Tuesday, June 30, 2015

Parallels Between Cryptanalysis and Crossword Solving

Fialka Cipher Machine During World War II, recruiters for Bletchley Park had looked for crossword solvers to join them, as it was believed that crossword experts would be good codebreakers. [The story is that in 1942, a challenge was issued to solve a Daily Telegraph crossword in under 12 minutes. Shortlisted candidates were invited for a live crossword test, after which six solvers were recruited.]

Bletchley Park's successes during the war proved that their crossword-inclined hiring policy worked. But have you wondered if this correlation was incidental? Interestingly, NSA's chief cryptologist William Friedman might have wondered so – in the treatise Military Cryptanalysis (originally dated 1938, 4th Edition dated 1952), under the heading "Mental equipment necessary for cryptanalytic work", he made a strong case against correlating cryptanalysis with crossword solving.

The present author deems it advisable to add that the kind of work involved in solving cryptograms is not at all similar to that involved in solving crossword puzzles, for example. The wide vogue the latter have had and continue to have is due to the appeal they make to the quite common interest in mysteries of one sort or another; but in solving a crossword puzzle there is usually no necessity for performing any preliminary labor, and palpable results become evident after the first minute or two of attention.

He went on to elaborate on the points of difference between the two skills (section I, p2).

Now try this: exclude that specific warning and replace 'cryptanalytic' with 'crossword solving', 'cryptogram' with 'puzzle', etc. in the manual's description of the "mental equipment". Do you also see that large excerpts of the text could pass off as a guide for crossword solvers?

I was especially struck with these parallels while reading Simon Singh's The Code Book, a narrative about the evolution of cryptography. In the hunt for structure and hidden meanings in text, in the battle of wits between codemakers and codebreakers, the similarities between cryptanalysis and crossword solving are hard to miss. A few examples of cryptanalytic techniques and their crossword parallels:

Frequency analysis

Every letter of a language has distinct character. The frequency with which the letter appears in text, the way it positions itself with respect to other letters in the alphabet, the types of letter clusters it appears in – all make the letter uniquely identifiable.

The frequency distribution of letters (singly or in sequences), a powerful tool for cracking substitution ciphers, has similar applicability in crossword solving – though we usually process this information instinctively rather than formally.

The appearance of more than one low-frequency letter (J K Q X Z) alerts the solver that the grid could be a pangram.

Longer letter sequence frequencies provide strong hints about possible answers in the crossword grid. Solvers watch for clusters like IN-, RE-, TH-, -ING, -TION in answers since they are occur commonly in English. When tackling a checked answer slot, say one that starts with ?H- or ends with -T?C, one can eliminate many letters from matching the ? because the resulting clusters do not appear in natural English words. 

Wartime cryptanalysts exploited the knowledge that certain words occur more frequently in military communication than in normal conversation. Likewise, experienced crossword solvers are well up on crosswordese and expressions typical of crosswords e.g. phrases normally used with 'your' in the real world tend to appear with ONE'S in crosswords (e.g. PUT ONE'S FOOT IN ONE'S MOUTH).


At Bletchley Park, the term cilly was used for predictable message keys that the cryptanalyst could guess based on the radio operator's habits: for example, an operator might have the habit of using consecutive letters such as QWE on the keyboard. Another type of cilly was the repetition of a message key by an operator, presumably the initials of a loved one.

Deciphering messages based on hunches about cillies is similar to cracking crossword clues based the setter's signature style. An Anax puzzle is more penetrable if you are aware that he often disguises verbal indicators as nouns, an AfterDark puzzle might unravel faster if you look out for something special in his grid.


Cryptanalysts used the term crib to refer to any known or suspected plaintext in an enciphered message. They would foretell cribs from the time and source of a message (e.g. a 6am message from X station would be a weather report), and this knowledge would give them a way to break the rest of the code.

Guessing a crossword's theme and possible answers based on the date and setter/publication is similar to using a suspected crib in cryptanalysis. We apply such information all the time to figure out a puzzle even before we have read any clues. Factors like an out-of-turn appearance by a setter, a special date of publication or a crossword numbering milestone, give us ideas about what to expect in the grid fills.

Vigenère Cipher with Running Key

The Vigenère Cipher with running key (i.e. key as long as the ciphertext) was considered unbreakable when it was first designed. Codebreakers soon found that this cipher too, like its predecessors, does not guarantee security if the key has structure and consists of recognizable words.

The process of breaking the Vigenère Cipher with running key goes like this: start with a crib (e.g. the), refer to the Vigenère Square to derive the key and check if the derived key looks meaningful. If it does, fill in other gaps and proceed to derive the rest of the message by alternating between the plaintext and the key. If you reach an impasse (i.e. meaningless text in either the plaintext or key), backtrack and resume on another track till you end with meaningful key as well as plaintext.

