Thursday, 4 February 2016

How To Solve The GCHQ Christmas 2015 Puzzle (Possibly?)

Now that the competition is closed I thought it was safe to publish this blog post.

I'm sure some of this is wrong but I'm fairly sure some is correct, so I thought I'd have a go at explaining the sorts of approach one might take to solving the GCHQ Christmas 2015 puzzle.  It's entirely possible I may have arrived at the right answer for the wrong reasons.

Where it's wrong or you can think of a better way to solve it, or explain how to solve it, please let me know.


Part 1

The initial puzzle that was delivered with the GCHQ Christmas card was this:




It is a nonogram.  There are plenty of sites that provide these types of puzzle, for example, http://www.puzzle-nonograms.com/

To solve a puzzle, one determines which squares should be shaded and which should be empty. Discovering which squares fall into which categories is equally important. One should never guess: only if the status of a cell can be determined logically should it be shaded or left blank in the final solution.

Techniques for solving these puzzles can be found on Wikipedia under “nonogram”: https://en.wikipedia.org/wiki/Nonogram

When solved correctly you should see this image:



Most people will recognise this as a QR code.  All you need do is install your favourite QR code reader on your smart phone and it will reveal the URL for the second part of the puzzle:

http://www.gchq.gov.uk/puzz/Pages/index.aspx

The QR code actually decodes as follows but typing this into the browser window is sufficient to take you to the full address:


Part 2

Part 2 has six questions.  The first is:

Q1. Which of these is not the odd one out?

A. STARLET
B. SONNET
C. SAFFRON
D. SHALLOT
E. TORRENT
F. SUGGEST

The solution is nothing to do with the meaning of the words but rather the patterns within the words.  You will see that all bar one of the words have the following characteristics:

1. Starts with a “S” and ends with a “T”
2. Has a double letter in the centre of the word
3. Comprises 7 letters
4. Is a noun

The only word that obeys all three of these, and hence is not the odd one out, is SHALLOT.

The second question is:

Q2. What comes after GREEN, RED, BROWN, RED, BLUE, -, YELLOW, PINK?

A. RED
B. YELLOW
C. GREEN
D. BROWN
E. BLUE
F. PINK

This relies upon you knowing the score value of snooker balls ie red balls worth one (1), yellow (2), green (3), brown (4), blue (5), pink (6) and black (7).

This makes the sequence in the question: 3, 1, 4, 1, 5, -, 2, 6

This is not the obvious puzzle ie some form of arithmetic sequence where each number is calculated by using the other.  It is the first few digits of the constant Pi which are 3.141592653...

Now you can see why there is a dash in the sequence of digits: there is no snooker ball with the value of 9.

So, the next digit should be five 5 which equates to the blue ball ie selection E in the list.

The third question is:

Q3. Which is the odd one out?

A. MATURE
B. LOVE
C. WILDE
D. BUCKET
E. BECKHAM
F. SHAKA

These are names of famous people.  The simplest thing is to search for them online:

A. Victor MATURE
B. Mike LOVE
C. Oscar WILDE
D. Charlie BUCKET
E. Romeo BECKHAM

[UPDATE: The theme previously failed to mention was the NATO phonetic alphabet.]

Which means that Shaka is the odd one out as it is a first name (actually he had only one given name) whilst the others are surnames.  So the selection should be F.

The fourth question is:

Q4. I was looking at a man on top of a hill using flag semaphore to send a message, but to me it looked like a very odd message. It began "ZGJJQ EZRXM" before seemingly ending with a hashtag. Which hashtag?

A. #SGM
B. #SEM
C. #SEN
D. #SGN
E. #TEN
F. #TGN

For this you need to look up semaphore.  Easily done on the web.  The letters spelt out in semaphore are:


But this assumes you are facing the man on the hill who is sending the semaphore.  Imagine you are behind him.  Now look for the mirror image of the letters in the message ZGJJQ EZRXM

You find it spells out HAPPY CHRIS

Being a Christmas quiz it’s safe to assume that the message is HAPPY CHRISTMAS so you are looking for the mirror flags for TMAS.  The mirror of “T” is “Numeric” ie the sign you make when about to send a number, a prefix commonly written as “#”.

So the mirror flags of TMAS are #SGM, making your selection A.

