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

### Twin Corresponding Sudoku

This sudoku requires you to have "double vision" - two Sudoku's for the price of one

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### Simultaneous Equations Sudoku

Solve the equations to identify the clue numbers in this Sudoku problem.

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### All-Variables Sudoku

The challenge is to find the values of the variables if you are to
solve this Sudoku.

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### LCM Sudoku II

You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.

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### Colour Islands Sudoku 2

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.

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### Advent Calendar 2011 - Secondary

Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.

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### River Crossing

There is nothing half so much worth doing as simply messing about in boats...

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### crossing the bridge

Four friends must cross a bridge. How can they all cross it in just 17 minutes?

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### Instant Insanity

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.

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### LOGO Challenge - Pentagram Pylons

Pentagram Pylons - can you elegantly recreate them? Or, the
European flag in LOGO - what poses the greater problem?

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### LOGO Challenge - Sequences and Pentagrams

Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?

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### LOGO Challenge - Following on

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.

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### Twin chute-swapping Sudoku

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?

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### Difference Dynamics

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

### The Tour de Clochemerle

Can you work out where these 5 riders came in a not-quite-so-famous bike race?

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### Symmetricality

Five equations and five unknowns. Is there an easy way to find the unknown values?

problem

Favourite

### Parabolic Patterns

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

### Constellation Sudoku

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.

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### A long time at the till

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?

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### Magic Caterpillars

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.

article

### Impuzzable

This is about a fiendishly difficult jigsaw and how to solve it
using a computer program.

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### Twin Equivalent Sudoku

This Sudoku problem consists of a pair of linked standard Suduko puzzles each with some starting digits

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### Function Pyramids

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?

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### W Mates

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.

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### Adding machine

Can you set the logic gates so that this machine can decide how many bulbs have been switched on?

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### Knights moving

Can you swap the black knights with the white knights in the minimum number of moves?

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### Stage 5 Cipher Challenge

Can you crack these very difficult challenge ciphers? How might you systematise the cracking of unknown ciphers?

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### Interpolating polynomials

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.