The D’Agapeyeff Cipher, Unsolved for 80 Years!

[Image courtesy of Derek Bruff.org.]

One of my all-time favorite cryptography stories comes from the book The Spy That Couldn’t Spell, a true-life espionage story about a dyslexic man who hid, then encrypted the locations of, thousands of pages of sensitive documents he had stolen from the U.S government.

Why is it one of my favorite stories? Well, because the man in question FORGOT one of the cipher words he used to encrypt the location of his caches.

And it sort of unravels your master plan when you can’t remember a key element of it.

Amazingly enough, this isn’t the only example of a self-trained cryptographer who forgot how to solve his own creation. In fact, one example of this very dilemma remains one of the most famous unsolved codes and ciphers in the world:

The D’Agapeyeff Cipher.

daga

This is the D’Agapeyeff Cipher. This seemingly simple list of numbers contains a secret message. The only problem is… the creator, Alexander D’Agapeyeff, can’t remember how to decrypt it.

When he published a starter book on cryptography — Codes and Ciphers, first edition — D’Agapeyeff included this chain of 5-digit number bundles as a final challenge for the readers to unravel.

One of the first steps many aspiring cryptographers take is to break the numbers down into pairs instead of groups of five:

daga 2

One result of this is the pattern that every pair has 6, 7, 8, 9, or 0 in the tens column and 1, 2, 3, 4, or 5 in the ones column, which doesn’t seem like a coincidence.

And see those sequences where the same number appears three times in a row? Some cryptographers believe that is also not a coincidence.

Then, they cut off the two double-zero pairings at the end — because they believe they were nulls, empty space-filling characters simply designed to fit the 5-letter groupings pattern of the original code as a way to throw off codecrackers. (And, to be fair, D’Agapeyeff himself wrote about null entries in the book Codes and Ciphers.)

If you remove those double-zero pairings, you can arrange the numbers into a 14×14 pairing grid, like so:

daga 3

See those sequences where the same number appears three times in a row? More of them now.

Many cryptographers consider this to be the true starting point of cracking the D’Agapeyeff Cipher.

But then what?

Some believe that the key to solving the grid lies in the Polybius Square, another encryption device mentioned by D’Agapeyeff.

Essentially, you place the alphabet into a 5×5 grid, and use those numbers to encrypt the letters. Here’s a straightforward example:

daga 4

In this case, the word PUZZLE would be 35 45 55 55 31 15.

Another way to use the cipher is to pick a keyword to start it. For instance, if you chose POLYBIUS as the key word, then you go across, then down, writing POLYBIUS and then the rest of the unused letters of the alphabet in order, like so:

daga 5

Instead of 1-5 both across and down, you could do 1-5 across the top and 6-0 across the side, reflecting the pairings in the D’Agapeyeff Cipher.

Or, as someone pointed out, perhaps we’re thinking in the wrong language. Triple-letters are uncommon in English words, but more common in Russian words, and D’Agapeyeff was Russian born.

Overlooking simple things like that can make you miss crucial ways into an encrypted message.

So, do you have any thoughts on how to solve this 80-year-old encrypted challenge, fellow puzzlers? Let us know in the comments section below! We’d love to hear from you.


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A Mysterious Message, Inscribed on a Sword, Found in a River

_103722388_d0c23635-6379-4bf7-bac8-478493c2d1c7

A few years ago, a very curious news story broke about an 8-year-old girl pulling a thousand-year-old sword out of a lake in Sweden.

Saga Vanecek — which sounds like the heroine of a YA novel series begging for a Netflix adaptation — discovered the sword while playing in the lake. The Jönköpings Läns Museum estimated that the sword is at least a thousand years old, and could be as old as 5th or 6th century.

No one is sure how it got there, but everyone agrees it’s an amazing find. (And many agree that Saga should now be queen. Hey, there are worse ways to choose a ruler.)

But there’s another story about a sword found in a body of water with an even stranger mystery attached: the River Witham sword.

river witham sword 1

There are actually two River Witham swords — it’s just the right river to go sword-hunting in, I suppose — but we’re talking about what’s known as the River Witham “knightly sword.”