The fifth question is:

Q5. What comes after 74, 105, 110, 103, 108, 101, 98, 101, 108, 108?

A. 108
B. 101
C. 115
D. 123
E. 111
F. 103

Anyone who has played with computers will probably recognise these as the decimal values for ASCII. 

When you decode the sequence in the question using these ASCII values it reveals the message "Jinglebell" And remember it’s a Christmas quiz so the letter they are looking for is “S” ie "Jinglebells". In ASCII the letter "s" is 115 meaning you should select answer C.

The sixth question is:

Q6. What comes next: D, D, P, V, C, C, D, ?

A. F
B. E
C. D
D. C
E. B
F. A

And yet again you have to remember this is a Christmas quiz.  And who is it that pulls Santa’s sleigh: Dasher, Dancer, Prancer, Vixen, Comet, Cupid, Dunder (variously spelled Donder and Donner), and Blixem (variously spelled Blitzen and Blixen).

However you spell it the missing name begins with a B which means you should select E.

Assuming you have entered selected the correct answers you will be redirected to a page containing new puzzles in Part 3.


Part 3

Question A is one of those that you should not look too deeply into.  Rather than think about the meanings of the words simply look at the sequence of the letters (minus the commas). 

If you were to add the word Cub (ie the letter C, U, B) to the end it becomes a palindrome.

Buck, Cod, Dahlia, Rook, Cuckoo, Rail, Haddock, ? becomes:

BUCKCODDAHLIAROOKCUCKOORAILHADDOCKCUB

Hence, Word A is “Cub”.

Question B is something to do with arithmetic as it uses mathematical symbols.  So how could the words be numbers.  Well, not everyone speaks English.  Think of these words in French. 

Then you see that they are anagrams of:

Sept = 7
Dix neuf = 19
Trois = 3

Plug those numbers into the equation to give:

7 +SQRT16 = 11

which is Onze in French.  The only meaningful anagram of onze is “zone”, which is the answer for Word B.

Question C has a big clue by mentioning Samuel as it was Samuel Morse who created one of the most famous codes.  Letters in Morse code are:



The word “agony” is  .---.----.-.--  which if you exchange dots for dashes gives
-…-….-.-.. which if you split it up correctly gives -..  .  -.  ..  .-  .-.. ie it spells “denial”.

The same is true of the words “witty” and “tepid”, the other word pair given in the question.

There are online Morse code translators if you want to try this for yourself.

Following this same pattern the word “smart” is converted to “often” which is thus Word C.

Question D contains clues like those you find in cryptic crosswords. 

It’s not possible to describe easily how such clues are solved but you may find it useful to read this entry.

  1. The word being sought by the first clue is WASSAIL. 
  2. The second clue is answered with ANTENNA.
  3. The third is STRINGY.
  4. The fourth is SEIZURE. 

And there the clues apparently stop.

But the thing that these have in common is that they all have seven letters.  Assuming the remainder of the answers have seven letters, and knowing there are seven answers, you can start to create a matrix:


W
A
S
S
A
I
L
A
N
T
E
N
N
A
S
T
R
I
N
G
Y
S
E
I
Z
U
R
E
?






?






?







You start to realise that the words read the same vertically as horizontally.  It’s appears to be a word square.

As it happens there are very few 7x7 word squares in the English language. Google it and the very first entry is http://digitalcommons.butler.edu/cgi/viewcontent.cgi?article=1914&context=wordways the last entry of which is a 7x7 word square that solves the above matrix


W
A
S
S
A
I
L
A
N
T
E
N
N
A
S
T
R
I
N
G
Y
S
E
I
Z
U
R
E
A
N
N
U
L
A
R
I
N
G
R
A
T
E
L
A
Y
E
R
E
D


Thus you have Word D as “layered”.

If you have entered these answers correctly you see the page display the following:



You simply need to follow the link given to Part 4.

Part 4

Question A will be familiar to many who work in computing where binary and powers of two (2) are commonplace. 

It is the sequence of the powers of 2 but displaying only the odd digits.  Powers of two (2) are:

2, 4, 8, 16, 32, 62, 128, 256, 512, 1024, 2048,...

From this you can see the  missing number is 512 or using only the odd digits it’s 52. 

Hence, Answer A is 52.

Question B has numbers that look very different: some are very large whilst others much smaller. 

