The GCHQ Puzzle Book (2016)

Foreword by Director GCHQ

For nearly one hundred years, the men and women of GCHQ, both civilian and military, have been solving problems. They have done so in the pursuit of our mission to keep the United Kingdom safe. They have put their talents at the service of the nation’s security through some of the darkest times in our history: the struggle against Nazism during World War II, when our staff at Bletchley Park played such a key role, and the battle to preserve the free world from totalitarian communism during the Cold War. Today, in this digital age, the same skills are being applied to fighting terrorism, countering cyberattacks and bringing the most dangerous criminals to justice.

Technology is at the heart of our work at GCHQ. Alan Turing created a novel electromagnetic device to help break the Enigma code, and Tommy Flowers, our greatest engineer, built the world’s first digital computer to help break the Tunny code. Our great mathematicians, James Ellis, Clifford Cocks and Malcolm Williamson, made the historic breakthrough which enabled the encryption upon which all of us who use the internet rely for our security and safety everyday: Public-key cryptography.

But at the heart of the mathematical, engineering and linguistic successes for which GCHQ is famous are individuals with skills, talent and commitment. As well as puzzling for the national good, many of them also do it for fun. They have created this book to share their hobby with you. I hope it will entertain you and perhaps inspire some younger readers to become our problem solvers in the future.

At GCHQ we are excited by the dazzling possibilities for human development offered by the internet, but we also know that this technology can be abused by a minority who seek to do harm. If we are to keep meeting these threats, we need creative, expert and dedicated staff. GCHQ has a proud history of valuing and supporting individuals who think differently; without them we would be of little value to the country. Not all are geniuses or brilliant mathematicians or famous names, but each is valued for his or her contribution to our mission.

Over the decades, we have come to understand the pressures on mental health which affect so many, regardless of age or background. I am therefore delighted that the proceeds from this book will go to the Heads Together group of mental health charities, which Their Royal Highnesses the Duke and Duchess of Cambridge and Prince Harry have done so much to encourage.

I want to thank all those GCHQ staff who have given their own time to create these puzzles over the years, and particularly those involved in creating this magnificent collection. I cannot name them, for obvious reasons, but I know how much they have put into this project.

Thank you for buying this book and supporting these charities; all of us at GCHQ hope you enjoy it.

Robert Hannigan

Director GCHQ

Cheltenham, September 2016

Solving Puzzles for Fun at GCHQ

Solving serious puzzles is at the heart of what GCHQ does, whether analytical, technical or cryptographic. It is not surprising then that many of us employed in GCHQ also enjoy setting and solving puzzles for fun.

For many years it was codes which formed the bulk of such puzzles, and they were also used in our recruitment literature. A less purely cryptographic puzzle/quiz began in the 1980s and started a tradition of puzzles for people to solve over the Christmas period. Typical questions were:

M N B V C X?

BAGG is to William the Conqueror as BEJC is to whom?

Which of GLITHGINRYO, UDLOTWIN, TIPSYCHATRY, CHASTIPLAW might complete the sentence: THRIPGUH is to ALMOOW as GUMP is to?

(Answers to questions in this chapter are given at the end of the chapter.)

After a short gap in the 1990s this was reborn as the Christmas Puzzle Quiz (CPQ), which continues to this day – and many of the puzzles in the book come from this source. The CPQ has always been a mix of general knowledge and puzzle solving, often including sets of questions connected to Cheltenham itself, and some questions where there doesn’t even appear to be a question. For example:

42º15’N 72º15’W, 53º52’N 44º50’E, 37º49’N 85º29’W, 39º37’N 75º56’W, 40º57’N 40º17’E, 51º54’N 02º04’W?

The CPQ has raised over £3,500 for various charities over the years. Like all of the puzzles and events I will describe in this piece, the puzzle creation and compilation is done outside the office.

An altogether tougher puzzle appeared for the first time in 1993, also to be solved over the Christmas period. This evolved into the Kristmas Kwiz, and concentrated more on letter, word, number and code puzzles. As time has moved on, this has become more and more popular within GCHQ as well as with our international partners, with entrants from 7 countries now taking part. Again many of the puzzles in this book were originally set as part of a Kristmas Kwiz. A typical Kwiz kwestion might be:

What word might finish the following sequence:

APE, VOL, TRAIT, REN, EURO, ON, LID, ENTICE, ROD?

Towards the end of this book you will find a complete Kristmas Kwiz challenge, giving you the opportunity to match yourself against the puzzle setters and solvers of GCHQ. Read the introduction to the challenge here to see how it works, and where and when you can find the answers.

