article
I've submitted a solution - what next?
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
interactivity
Introducing NRICH TWILGO
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?
article
Phiddlywinks - a tribute to John Conway
Read this article to find out more about the inspiration for NRICH's game, Phiddlywinks.
article
Latin Squares
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.
article
Corresponding Sudokus
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
problem
Simultaneous Equations Sudoku
Age
11 to 18
Challenge level
Solve the equations to identify the clue numbers in this Sudoku problem.
problem
All-Variables Sudoku
Age
11 to 18
Challenge level
The challenge is to find the values of the variables if you are to
solve this Sudoku.
problem
LCM Sudoku II
Age
11 to 18
Challenge level
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
problem
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.
problem
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.
problem
River Crossing
Age
11 to 18
Challenge level
There is nothing half so much worth doing as simply messing about in boats...
problem
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
problem
crossing the bridge
Age
11 to 18
Challenge level
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
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.
problem
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?
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?
problem
LOGO Challenge - Following on
Age
11 to 18
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?
article
Binomial Coefficients
An introduction to the binomial coefficient, and exploration of some of the formulae it satisfies.
problem
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?
problem
Sorted
Age
14 to 18
Challenge level
How can you quickly sort a suit of cards in order from Ace to King?
problem
The Tour de Clochemerle
Age
14 to 18
Challenge level
Can you work out where these 5 riders came in a not-quite-so-famous bike race?
problem
Symmetricality
Age
14 to 18
Challenge level
Five equations and five unknowns. Is there an easy way to find the unknown values?
problem
Favourite
Parabolic Patterns
Age
14 to 18
Challenge level
The illustration shows the graphs of fifteen functions. Two of them have equations $y=x^2$ and $y=-(x-4)^2$. Find the equations of all the other graphs.
problem
Pole Star Sudoku
Age
14 to 18
Challenge level
A Sudoku based on clues that give the differences between adjacent cells.
problem
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?
problem
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.
problem
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.
problem
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?
article
Impuzzable
This is about a fiendishly difficult jigsaw and how to solve it
using a computer program.
problem
Function Pyramids
Age
16 to 18
Challenge level
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?
problem
Purr-fection
Age
16 to 18
Challenge level
What is the smallest perfect square that ends with the four digits
9009?
problem
W Mates
Age
16 to 18
Challenge level
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.
problem
Twin Equivalent Sudoku
Age
16 to 18
Challenge level
This Sudoku problem consists of a pair of linked standard Suduko puzzles each with some starting digits
problem
Exhaustion
Age
16 to 18
Challenge level
Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2
problem
Adding machine
Age
16 to 18
Challenge level
Can you set the logic gates so that this machine can decide how many bulbs have been switched on?
problem
Stage 5 Cipher Challenge
Age
16 to 18
Challenge level
Can you crack these very difficult challenge ciphers? How might you systematise the cracking of unknown ciphers?
problem
Interpolating polynomials
Age
16 to 18
Challenge level
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.
problem
Knights moving
Age
16 to 18
Challenge level
Can you swap the black knights with the white knights in the minimum number of moves?