A clue to Answer B is given by the fact that they say you should be looking to construct an IP address A.B.C. However, those familiar with the Internet will know that that IP addresses always have the format A.B.C.D.  The only way in which their given format can be turned into an IP address is if Answers B is a decimal.



Assuming they are using some form of powers (they previously showed interest in powers of 2) and knowing that the numbers are large (meaning they probably need to be multiplied by a large factor if this is part of some pattern), and knowing there are some negative numbers so it is likely to have to include use of odd powers (otherwise everything is made positive), we can start to look for sequences.

After some playing you find that there is a sequence of descending and ascending numbers that gives the numbers in the question (type these into Google to see that they produce the numbers in the question):

9^2 x -5^3 x 10^4
8^2 x -3^3 x 10^3
7^2 x -1^3 x 10^2
6^2 x 1^3 x 10^1
5^2 x 3^3 x 10^0
4^2 x 5^3 X 10^-1

If you continue the pattern you have 3^2 x 7^3 x 10^-2

This gives the answer 30.87

Question C is one where you need not to be fooled by the presentation – think of what would happen if you wrote the numbers with each of the three digits on a different line to build a matrix – rotate the line on which the number starts when writing it vertically. So that 321, 444, 675, 680, 370, 268, 949, 206, 851, is written as:

3, 4, 5, 6, 7, 8, 9, 0, 1
2, 4, 6, 8, 0, 2, 4, 6, 8
1, 4, 7, 0, 3, 6, 9, 2, 5

Which means the first line is counting by 1, rolling over at 10, the second is counting by 2, again rolling over at 10 and the third is counting by 3.

[UPDATE: A better way of explaining this is to write the digits in columns:

3 2 1 
4 4 4 
6 7 5 
6 8 0 
3 7 0 
2 6 8 
9 4 9 
2 0 6 
8 5 1  

If you look down the diagonals (upper left to lower right) you see that the numbers increase by 1's, 2's and 3's modulo 10.

If the sequence is continued on each line it gives you 2 0 8.

If you have put in the correct answers you are presented with this text:



And sure enough if you type in 52.30.87.208/next.html into your browser you are redirected to Part 5 of the puzzle at http://www.gchq.gov.uk/58aa7ef96f3051b0/pages/index.aspx

Part 5

The first question is:



General knowledge, and a bit of Googling, reveals that there are several categories into which the words fall:

  • John LeCarre Novels
  • Types of bear
  • Preceded by the word ONE
  • Dr Who monsters
  • Preceded by the sound “sigh”
  • Replacing the first letter results in a word that means “nothing” ie nada, zero, zip
  • Computer programing languages

And, the completed words are:

CAN-ADA
ARM-BANDIT
TRACT-ATORS
BLACK-HOLE
BROWN-TROUT
MIDDLE-C
CI-TED
CY-CLONE
SEA-DEVILS
FELL-SWOOP
SALLY-FORTH
CONSTANT-GARDENER
GOBI-DESERT
GRIZZLY ADAMS
SLIT-HEEN
HIT-WONDER
HORSE-TOWN
RUSSIA-HOUSE
LINCOLN-IMP
KODIAK-ARCHIPELIGO
FRONTAL-LISP
DOVE-LOVE
MAN-BAND
NIGHT-MANAGER
CYBER-MEN
LEICESTER-MERCURY
DADA-NADA
NIGHT-STAND
OIL-NIL
ZONE-NONE
BOUGHT-NOUGHT
AUTO-NS
PRIM-ORDS
BLAISE-PASCAL
SECRET-PILGRIM
POLAR-ICECAP
PSI-ON
PSY-CHIC
MONTY-PYTHON
HONOURABLE-SCHOOLBOY
SCI-FI
SCY-THE
SI-DELIGHT
SIGH-TREADING
MISSION-SONG
SPECTACLED-CAIMAN
PERFECT-SPY
SON-TARONS
TEDDY-SHERINGHAM
TRICK-PONY
DELICATE-TRUTH
ICE-WARRIORS
WAY-STREET
HERO-ZERO
FILCH-ZILCH
NIP-ZIP

Ordering the list as requested in the question you find that the “cyber” is in a position that means the answers they want is:

MANAGER MEN MERCURY or with no spaces as requested MANAGERMENMERCURY

The second question is:




It’s clearly a mathematical puzzle due to the symbols but as in earlier stages numbers are not always written in Arabic numerals.  In this case it is Roman numerals.