It was discovered in the river in 1825 and turned over to the Royal Archaeological Institute. It is now in the hands of the British Library.

And for more than two centuries, the meaning of the inscription has remained a mystery.

Inlaid along one of the sword’s edges, spelled out in gold wire, curious eyes find the following chain of letters:

+NDXOXCHWDRGHDXORVI+

Is it an abbreviation? An encryption? Or simply patterning in the shape of letters? No solid answers emerged during decades of study.

Eventually, the British Library decided to crowdsource the puzzle in the hopes of finding a solution. In 2015, officials from the library officially reached out to the public to finally crack the code detailed along the blade.

All sorts of amateurs and professionals weighed in, exploring possibilities in Latin, Welsh, German, Irish, Sicilian, and others. They compared it to the medal of St. Benedict and other medieval engravings in search of patterns.

And the British Library shared one contributor’s thoughts as an addendum to their original post about the River Witham sword.

alphen blade

[The Alphen aan den Rijn sword-blade.]

Historian Marc van Hasselt compared the sword to others from the same time period, roughly around the year 1200, and believed it was safe to assume the language was Latin.

He compared the inscription from the River Witham sword — +NDXOXCHWDRGHDXORVI+ — with an inscription on a Dutch sword-blade found in Alphen aan den Rijn, the Netherlands. That blade was inscribed on both sides:

+BENEDOXOFTISSCSDRRISCDICECMTINIUSCSDNI+

+DIOXMTINIUSESDIOMTINIUSCSDICCCMTDICIIZISI+

He explains his thought process:

To elaborate, let’s compare the River Witham sword to the sword from Alphen: both start with some sort of invocation. On the River Witham sword, it is NDXOX, possibly standing for Nostrum Dominus (our Lord) or Nomine Domini (name of the Lord) followed by XOX.

On the sword from Alphen, the starting letters read BENEDOXO. Quite likely, this reads as Benedicat (A blessing), followed by OXO. Perhaps these letter combinations – XOX and OXO – refer to the Holy Trinity. On the sword from Alphen, one letter combination is then repeated three times: MTINIUSCS, which I interpret as Martinius Sanctus – Saint Martin. Perhaps a saint is being invoked on the River Witham sword as well?

Unfortunately, the British Library’s investigation seems to have stopped there after the intriguing contributions of van Hasselt.

But, thankfully, there is always SOMEONE on the Internet trying to solve a seemingly unsolvable mystery. I did a bit of sleuthing and found a post on medium.com, originally posted in February of 2017, with a very through breakdown of a potential solution to the River Witham sword!

river witham sword 2

[A closer look at the River Witham sword inscription.]

The author of the piece, Stieg Hedlund, started by focusing on the W in the inscription, since the classical Latin alphabet didn’t have a W. Surmising that the inscription was an initialism — which is common for Latin inscriptions — he started looking for an aristocratic name starting with W.

Why aristocratic? Well, not just anyone in the 1200s or 1300s could afford a sword with gold wire inscriptions.

He quickly settled on some variation of William for the W, and then narrowed his search to Willem II of Holland, a count, and the initialism CHW on the sword could mean Comes Hollandia Willelmus, his name and title in Latin.

william of holland

Following that line of thought and digging into the history of Willem II revealed that he ruled not only Germany, but the southern Belgian region of Hainault as well.

This gives him “Comes Hollandia Willelmus Dei gratia, Rex Germania et Hainault Dei nutu” to cover CHWDRGHD in the inscription.

When he turned his attention to the first five letters, he agreed with the supposition of Marc van Hasselt and others that it referenced “in Nomine Domini” and the XOX represented the Holy Trinity.

So that covers NDXOXCHWDRGHD, approximately two-thirds of the inscription. What about XORVI?

Well, Hedlund believes the solution lies in Laudes Regiæ, a Catholic hymn most famous for its opening words: Christus vincit! Christus regnat! Christus imperat! (In English: Christ conquers, Christ reigns, Christ commands.)

Abbreviated versions of these words were often used by kings and royalty to solidify their position by tying themselves to the church. On a coin issued by Holy Roman Emperor Charles VI in 1384, you can read one rendition of the phrase: XPiσtoC VinCIT XPiσtoC RegnAT XPiσtoC InPERAT.