The snapshot below from The Code Book shows three routes a cryptanalyst might take to decipher a message with this approach. In the first, the plaintext is gibberish and cannot be right. The second looks possible but if we proceed on that route, it soon ends in deadlock. The last, with the plaintext string 'at the', seems the most promising – and it does turn out to be the right one.

Deciphering the Vigenère Cipher 

The cipher's plaintext is analogous to crossword answers in one direction (Across or Down), the key to its intersecting answers in the perpendicular direction. When we use a grid-centric approach to solving, we essentially do the same as cracking the Vigenère Cipher: derive answers based on factors like enumeration (e.g. 4,2,7 might be NEXT TO NOTHING), and validate that they fit into the grid generating workable crossings.

In the grid below, without glancing at the clues, one can tell that something is not right with the filled-in Down answers as this grid will end in deadlock at 14Across. At this point the solver would revise the Down answers, just as a cryptanalyst would discard the key trial if it led to such a pattern in the plaintext.

Partly Solved Grid

While cryptanalysis shares its approach with crossword solving, some forms of encipherment have shades of cryptic clueing. Navajo, for example, which was based on a native American language and formally developed for secret communication by US Marines. This language had a complex structure which made it unintelligible to anyone who did not know the rules for parsing it. The code used creative substitutions for military terms (e.g. platoons = mud clans, mortars = guns that squat), similar to lateral clue definitions. Some words that could not be translated directly to Navajo were split and encoded using a phonetic alphabet or through homophones. Nicknames were added to the Navajo lexicon to refer to nations - Australia became 'Rolled Hat', Spain was 'Sheep Pain' – somewhat like rhyming slang.

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Wednesday, June 17, 2015

Hot Fuzz: Crossword Conversation

A reader shared this video clip with me from the movie Hot Fuzz. I recalled its (quite scathing) mention in the Guardian Crossword blog's entertaining series on crosswords in fiction, and watched it with great curiosity.

This makes for an interesting spot-the-errors exercise, apart from the peculiar grid.

Joyce Cooper gives out the clue number for FASCIST as 7 Across but runs her pen over a Down clue while reading it out. FASCIST does fit into the grid slot for 7 Across, but the corresponding clue on screen is too short to match "System of government categorized by extreme dictatorship".

There is another Down clue slot with a leading F already filled in the grid and the checkers A and I in place – it would seem that that's where this answer should go in.

HotFuzz Crossword

It gets weirder when Sergeant Angel retorts with "Evil old woman, considered frightful or ugly. It's 12 Down." Because, if the grid shown in the movie followed normal crossword numbering, it wouldn't have a 12 Down at all.

What other bloopers do you see?

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Tuesday, May 26, 2015

5 Works of Art Inspired by Crosswords

The sight of a crossword affects not just people like us who solve or set. The stark geometry of its grid, the passion it inspires in people who engage with it, are subjects of fascination to artists too.

A few crossword-driven works of art for you to savour, with commentary by the artists.

1 Crossword Puzzle [Ink wash drawing by Max Ferguson]

The scene is of a man in a pub in London, whom the artist Max Ferguson chanced upon while traveling through the city in 2004. By the look of it, the solver is battling a particularly fiendish cryptic.

Crossword Puzzle: Max Ferguson

Most of Max Ferguson's paintings are in oil paint and highly polished, with true-to-life colours. It's probably fitting that this one, centered on a crossword, is in monochrome. He says:

This was rather challenging as ink wash has to be done very quickly and is a very unforgiving medium. When I am about to begin a new piece I think about what medium / size would work well for that particular image. In this case I felt a small (10 x 12 inches) ink wash drawing would be well-suited.

This drawing is available at the time of writing this – visit Max Ferguson's site for more.

2 Crossword Puzzle with Lady in Black Coat [Gouache by Paulina Olowska]

Gouache-on-canvas artwork from Paulina Olowska​'s exhibition 'Au Bonheur des Dames' (The Ladies' Delight) at Stedelijk Museum, Amsterdam, in 2009. Photo from another angle here shows the imposing size of this work.

Crossword Puzzle with Lady in Black Coat: Paulina Olowska

A crossword person will no doubt notice the unorthodox checking and clue slot numbering of the grid. Perhaps it represents a puzzle that's not meant to be solved?