Hence the sum is (SQRT((3+672)/3)) -1 which is 14 or XIV in Roman numerals.

Of course, x might not be ten in Roman numerals but instead might be used as it usually is: as a multiplication symbol.  That means there are a number of possible solutions to this sum. 

SQRT((3+(650x12))/3) - 1 which gives 50 or L in Roman numerals.

SQRT((3+(660x2))/3) - 1 which gives 20 or XX in Roman numerals.

The alternative solutions do suggest they are part of some valid pattern as the square root of the numbers in each are integer, which is all that Roman numerals can cope with.

Plus the square root of a number can be both positive and negative.

[UPDATE: Of the answers given here, this is the one that is incomplete - there were several other possible interpretations of the "x", albeit on the right hand side of the equation.  The correct answer is given in the proper GCHQ model answer sheet discussed in the next blog entry.  These additional interpretations eluded me completely.]


The third question is:



Simply follow the rules of multiplication shown in the question – you don’t need to understand Kronecker products as the question tells you what to do.

The multiplication tables come out as:



Use these to calculate each multiplication and the resulting matrix shows the position of the pieces on the boards.  If you follow the rules for a Kronecker product (as explained in the question) you will find that a 4x2 matrix multiplied by a 2x4 matrix results in an 8x8 matrix ie the size of a chess board.

I haven't worked out how to draw the results simply on a web page.  I'm sure larger brains than mine will. That's not quite the end though. the result of the positions on the boards can then be used to find a further word.

[UPDATE: As I tried to hint at without drawing the chess board, the moves spell out the word KRONECKER.]

The fourth question is:


Which has a very big clue in the diagram that is included with the question ie:


This square is the fundamental polygon of a torus which in mathematics is a form of “manifold”.
We’ll revisit why the idea of a torus later.

The first and most obvious thing to complete are the words. They are two word movie titles.  Even if you don’t know them all some simple Googling will help you complete the list as shown below:



Next match the colours.  There are two ways to match as there are four of each colour. There is nothing that says you cannot reorient a single square in order to complete the pattern or use the squares more than once.  I made the first row of my match as follows:






Now repeat the same matches spreading out from the centre initial line.  If you use my initial line you get a pattern in which each colour is matched at least once ie all four of a colour has a place next to its match.  This gives you:


You start to see the pattern repeating and wrapping around as if it were draw on the surface of a piece of paper that twists as it wraps – just like the way in which a toilet roll is made.




If you think back to the initial line that is at the centre of this repeating pattern and take a look at the second word of the movie title (the ones you found) of the titles in the squares above and below the central line, and you choose the letter indicated by the dice number you see it is the same letter.
You find a words that emerges is: ORIENTABLE. 


This is also a pun as in mathematics for an orientable surface, a consistent choice of "clockwise" (as opposed to counter-clockwise) is called an orientation, and the surface is called oriented.  A tube constructed like a toilet roll and joined at its ends is a torus and this torus is one which is has a surface that is oriented.

Also, anyone who has watched TV reports about GCHQ will have seen that their head office is shaped like a donut which is a torus.

The fifth question is:




The words on the spokes are clues to a word.  Each spoke multiple clues leading to multiple words.  Hence, the semi-colon.  You approach this just like a simple definitions crossword ie not cryptic.

Working clockwise the answers to the clues are:

Sphere; Grin
Siam; Wiser
Lego; Leads
Aragog; Ron
Born; To; Mir
Grim; Lii (Roman numerals again)
Mercia; Dock
Fro; Doer

The next clue is the picture itself.  It is a golden ring with six groups of words.  For those who know The Lord of the Rings trilogy they will recognise the ring.  If you look at each group set of words and look for words from the story you can make:

Peregrin
Samwise
Legol
Aragorn
Boromir
Gimli
Meriadoc
Frodo

But there is still one set of words unsolved – the M and A. There appears to be no clue as to what these are. However, Roman numerals is a theme in this puzzle so M is probably Grand ie slang for 1000. And in the NATO phonetic alphabet used by radio operators A is transmitted as Alfa (not Alpha as many assume). 

From Grand and Alfa we can construct another Lord of the Rings related word – Gandalf.