Over the next few years a number of other puzzle events were created, not least to ensure that people’s brains could be kept active through the whole year and not just at Christmas. The first was the Treasure Hunt in 1997. This means that one Sunday a year about 50 of us descend on some town in the Cotswolds and walk around with clipboards solving puzzles that lead to a Treasure. The idea of a Treasure Hunt is not unique to GCHQ, of course, but the nature of some of the questions perhaps is. For example:

What is 2m(4a-3p)?

Calculating this equation gave the answer 8am-6pm, which referred to local parking restrictions. Not all questions are like this though. For example: ‘What is the most fashionable place around here?’, to which the answer was ‘This postbox’ – as a label on the nearby postbox read: THIS POSTBOX HAS THE LATEST COLLECTION IN THE AREA!

In 1999 an event began which I believe is unique to GCHQ. The style is that of a pub quiz, in that teams of four spend an evening answering rounds of questions, most of which are read out. However, none of the questions are general knowledge, they are all puzzles. There might be rounds of word puzzles or number puzzles, but over the years there have also been memory rounds and ‘physical rounds’ – such as colouring a toilet roll to demonstrate a mapping problem, balancing eggs on towers, or deriving a code from tasting jellybeans.

To give a flavour of this event here are a couple of questions:

Yesterday I looked out of the window and saw something. I then glanced at my watch and noticed two things:

* it was 3 minutes past 8

* what I had just seen through the window was written on my watch.

What had I seen?

Last night I wrote down the numbers from 1 to 99. I then rearranged them into alphabetical order. Which number didn’t move?

In 2004 the idea arose of running a puzzle over the Easter period, and the Easter Teaser was born. If you noted the anagram then you might appreciate that the 2005 version was entitled ‘Easter Teaser – a Reset’! This has taken a variety of forms over the years, one of which ended up appearing as a competition in The Times in connection with the 2011 Cheltenham Science Festival.

An early Easter Teaser question was:

Mr Green likes bottles of champagne, minstrels and fallen women. What’s his favourite game?

Most recently the annual Puzzle Hunt, which is similar to other existing Puzzle Hunts, has been added to the calendar since 2014. This consists of a set of pictorial puzzles which have to be completed by teams in one evening. Although the answer to each puzzle is a word or phrase, none of the puzzles actually have questions. The aim is to work out what to do from the picture itself, sometimes using a hint in the puzzle title. At the end of the evening the answers you have found fit into a final meta-puzzle, which itself has no question. As with the Kristmas Kwiz mentioned earlier you have an opportunity to match yourself against us – the first colour section contains a complete Puzzle Hunt, including a Meta Puzzle. Why not see how you and your friends get on over an evening?

Although the puzzles and events described above are enjoyed by GCHQ staff and their families, with some also shared with colleagues in partner agencies abroad, there have been some special occasions when we have created puzzles for people outside GCHQ. One such was the centenary of Alan Turing’s birth in 2012, which was commemorated by an exhibition of his life and work in the Science Museum. As part of this event a few of us produced a set of puzzles aimed at children. For example:

What 13-letter placename is hidden in this sentence?

You need the ability to receive clues e.g. noticing exactly 13 examples of one vowel in a sentence – the letters just before every appearance of one of a, e, i, o or u may inspire your brain to spot the trickiness.

In 2013 we were asked by the magazine Physics World to produce some physics-themed puzzles to celebrate their 25th anniversary. Five appeared around the anniversary itself, followed by another that Christmas, and one again the following Christmas. This was the first time we’d really had an opportunity to see how popular these sorts of puzzles were beyond our own community – over 5,000 people solved the first one, and we were delighted to see the large number of positive comments posted on the Physics World website.

The first puzzle, repeated here by kind permission of Physics World, was:

There is a word missing from the following. What is it? (Give the answer in its encrypted form.)

TNVERI SMH EG ZSMRNPMUD: M SLRN PYMP VERRNVPT M ZSMRNP PE PYN TQR THNNZT EQP NXQMS MUNMT LR NXQMS PLKNT

The full set of puzzles can be found at: www.physicsworld.com/puzzle.

More recently still, in 2015 the Director of GCHQ asked some of us to create a puzzle which he could include in his official Christmas card. This needed to be something which would appeal to as many people as possible, but which ideally would not be completely solvable by anyone. The resulting challenge took the form of a Nonogram (or Hanjie) in the actual card itself (reproduced in the first colour section). Correctly completing this led entrants to a web address, and a set of multiple choice puzzles. Solving these led in turn to a set of word puzzles, then number puzzles, and finally a large number of different sorts of puzzles, some hidden, and some with more than one answer.