He believes XORVI is an abbreviated version, reading “XpiσtOσ Regnat! (xpiσtoσ) Vincit! (xpiσtoσ) Imperat!” where the capital letters form the inscribed message.

So, the completed message would read:

(in) Nomine Domini
Comes Hollandia Willelmus Dei (gratia), Rex Germania et Hainault Dei (nutu)
XpiσtOσ Regnat! (xpiσtoσ) Vincit! (xpiσtoσ) Imperat!

Or, in English:

In the Name of the Lord; of the Father and of the Son, and of the Holy Ghost
Count of Holland Willem by the grace of God, King of Germany and Hainault by the will of God
Christ reigns! Christ conquers! Christ commands!

It’s a compelling case, and certainly the most complete interpretation and explanation I’ve been able to find.

Imagine. All of that in that brief, beautiful, confusing inscription. It’s fascinating, and makes the mind positively whirl with possibilities.

Oh, and if you find any centuries-old swords while you’re perusing the nearby waterways, let me know! We might have a new mystery to solve.


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Puzzles in Plain Sight: Spinning Yellow Circles edition

Adobe_Semaphore_Wide_768x512.0

About six months ago, I shared the story of a secret code lurking in plain sight, sitting atop the Capitol Records Building in Los Angeles. It’s not the only time that buildings have made their way into the blog; in previous posts, we’ve discussed the giant crossword adorning the side of an apartment building in Lvov, Ukraine, as well as the optical illusion awaiting art lovers in a Roman palace.

But it was the only time we’ve discussed a secret code being shared on the side of a building.

Until today, that is.

Yes, my friends and fellow puzzlers, there’s another building out there broadcasting secret messages for all to see. It’s also in California. And this one is more devious than the blinking light on the Capitol Records Building.

adobe semaphore 1

Say hello to Almaden Tower, the San Jose headquarters of Adobe, the software company behind Acrobat, Illustrator, and numerous other editing programs.

As you can see, there are four bright yellow circles beside the Adobe logo. These 10-foot-high digital lights all rotate. And if you pay enough attention, you might discover the secret message being broadcast.

The messages began transmitting in 2006. The code was cracked for the first time in 2007, and it wasn’t a brief message either. The lights were secretly transmitting the entire text of the Thomas Pynchon novel The Crying of Lot 49.

You see, the rotating circles allow for a form of semaphore alphabet, a way of secretly forming letters or symbols based on the position of each of the circles. They can be horizontal, vertical, a left-leaning diagonal, or a right-leaning diagonal. The various combinations of these positions create a semaphore alphabet of 256 possible characters.

adobe semaphore 2

But this was only the first part of the encryption. Even if you uncovered and charted this pattern, you still had to decode the secret messages detailing specific key words that would help you break the Vigenere encryption of the actual text.

It took MONTHS for two tech workers to figure out the semaphore language, decipher the code, and uncover the final message.

So naturally, just like the hidden alien language in the animated sci-fi comedy Futurama, it was replaced with a second, more complex code to be unraveled.

That code, which started transmitting in 2012, wasn’t broken until 2017 when a math professor started streaming footage of the Adobe building and charting the various positions of the circles.

But his examination led him to believe that it wasn’t just text being broadcast this time… it was an audio message. After discovering a chain of symbols that he believed was a space or bit of silence in an audio broadcast, he graphed the results, which resembled an audio wave.

It turns out, his suspicions were correct, and further analysis resulted in the true audio being uncovered: Neil Armstrong’s famous message from the moon landing.

Apparently, a new code and message are currently being brainstormed for Adobe’s devious puzzle monument. Who knows what Ben Rubin, the designer, has in store for solvers this time?


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Puzzles in Pop Culture: The Challenge: Total Madness

totalmad head

[Image courtesy of The Nikki Sin.]

One of the first reality TV shows to make an impact was MTV’s The Real World, which debuted back in 1992. A show wherein seven strangers would live together in a house and have their lives and interactions taped, it is credited with helping launch the modern reality TV genre.