You can find most of what you need by reading about Bilbo Baggins and the plots for Lord of the Rings. although Bilbo's story is really in the precursor book The Hobbitt.

Assuming all of the above is correct then there are a series of letters left over.  These spell out, in the order in which they occur:

S H I R E D R A G O N T R I C K E R

In the story who was the character who tricked the dragon?  The answer is Bilbo as in Bilbo Baggins

Also if you say the abbreviation of Lord of the Rings (LOTR) it sounds like Looter, the title of this question.

The sixth question is:



This is solved in exactly the same way as a Sudoku (a Wordoku) only using the 26 letters of the alphabet instead of the digits 0-9.  There are online solvers which will show you the possible candidate solutions to a Worduku.   There are a number of candidate solutions.



You can see from these which has a possible message in the squares mentioned in the question – the correct message is obvious when you see it.  After all it is a Christmas quiz.

The message in the squares on the top line appears to be is MERRY XMAS. 

See http://www.sudoku-solutions.com/index.php?page=wordoku9by9&SUDOKU_TYPE=6 to try this for yourself.

[UPDATE: There are two possible solutions (shown above) where the message contained in the highlighted squares is MERRY CHRISTMAS and HAPPY CHRISTMAS.  When the wordoku is solved using these messages the remainder of the solution means that the first letters in the first line are MXAHRYESP and HXRMSAEP.]

The seventh question is:




Graph A shows you the way in which the others should be constructed.  In the first you are looking for a set of “things” which have two characteristics which are documented by the connection and direction of the arrows.

Graph A  has a big clue is that it is obviously all of the letters of the alphabet.  If you were to put the words for each letter from the NATO radio alphabet (Alfa, Bravo, Charlie, etc) in place of the letters you see that the relationships in the graphs are those for letters appearing in the words for each letter. So, Charlie (C), Mike (M) and Yankee (Y) all have an E in them hence arrows form C, M and Y point to E. 

Not every relationship has to be shown ie Yankee doesn’t have to also point at A, N, and K. It is not possible to draw a graph such as this (known as a Tree) showing every relationship without going back over certain points.  It is was exactly such a solution that Euler used when seeing if the seven bridges of Konigsberg could be traversed with crossing any of them twice, that resulted in what we known call Graph Theory.

If the letters are the NATO alphabet then obvious E stands for ECHO.

Graph B presumably follows the same design criteria as graph A: you are looking for a set of “things” that number 12 in total. 

You are also told that the numbers 3 and 5 have a two way relationship so presumably we are looking for a pattern where each member of the set has two characteristics which inter-relate for those particular elements of the set.

The most obvious complete set of twelve in daily use is months.  If you assume the characteristics of these months are their position in the year and the number of letters in the word that spells the month, then the graph can be made to work.  For example, March is the 3rd month and has 5 letters, whereas May is the 5th month and has 3 letters – the letters 3 and 5 are shown as a two way relation on the graph.

Putting all the other months in their appropriate place leaves you with a month which has no relationship of its position in the year to the number of letters in a month’s spelling (or vice versa). 

It is SEPTEMBER, which is the answer as it is the 9th month and has 9 letters, which holds no relation to the other months.

Graph C  presumably is another complete set of 8 items. 

The most obvious such set are the planets in the solar system - at least it is since Pluto was demoted. If you repeat the exercise used in graph B using the position of a planet in the solar system and the number of letters in its name the graph works if the answer is URANUS.

Graph D is a set of 10 elements. 

The most obvious are digits 0-9.  But this does not work. 

However, if you use 1-10 but, taking the hint from graph A, spell the numbers and assign the score you get for each in Scrabble you can make the graph work assign the scores such spellings you find that you can make the graph work.

This starts to make more sense when you realise that there could be many ways of spelling 0 (zero, nil, nought, etc – as we found from the word association puzzle at the beginning of Part 5).  It also makes sense as the scrabble score for ZERO does not lie in the range 0-9 and so it would not be an inter-related characteristic.

Using this method gives the answer of EIGHT.


The eighth question is:



This is an exercise in not assuming that all words are in English. 

The “category” to which the question refers appears to be countries. But the words are in the native language of those countries (or at least the transliterated forms of the language).