3 Dad's Crossword [Oil/linen by Duane Keiser]

Duane Keiser made this painting as part of his popular A Painting A Day project in 2013. The painting is of a Washington Post grid, which his dad solves almost everyday. As Duane puts it:

I don't think he even reads the news anymore in the paper-- he pulls out the crossword and throws the rest away.

Hands up all of you who do the same? [My hand is raised!]

Dad's Crossword: Duane Keiser

This oil on linen artwork is 6 x 7 inches, almost life-sized to the actual crossword. It was sold via auction on Duane's blog. [You can request for a print here if you're interested.]

Describing the thought behind the painting, Duane says:

There are a couple of things that attracted me to this scene: in comparison to the now ubiquitous digital media, newsprint has a kind of warmth and intimacy to it now. I zoomed in close to the subject to give a sense of being lost in concentration while the outside world momentarily disappears. Lastly, I liked the calligraphic aspects of the marks and the geometry of the crossword juxtaposed with the curves of the glasses.

It was a challenge to keep the structure of the crossword but not get bogged down in unnecessary detail. I was mostly interested in the visual rhythm of the words rather than simply copying them. You can almost read the words, but not quite - it is what you'd see if you glanced at it.

4 Crossword Tools [Oil painting by Sarah Lytle]

Coffee, reading glasses, and a pen – 'crossword tools' as the artist calls them. Sarah Lytle is not a coffee drinker or a crossword person (she prefers the Sudoku!) – this painting was prompted by her mother's tools of choice. Sarah describes her mother as a crossword fan who can solve the hardest of puzzles.

She must have her glasses, her morning coffee and her pen. I can see her sitting at the breakfast table or curled up in the chair, glasses perched on her nose, newspaper folded in half to the puzzle, working away. It makes me smile thinking about it.

Crossword Tools: Sarah Lytle

This 8 x 8 inch painting was made wet-on-wet (alla prima, meaning 'at first attempt' in Italian). 'Crossword Tools' is sold already, but you can reach out to Sarah for commissioned work.

5 Red Tomatoes on Crossword Puzzle [Watercolour by Carolyn Watson]

At artist Carolyin Watson's home, garden tomatoes were laid out on newspaper on the floor to ripen, when she was struck by the contrast of the red over black-and-white.

I loved the way the red of the tomatoes was reflected into the shadows and how the black of the newsprint was darker in the shadow.

This led to a series of watercolors of vegetables placed over crosswords.

Tomatoes on Crossword: Carolyn Watson 

These tomatoes eclipse the clues too, in making the grid fills: VINE, RIPE, HOME, GROWN, TOMATO - and the US-style grid gives neat placeholders for the words on the left hand side.

Another interesting painting from the series is Red Peppers on Crossword, which looks as if someone abandoned solving midway and started doodling on the grid instead.

The originals are sold, but you can buy prints and request for commissioned originals of the peppers on crossword with customized grid fills.

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Monday, May 18, 2015

13 Imaginative Ways to Talk of Prison

prison That place of confinement can boast of many imaginative substitutes for its name. Clues that show how these get used in crosswords.

1. JUG
Times 25628: Maybe go through mood changes of criminal: prison worried (9) CONJUGATE
CON (criminal) JUG (prison) ATE (worried)

Times 25775: Create revolutionary movement in prison (4) STIR
Double definition; 'stir' is slang for prison.

On the history and possible origin of this meaning of 'stir', Grammarphobia has an interesting write-up.

FT 14540 (Orense): Wake up cooler (4) STIR
Double definition; 'cooler' refers to prison, usually meant for the more dangerous criminals.

4. CAN
Indy 8876 (Phi): Prison Director guided to reduce light (6) CANDLE
CAN (prison) D (director) LE[d] (guided to reduce i.e. cut short)

[Not to forget, 'can' means other things too.]

Times 25869: Nick — adolescent making a mess (7) CANTEEN
CAN (nick - slang for prison) TEEN (adoloscent)

You'll usually find 'nick' on the clue's surface dressed as a proper noun, or as a verb meaning 'steal' or 'cut'.

Times 25964: Remove a key from prison outfit (3) RIG
BRIG (prison) – B (key, of music)

'Brig' is a military prison, especially in a navy ship.

FT14791 (Bradman): Imprisoned maiden? That gets media treatment (8) COVERAGE 
OVER (maiden, as in cricket) imprisoned i.e. put inside prison (CAGE)

FT14184 (Jason): One in pokey with excellent natter (6) CONFAB
CON (one in pokey - slang for prison) FAB (excellent)

Guardian 26203 (Rufus): Jug can clink (6) PRISON
Triple definition

10. TIME
Indy 8775 (Phi): Event enabling you to live out of time? (9) JAILBREAK cd
To 'do time' is to serve a prison sentence. 