In the decades since, one of the show’s longest-lasting spin-offs has been The Challenge, a competition show where former Real World alums and other reality show figures compete against each other in physical and mental games, both individually and as teams. There is also a social element to the show, as players form alliances, scheme against other competitors, and often vote out players at regular intervals.

Challenge 35

[Image courtesy of TV Guide.]

As you might expect, puzzles have worked their way into The Challenge from time to time. Memory games, riddles, anagrams, sliding tile puzzles, and variations on the Tower of Hanoi puzzle have all appeared in past seasons.

The most recent iteration of the show, The Challenge: Total Madness, pits the players against each other in the hopes of making it to the finals and winning a big cash prize.

In last week’s episode, the players arrived at a quarry, where a puzzly surprise awaited them: Decode and Detonate.

totalmad1

The players each had a sign bearing a sequence of symbols. Their job was to decode the sequence and display the correct decryption below the sign, using letter and number cards found in a box below the sign.

But in order to decode the sign, they would have to acquire the key to the puzzle.

Well, keys.

totalmad2

Yes, the key indicating which symbols represented which letters / numbers was split between two boards a fair distance apart. With two puzzle keys to run to — and each key only bearing some of the symbols on your sign — you’re going to have to run to both puzzle keys at some point. And that doesn’t include any running back to your sign you have to do in order to decode the letters you can remember.

totalmad3

Once you’ve decoded your sign (and it’s been confirmed as correct by the judges), you have to run to a detonator and push down the plunger, blowing up one of the two trucks perched on the bluff high above. Out of 26 competitors, only 2 can push a detonator and win the game.

totalmad4

The players, as you might expect, had different strategies going into today’s challenge.

Swaggy C, a rookie, bragged about relying on his photographic memory. CT, a veteran, immediately created a memorization tool for himself, associating each character with an image or something familiar so he could better remember it.

totalmad8

Jordan hoped to remember four or five symbols on his first run, figuring he could make up time because of his endurance. Fessy, meanwhile, kept it simpler, hoping to remember three symbols, because he thought trying to remember too many would cause him to jumble them up and get confused.

Wes opted to group the symbols in sets of four, hoping to keep each smaller bundle of characters in his brain more efficiently, and then make up time during the runs between stations.

totalmad6

After a fair amount of running, Swaggy C and CT were neck and neck. Swaggy C was the first to call for a check — asking the judges to confirm his solution — but it was incorrect. So much for that photographic memory of his.

totalmad7

CT called for a check and was correct, becoming the first competitor to run to one of the detonators and blow up a truck, earning him the win and power going forward in the game.

When the truck exploded, all of the competitors, no matter how far away, now knew that someone had completed the puzzle. Only one spot left.

totalmad9

You might think people would pair up to divide and conquer, hitting both puzzle keys at once and reconvening to see how many letters they could cobble together as a team.

No one opted to pair up. But one player DID consult another player’s work.

totalmad10

Bayleigh took advantage of the fact that everyone was using the same code language. One of the other competitors, Jenny, had the same C-shaped coded letter Bayleigh had on her sign, and had placed a decoded letter beneath it. Bayleigh took a chance that Jenny was right about the decryption, and used the information to complete her sign’s coded sequence.

When she asked for a check, it was correct. TRICKY. Not exactly in the spirit of the challenge, but effective nonetheless.

totalmad11

Bayleigh then sprinted to the second detonator and blew up the second truck, joining CT in victory and bringing the day’s challenge to a close.

totalmad12

One of the cleverest things about the way The Challenge uses puzzles is that they incorporate physical obstacles as well.

For instance, solving a puzzle on a hot day, and making the players run all over. As you get tired, you’re not in peak puzzle-solving condition, and it makes memorization and recall harder. Even if you have a (supposedly) photographic memory under normal circumstances, stressing the body always makes mental tasks more taxing.

totalmad5

Although this wasn’t the most difficult puzzle-based event I’ve seen in previous editions of The Challenge, it was a nice variation and certainly kept the competitors on their toes. I look forward to seeing if there are more puzzly obstacles awaiting the two teams as the competition continues.


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Did a Typo Help Defeat the Enigma Code and Win World War II?