Countries found are:

ZHONGGUO – CHINA
SRBIJA – SERBIA
POLSKA – POLAND
HRVATSKA – CROATIA
AOTEROA – NEW ZEALAND
BHARAT – INDIA
DRUK YUL-  BHUTAN
EESTI – ESTONIA
HAYASTAN – ARMENIA
NIHON – JAPAN
SAKARTVELO – GEORGIA
SHQIPERIA – ALBANIA
SUOMI – FINLAND
VITI – FIJI
ESWATINI – SWAZILAND
HANGUK - KOREA
ELLAS - GREECE
ERTRA - ERITREA
DHIVEHI RAAJJE - MALDIVES

[UPDATE: The point previously not explained was that DHIVEHI RAJJE does not appear as a complete word as do the others.  It is amongst the left over letters when the others are removed.  You still then need to remove the letters that comprise DHIVEHI RAJJE to arrive at the answer.]

Assuming these to be correct it leaves the letters EARUSTER which spell TREASURE: rather apt for a puzzle in which you are searching for a word.

The ninth question is:



The question itself gives the clue that what one should do is construct a 10x10 matrix.  The clues after the register entries allow you to apply logic in the way familiar to puzzle book fans so that the matrix can be filled in.  It is not dissimilar to the very first question ie the nonogram. 


I think it’s supposed to be a duck.

[UPDATE: A fellow solver has pointed out that the first letter from each sentence in the question spells out GET DOWN, in other words DUCK.  Suggests the picture is a duck.]

The tenth question is a standard cryptic crossword that will be familiar to those who do such puzzles. 

As mentioned earlier, it is difficult to describe how one solves such puzzles as it requires a degree of general knowledge as well as a level of intuition for what the word or phrase that fits the grid might be.  A good description of how to solve such puzzles is contained in, where else,  Wikipedia or use the link previously given.

This gives the following answers:

Across

(1A) A Spanish greeting returned - in Oahu? (5) = ALOHA
(5A) Addicts in American casualty head south. (5) = USERS
9A) Organist confused by criticism. (8) = ROASTING
(10A) Own all of company run by short geek. (6) = CORNER
(12A) Recess in a primary school enjoyable initially. (4) = APSE
(14A) Local fathers hold back musical, and they are shunned. (7) = PARIAHS
(16A) Crude language. (5) = BASIC
(19A) A dog - more than one - need to be in early. (6) = CURFEW
(20A) South African diver goes to bar. (6) = SALOON
(22A) Scottish athlete. (4) = JOCK
(24A) Bird - woman - left nothing. (8) = SHELDUCK
(25A) Old cat heard music. (4) = OPUS
(26A) Joint festered endlessly. (5) = ANKLE
(27A) A jewel for each one. (7) = PERIDOT
(28A) Pay three notes. (3) = FEE
(29A) Mixed bones a good food supply for horse. (7) = NOSEBAG

Down

(1D) Affected men, possibly those from York or Liverpool. (11) = ARCHBISHOPS
(2D) Sponge from backward idiot and a hothead. (6) = LOOFAH
(3D) Decoration misses point - it's too colourful. (6) = GARISH
(4D) Greek troublemaker sent back letter. (3) = ATE
(6D) Eaten by French partners with garlic. (5) = SNAIL
(7D) Reckless complaint. (4) = RASH
(8D) Observes one with child's toy. (6) = SEESAW
(11D) Made coffee from earth? (6) = GROUND
(13D) Walk quietly by harbour and small field. (7) = HADDOCK
(15D) Commendation brought back from medal occasion. (8) = ACCOLADE
(17D) Jeered - a mild curse came first. (7) = HECKLED
(18D) Paper is article by MI6. (6) = THESIS
(21D) Snake points to tree. (5) = ASPEN
(22D) Jaunt turns into military coup. (5) = JUNTA
(23D) Mr Armstrong is heard to pay respect. (5) = KNEEL

Place the answers in the grid:




But in answering you find that there are 4 squares where the answers do not correspond so when you look for alternate words you see that 4 squares have the letters PALM as an alternate. 

This presumably is a “hidden” word being sought.

