
Stage: 3, 4 and 5 Challenge Level:
Solve the equations to identify the clue numbers in this Sudoku problem.
LOGO Challenge - Recollection
Stage: 3, 4 and 5 Challenge Level:
Several procedures to think about but there are several things you can do to help yourself such as breaking the procedures down stepwise (rather than into smaller peices) What does the first line do?. . . .
LCM Sudoku
Stage: 4 and 5 Challenge Level:
Use the information about the lowest common multiples of the unknown numbers to help you solve this Sudoku.
Excel Interactive Resource: Fraction Addition & Fraction Subtraction
Stage: 3 and 4 Challenge Level:
Use Excel to practise adding and subtracting fractions.
Alphabetti Sudoku
Stage: 3 and 4 Challenge Level:
This Sudoku requires you to do some working backwards before working forwards.
Addition Equation Sudoku
Stage: 3, 4 and 5 Challenge Level:
You need to find the values of the stars before you can apply normal Sudoku rules.
The Naked Pair in Sudoku
Stage: 2, 3 and 4
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Making Maths: Stars
Stage: 2 Challenge Level:
Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?
LCM Sudoku II
Stage: 3, 4 and 5 Challenge Level:
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
Euler's Buckling Formula
Stage: 5 Challenge Level:
Derive Euler's buckling formula from first principles.
Links and Knots
Stage: 5
Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots, prime knots, crossing numbers and knot arithmetic.
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NRICH is part of the family of activities in the Millennium Mathematics Project, which also includes the Plus and Motivate sites.
email: nrich@damtp.cam.ac.uk