It is still possible for you to attempt the Christmas Card Puzzle, either by solving the Hanjie or by going to: https://www.gchq.gov.uk/puzz.

The response to the Christmas Card Puzzle was breathtaking, and global. More than half a million people tried to solve the first stage, and more than 10,000 of these reached the final stage. Those trying came from all over the world, and 550 people submitted answers. No one completely solved the puzzle, although six people got very close – and three of these were chosen to win prizes based on the quality of their reasoning. Those who enjoyed the Christmas Card puzzle were encouraged to donate to the NSPCC. Similarly, all the profits from this book will be donated to Heads Together – a grouping of eight mental health charities which together are tackling stigma, raising awareness, and providing vital help for people with mental health challenges.

It was the unprecedented level of interest in the Christmas Card puzzle which led to the idea for this book, which contains a whole range of different puzzles set by staff who work, or have worked, at GCHQ.

We hope you enjoy it.

Answers to questions in this chapter:

M N B V C X?

Answer: Z. The sequence is the bottom row of a typewriter keyboard in reverse.

BAGG is to William the Conqueror as BEJC is to whom?

Answer: 1492. Christopher Columbus. BAGG represents 1066, with each letter representing its place in the alphabet minus one ie A=0, B=1, C=2 etc. BEJC is therefore 1492.

Which of GLITHGINRYO, UDLOTWIN, TIPSYCHATRY, CHASTIPLAW might complete the sentence: THRIPGUH is to ALMOOW as GUMP is to?

Answer: UDLOTWIN (uDlOtWiN). Reading every second letter in the groups in the sentence gives HIGH is to LOW as UP is to DOWN.

42º15’N 72º15’W, 53º52’N 44º50’E, 37º49’N 85º29’W, 39º37’N 75º56’W, 40º57’N 40º17’E, 51º54’N 02º04’W?

Answer: 52º12’N 1º41’W. The coordinates in the question are the latitudes/longitudes of: Ware, Issa, Bardstown, North East, Of, Cheltenham. Read as the question: Where is a Bard’s town North-East of Cheltenham, the answer is Stratford-on-Avon – and the answer is its latitude/longitude.

What word might finish the following sequence:

APE, VOL, TRAIT, REN, EURO, ON, LID, ENTICE, ROD?

Answer: TART. From the sequence you can form new words by adding the same letter at the start and end, and these words spell out Los Angeles. In fact any word from which you can form a new word by adding an S at the start and end is a correct answer.

LapeL, OvolO, StraitS, ArenA, NeuroN, GonG, ElidE, LenticeL, ErodE, StartS

Yesterday I looked out of the window and saw something. I then glanced at my watch and noticed two things:

* it was 3 minutes past 8

* what I had just seen through the window was written on my watch.

What had I seen?

Answer: MOON. My watch said image, which when read sideways spells MOON.

Last night I wrote down the numbers from 1 to 99. I then re-arranged them into alphabetical order. Which number didn’t move?

Answer: sixty-nine.

Mr Green likes bottles of champagne, minstrels and fallen women. What’s his favourite game?

Answer: Othello. The question refers to English translations of the Italian: Giuseppe Verdi (Mr Green) composed Otello, Nabucco (Nebuchadnezzar), Il Trovatore (The Troubadour) and La Traviata (The Fallen Women).

What 13-letter placename is hidden in this sentence?

You need the ability to receive clues e.g. noticing exactly 13 examples of one vowel in a sentence – the letters just before every appearance of one of a, e, i, o or u may inspire your brain to spot the trickiness.

Answer: Bletchley Park. As described in the sentence, one of the vowels, i, appears exactly 13 times. The letters which appear immediately before each i spell Bletchley Park.

There is a word missing from the following. What is it? (Give the answer in its encrypted form.)

TNVERI SMH EG ZSMRNPMUD: M SLRN PYMP VERRNVPT M ZSMRNP PE PYN TQR THNNZT EQP NXQMS MUNMT LR NXQMS PLKNT

Answer: KEPLER. The text reads: Second Law of planetary: A line that connects a planet to the sun sweeps out equal areas in equal times. The missing word is MOTION, and this encodes to Kepler, whose law it is. The cipher alphabet in full is:

Image.missing

which begins appropriately: ‘moving by laws’.