The eleventh, and apparently final question is:



The most obvious place to start is to check to see if this is a substitution cipher.  But there needs to be some pattern for dividing up the digits.  It is likely to be at least two’s as there are 26 letters in the alphabet but nothing works with that so next try triplets:

211, 412, 524, 645, 867, 889, 909,121, 242, 443, 643, 865, 885,085, 205, 416, 516, 626, 828,040, 042, 142, 252, 474, 595, 796,718, 838, 050, 062, 084, 185, 386, 586, 696

Then try subtracting the digits in one number from the digits in the previous number to arrive at the triplet for the cipher, which gives (assuming the first three digits subtracts 000 as there is nothing preceding it) [UPDATE: Fellow solver pointed out that you have to clear that you are subtracting individual digits in each triplet not simply subtracting one number from the other as a whole]:

211, 201, 112, 121, 222, 022, 120, 222, 121, 201, 200, 222, 020, 200, 220, 211, 100, 110, 202, 222, 002, 100, 110, 222, 121, 201, 022, 120, 222, 012, 022, 101, 201, 200, 110

This very notably uses only the digits 0, 1 and 2.  Therefore assume this is Base 3 and convert to Base 10 (we all work better in Base 10 when looking for substitutions).  This gives you:

22, 19, 14, 16, 26, 8, 15, 26, 16, 19, 18, 26, 6, 18, 24, 22, 9, 12, 20, 26, 2, 9, 12, 26, 16, 19, 8, 15, 26, 5, 8, 10, 19, 18, 12

This looks promising as it results in numbers between 1 and 26 ie the number of letters in the English alphabet.

Using the classic cryptanalytic technique of frequency analysis, and searching for words which make sense, and are likely in this context you come up with a mapping you eventually find that:

F=2
C=5
K=6
I=8
O=9
P=10
R=12
A=14
S=15
T=16
E=18
H=19
D=10
W=22
Y=24
SPACE = 26

Which gives you the message WHAT IS THE KEYWORD FOR THIS CIPHER

But this is a question so it suggests there is a word being sought, presumably something that will allow further messages to be written in this particular cipher.

Using the normal alphabet and mapping it to the numbers we know therefore can be viewed as:

But we know from our decoded message that F=2 so presumably F maps to C in the cipher text alphabet. Continuing this with the letters we have from our message we get:

F > C
C > F
G > K
I > I
J > O
K > P
M > R
O > A
P > S
Q > T
S> E
T > H
U > D
W > W
Y > Y

Which when you tabulate it looks like this:


Next apply some common sense. The way simple substitution ciphers work is by writing the keyword under the normal alphabet and then continuing the remaining letters in the order in which they occur.

What is a cipher intended to do? It is OBFUSCATING a message.

OBFUSCATIN fits in as a word at the beginning of the cipher text alphabet and in so doing the remaining letters would fit in the rest of the cipher text alphabet being written as it occurs in the normal alphabet.  That’s exactly what you would expect.

So, the answer they are looking for is OBFUSCATING ie the answer to the decoded message WHAT IS THE KEYWORD FOR THIS CIPHER. 

By completing the table above you could write further coded messages using the same cipher.

Hidden Puzzle

There also appears to be a hidden puzzle.  If one clicks on the header and footer image it takes you to a high resolution version of each. 





When you look closely you see that the leaves are shaded but not every circle of leaves is not shaded identically. 

If you assume that a shaded leaf is a 1 and no shading equates to a zero, you find that the semi circles of leaves give the following 0’s and 1’s, which if you assume each semi-circle is the digital ASCII code for a character (see earlier for ASCII codes), spells out the message:

Name the technique of hiding messages in images.

See below for the decoding:

01001110 = N
01100001 = a
01101101 = m
01100101 = e
00100000 = Space
01110100 = t
01101000 = h
01100101 = e
00100000 = Space
01110100 = t
01100101 = e
01100011 = c
01101000 = h
01101110 = n
01101001 = i
01110001 = q
01110101 = u
01100101 = e
00100000 = Space
01101111 = o
01100110 = f
00100000 = Space
01101000 = h
01101001 = i
01100100 = d
01101001 = i
01101110 = n
01100111 = g
00100000 = Space
01101101 = m
01100101 = e
01110011 = s
01110011 = s
01100001 = a
01100111 = g
01100101 = e
01110011 = s
00100000 = Space
01101001 = i
01101110 = n
00100000 = Space
01101001 = i
01101101 = m
01100001 = a
01100111 = g
01100101 = e
01110011 = s
00101110 = . (Full Stop)

The answer to the question is STEGANOGRAPHY – very appropriate for how the question was delivered.