11. BIRD
Sunday Times 4622 (Jeff Pearce): Fool can get drunk in bar (9) BIRDBRAIN
BIRD (can i.e. prison) (IN BAR)*

'Bird' can mean prison, a term in prison, or a prison inmate (short for jailbird). The word comes from bird-lime, rhyming slang for 'time'. Often used in the phrase 'do bird', which means 'do time'.


Similar to 'bird', 'porridge' can mean prison or a term in prison, especially in the phrase 'do porridge' (serve a prison sentence). The word gained wider currency with the BBC TV series Porridge, a sitcom about prison inmates.

FT14822 (Monk): Bishop, one putting on fat in time (8) PORRIDGE
RR (bishop - Right Reverend) I (one), putting on i.e. inside PODGE (fat). The definition 'time'

Wikipedia attributes this usage of 'porridge' to the staple diet of porridge in UK prisons.


Times 25303: One violently smashing lip has for a start to be imprisoned (12) SLEDGEHAMMER
EDGE (lip) H ('has', for a start), to be 'imprisoned' i.e. to be inside SLAMMER

With such diversity of synonyms, it's not uncommon to find multi-definition clues associated with 'prison'. Till a while back, the maximum count of definitions that I'd seen in a single clue was in this clue for SET. Then in Dec 2014, I came across this outstanding 7-definitional:

Indy 8797 (Hieroglyph): Nick Cage can stir porridge inside big house in the States (6)
'nick', 'cage', 'can', 'stir', 'porridge', 'inside', 'big house' (in the States) - all mean prison.

Any other interesting prison terms you can think of? Add to the list in the comments section.

Update (23-Jun-2015) Bhala suggests more terms: QUOD, CHOKEY.

Times 26132: Briefly stir drink: that's enough to achieve motion? (6) QUORUM
QUO[d] (stir, briefly) RUM (drink)

Solve These

More clues that play on words referring to 'prison'. Have fun solving!

Sunday Times 4584 (Dean Mayer): A handle for jug, all in enamel (8) N_______
Times 25900: Fine golden bird on toy stall (4,3,4) P___ ___ ___E
Indy 8647 (Dac): Tough jailbird shown round a prison (4-4) C___-____
Times 24571: Cooler name rejected by psychologist (3)

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Thursday, April 30, 2015


Janus A few years ago, I was awestruck with the cleverness of this winning clue from the Azed Slip Archive:

The jungly mass one cleaves (7) MACHETE
[M (mass) +ACE (one)] cleaves i.e. holds (THE)* 
The whole clue is the definition: a machete is something that cleaves i.e. cuts through the jungly mass.

This clue plays on a special property of 'cleave': the word has two meanings diametrically opposed to each other. The clue's wordplay uses one meaning of 'cleave' (to hold/cling), while its definition uses the opposite (to cut/divide).

Thanks to a Mental Floss article, I found a name for such words with contradictory meanings. They are called contronyms (or contranyms), from the Latin contr[a] (contrary, in opposition) + –onym. Contronyms go by many other names: autoantonyms, antagonyms, or Janus words, called so after the Roman god of beginnings and endings, usually depicted with two faces looking in opposite directions. [T-Rex must be alone in calling them homographic homophonic autantonyms.]

A few examples we use commonly: DUST (to remove dust; to add dust), SCREEN (to show; to conceal), VARIETY (many types; a specific type). The folks at DailyWritingTips have compiled a pretty long list. Many contronyms are formed due to the prefix 'RE-' added to imply 'again': this meaning may contradict a separate meaning. RESIGN (renew a contract; give up on a contract), REPROVE (support or prove again; strongly disapprove), REPLACE (restore to initial position; remove from initial position) are some such words.

As you can guess, contronyms have great potential in cryptic clueing. They make even the basic double definition delightful.

Times 25889: Good or bad (6) WICKED
Independent 8822 (Phi): Spring and fall (4) TRIP

Contronyms can add mystery to the clue's definition.

Guardian 26124 (Nutmeg): Using old Latin in will could be wise or foolish (6) OWLISH
O (old) + L (Latin) in WISH (will). 'Owlish' could mean wise or foolish.

Or they can act as deceptive double-edged indicators.

Can you think of contronyms in other languages? One in Hindi is कल (KAL), which might mean yesterday/in the past or tomorrow/in the future.

Solve These

A few contronym-based clues for you to solve.

Times 25743: Making harder or softer (9) T________
Times 23609: On right, with fixed agenda, no Democrat! (6) ___G__
Guardian 25731 (Rufus): Certainly less than 50% (3,4) ___ H___

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