During World War II, the Enigma code was one of the most daunting weapons in the German arsenal. Cracking the code would be the key to intercepting crucial information and outmaneuvering the Nazi war machine. In fact, unraveling the secrets of Enigma was so important that both England and the United States poured massive resources into building their own codebreaking operations, Bletchley Park and Arlington Hall, respectively.

Loads of fascinating information about the day-to-day operations of Bletchley Park and Arlington Hall have emerged over the last decade or so, and one of the most peculiar anecdotes to make the rounds recently claims that a typo is partially responsible for cracking Enigma.

As the story goes, a man named Geoffrey Tandy was recruited by the UK Ministry of Defense to work at Bletchley Park as part of their growing team of cryptography experts. Scholars and professions from all over the country were being enlisted in the war effort, and cryptographers (or cryptogramists) were at the top of the list.

But Tandy wasn’t a cryptogramist. He was a cryptogamist, aka an expert on mosses, algae, and lichen.

Despite the error, Tandy remained at Bletchley Park, and a year or two after his mistaken hiring, his expertise proved invaluable when a German U-boat was sunk and cryptographic documents relating to Enigma were recovered. You see, his experience preserving water-damaged materials and specimens helped salvage the water-logged documents so they could be used to crack the German code.

And thus, a typo helped end World War II.

cryptogam

[Image courtesy of Did You Know Facts.]

It’s a great story. And like many great stories, there’s a hint of truth to it. There’s also a lot of exaggeration to make it a tale for the ages.

It was no fluke that Tandy was recruited for Bletchley Park. In addition to his cryptogamist credentials, he was assistant keeper of botany at the National History Museum of London. His work included managing the voluminous library, working with fragile documents and samples, and a facility with multiple languages.

Those linguistic skills and organizational talents made him a perfect choice for Bletchley Park, since they were recruiting all sorts of experts. Remember that the field of cryptography was in its early stages. You couldn’t just go looking for cryptographers. You had to build them from scratch, as well as the folks who would be support staff for those codebreakers-in-training.

That would be Tandy’s role. He was part of a division known as NS VI, responsible for archiving foreign documents and helping the cryptographers deal with any technical jargon they might encounter, particularly in foreign languages.

tandy

[Image courtesy of the National Museum of Australia.]

So where did the typo idea come from?

Well, it’s entirely possible it came from Tandy. The cryptogram/cryptogam mistake is just the sort of joke that would appeal to linguists and other professorial types, so either another member of the Bletchley Park team or Tandy himself could have downplayed his credentials in tongue-in-cheek fashion with the story of an erroneous typo.

As for the other part of the story — where he saved the documents — there is some debate as to whether that happened. As the story goes, he used his knowledge of preserving documents to save a waterlogged set of cryptographic codes from a sunken U-boat.

[Image courtesy of Military Factory.]

The anecdote as reported usually cites the year 1941, whereas many books about Bletchley Park’s codebreaking efforts reference a U-boat from 1942, U-559, where documents AND a working Enigma machine were recovered.

I believe he DID participate in rescuing/preserving documents from a U-boat because it’s not some great heroic deed, it’s literally part of why he was hired in the first place. The crux of the anecdote is on the wordplay and the faux-fortuitousness of his employment, not on the actual events.

So, in the end, no, a typo didn’t help end World War II. But Geoffrey Tandy certainly did.


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The Tap Code (and a Puzzly Love Story)

puzzlelove

Instead of offering a puzzle for Valentine’s Day, this year I thought I’d do something different and share a story, a wartime puzzly love story for the ages.


Our tale begins in Vietnam on April 4, 1965, when Air Force pilot Carlyle Harris is shot down during a failed bombing run. Over the next eight years, Captain Harris — Smitty to his friends — was a POW in Vietnamese hands.

He would be imprisoned in numerous camps over the years — Briarpatch, “the Zoo,” Son Tay, Dogpatch, and even the infamous Hanoi Hilton — enduring illness, mistreatment, psychological and physical torture, and whatever other horrors his captors could conjure up.

