# Ducks, Lord of the Rings, movies and maths: The GCHQ Xmas puzzle solutions revealed

## Much easier when you know the answers

And yes, there is also a puzzle in this screenshot

GCHQ has posted the answers to its Xmas puzzle, a five-part crypto extravaganza that saw 600,000 people start but just three win – and even they didn't get it all right.

The lucky winners, one from Scotland, one from Belgium and another unnamed, will be given a GCHQ paperweight (presumably with a bug implanted), a biography of Alan Turing with a personal message from GCHQ director Robert Hannigan written inside and "major bragging rights," according to the spy agency.

Apparently 30,000 people made it to the final stage before being stumped by a combination of Lord of the Rings references, native language place names, Christmas greetings and a picture of a rubber ducky.

It didn't help that the final part was deliberately kept "open-ended by ensuring that a definitive complete solution could not be readily identified" – or in other words, utterly confusing on purpose.

Going through the answers [PDF] is an interesting exercise. The first puzzle started off pretty simply and with explicit instructions on how to do it. It was a crossword grid that, when filled in, made out a QR code that then led to the second stage hosted on GCHQ's website at http://www.gchq.gov.uk/puzz.

Then followed a series of not-too-difficult word puzzles that referred to snooker balls, the phonetic alphabet (Charlie Tango etc), semaphore, and then a number of Christmas-themed word games. The decimal representations of ASCII characters that spelt out the song "Jinglebells" was probably the toughest to crack in Part 2.

### Zut alors

Part 3 stepped things up a little, using anagrams of French numbers to work out a square root sum, crossword clues and grids and Morse code before leading into Part 4.

Part 4's number puzzles started causing real problems. A number sequence was a double-puzzle, in that it required you to recognize that alternate digits to the answer were being used in a logical sequence.

So the obvious sequence of 2, 4, 8, 16, 32, 64, 128, 256, 512 etc was rendered as 2, 4, 8, 1, 3, 6, 18, 26, ?. And the answer was 52.

That was the easy one. The sequence "-101250000, -1728000, -4900, 360, 675, 200, ?, ..." saw people write computer programs to identify possible solutions. The answer was n2m310r where n and r decreased by one each time, and m increased by two.

Yep, that's where it started getting a little odd. If you know about arithmetic progressions, you might then have got to the last answer, which helped build an IP address to where the final part of the puzzle could be found.

To save you the trouble though, it's at: http://52.30.87.208/next.

And there are a slew of widely varying puzzles from crosswords to logic puzzles to a cipher to movie name board games to Lord of the Rings references to chess moves. And, for good measure, the rubber duck.

Get down. Duck. Also getting down from a duck. James Brown not included

If you want to figure those out, you'll need to grab the answer sheet [PDF] and walk them through yourself. But just as a spoiler, the answers are:

MANAGERMENMERCURY
XIV
XX
L
XXXI
XXII
LXI
XXV
KRONECKER
ORIENTABLE
BILBO
MXAHRYESP
HXRMSAEPY
ECHO
SEPTEMBER
URANUS
EIGHT (or FOURTH)
TREASURE
DUCK
PALM
OBFUSCATING
STEGANOGRAPHY

Which of course makes everything clear. Except it didn't, because it was designed not to. Oh – and there was a hidden puzzle in the banner picture too. And they made a mistake – putting 27 instead of 17.

So if you were wondering how only three people got prizes, now you know. ®