But nothing was more taxing than being separated from his beloved wife Louise. With two daughters to raise, a son on the way, and a husband trapped on the other side of the world, Louise became one of the first POW wives. (Smitty was only the sixth American POW captured by the Vietnamese at that time.)

Louise worked hard not only to care for her family, but to try to contact Smitty and keep his spirits up. She also fought for personal rights, including access to her husband’s pay during his imprisonment, becoming a role model for other POW wives to come.

But what, you might be wondering, makes this a puzzly tale?

The Tap Code.

tapcode4

A World War II-era form of communication developed by a POW in Germany, the Tap Code was devised to allow communication when verbal commands wouldn’t do. The simple five-by-five matrix allows each letter to be identified by two simple sets of taps. (The lack of a need for dashes made the Tap Code superior to Morse Code for their efforts.)

Smitty taught it to fellow POWs when given the opportunity, and they taught it to others, and soon, the prisoners could communicate by tapping on walls and water pipes, knocking on buckets, or even through the movements of a broom while sweeping. (Naturally, everyone using the Tap Code did so lightly, so as not to alert the guards to their efforts at clandestine communication.)

This wasn’t the only method of communication employed by the POWs. A one-handed code system similar to American Sign Language was also developed. Some used coughing as a signal that they were being moved, while others managed to pass notes, eventually assembling mental lists of all of the POWs in a given camp.

Of course, Morse Code also proved useful. When one POW was placed on television as a Vietnamese propaganda effort, Jeremiah Denton blinked a message in Morse Code for the world to see. His message? T-O-R-T-U-R-E.

These methods, along with the Tap Code, not only kept morale up, but allowed the POWs to keep track of their ranks even when moved between camps/prisons.

tapcode2

[Image courtesy of PBS.]

It also allowed for covert operations within the camps. An SRO (senior ranking officer) would be chosen for the group, and he could assign tasks to fellow POWs as well as establish rules for newcomers to help them survive the experience.

Key Tap Code abbreviations also emerged:

  • GNST: Good Night, Sleep Tight
  • DLTBBB: Don’t let the bed bugs bite. (A sadly literal wish for the POWs.)
  • GBU: God Bless You.

GBU became shorthand for “you are not alone,” a reassurance that both God and fellow POWs were on your side, watching over you.

But Smitty and his fellow POWs weren’t the only ones using coded messages. Louise was also learning codes in order to both support the war effort and communicate with her husband. She and other POW wives would participate by using the Letter Code:

The long process began when Louise would write a short letter in longhand and send it to the Pentagon. They would rewrite it in code, while at the same time keeping the spirit of what she had written. They would then send the letter back to Louise, and she would rewrite it in longhand on the prescribed form. These then would be mailed to North Vietnam, which didn’t know about the secret strategy. It was a complicated code, and only a select few had been taught how to do it in survival training.

Smitty taught a select few the Letter Code for their own coded messages to send home, but it was hard to tell how many made it out of the camps.

tapcode3

[Image courtesy of The Daily Journal.]

All through that time, Louise was constantly writing letters, sending packages, and making entreaties on behalf of her husband, reaching out to him in any way possible. Although the Vietnamese combed through every package and seized much of the contents for themselves, some items still slipped through, becoming treasures for Smitty to hold onto. (And yes, the US government managed to slip some info and supplies to the POWs spy-style through these packages, including microfilm, maps, and more.)

Louise’s unflagging efforts and Smitty’s determination were finally rewarded when negotiations between the US and Vietnam bore fruit. Before returning to the United States, Smitty was allowed to speak to Louise on the phone. It had been 2,871 days since his capture.

But that wasn’t the end for the Tap Code — later referred to as the Smitty Harris Tap Code after the successes with it during Vietnam. Even when the POWs were finally returned home, staying in a hotel before going their separate ways, they used the Tap Code all night to communicate with each other. Old habits are hard to break.


Not only is this a story of puzzly innovation and determination, but it’s also an inspiring tale of two people in love who never gave up on seeing each other again.

You can read the full story of Smitty and Louise’s trials and tribulations in Tap Code: The Epic Survival Tale of a Vietnam POW and the Secret Code That Changed Everything.

tapcode1

[Image courtesy of Amazon.]


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