Thanks to the recently unveiled FBI files regarding the disappearance of Donna Lass (25), last seen at the Sahara Tahoe Hotel & Casino on September 6th 1970 at 2:00 am, it is safe to say that Donna Lass was not abducted from the casino (or its parking lot) at the end of her shift, and didn't meet foul play by the hands of a random stranger, who intercepted her journey while she returned back to her apartment in the early morning hours (whether she was walking or in a vehicle).

Donna Lass had changed out of her nurse's uniform and into a navy blue slack suit shortly before her shift end at 2 am. These were the clothes the young woman was last seen wearing at the Sahara Tahoe Hotel & Casino, that were not found in her apartment by investigators, which may lead some to believe she never arrived home that morning. However, her purse (handbag for carrying personal items) was discovered in her apartment, containing money, her personal cosmetics and car keys, which almost certainly suggests she returned back to her home after leaving the casino. She may have walked home, or accepted a lift from somebody at the casino (or during her journey), but the important thing to remember here, is that her navy blue slack suit was missing, yet her purse wasn't.

Her 1968 Chevrolet Camaro was found outside her Monte Verdi apartments on 3893 Pioneer Trail Road by the South Lake Tahoe Police Department on September 13th 1970, which suggests, that had she met foul play that morning, we are still unable to rule out that she drove to work on September 5th 1970, and returned home in her car on September 6th 1970, knowing now her car keys were found in her purse inside the apartment. In absence of any confirmed sightings of Donna Lass after 2 am on September 6th 1970, the fact that her navy blue slack suit was never seen again, strongly indicates she didn't change out of these clothes after arriving home that morning. Especially when we consider a malicious phone call was received by the Sahara Tahoe Hotel & Casino on September 7th 1970, claiming falsely that Donna Lass had been called out of town for a family illness and would not be returning to work for a few days. This obviously means that Donna Lass met foul play between the time she returned to her apartment on September 6th 1970, to the time the malevolent call was made to the casino the following day (September 7th 1970). And it tells us that she never likely removed her navy blue slack suit and went to bed.

The private investigator's report stated that the mysterious caller identified himself as Mr. Davis (Donna's new landlord), which Nick Davis vehemently denied was him. It would have been extremely stupid to have murdered Donna Lass and then used your own name to excuse her absence due to family illness, that obviously would have been discovered in due course by investigators. If this was the case, the caller wasn't Nick Davis. But this detail about "Mr. Davis" was not mentioned in the FBI files, which only referred to the phone caller as an unknown male. Even if the caller mentioned no name, it is clear that this person was involved in the disappearance (and likely murder) of Donna Lass, who knew where she worked, and felt the need to buy time and phone the casino to excuse her absence.

A random killer (unknown to Donna Lass and living distant from her residence), who murdered her at the apartment or abducted her from it, has absolutely no need to make contact with the Sahara Tahoe Hotel & Casino and make a bunch of excuses. The only person who needs to buy time is somebody the police would have chosen to visit first, such as friends, neighbors  and work colleagues. Somebody who may have given Donna Lass a lift in the early hours of September 6th 1970, somebody who rode in her vehicle that morning, or somebody that visited her apartment after she arrived home from work. Somebody that killed or abducted her while she was still wearing her navy blue slack suit, who needed to confuse the timeline of her disappearance and murder. The clothes she left work in vanished alongside her, but her purse, that she almost certainly carried with her when she arrived at work on September 5th 1970, found its way back to her apartment on September 6th 1970.

​It appears as though Donna Lass met her demise shortly after leaving work and arriving home. Was it a co-worker or a resident at the Monte Verdi apartment complex at ​3893 Pioneer Trail Road? The final question is why did the "killer" make the phone call on September 7th 1970 and inform the casino that Donna had gone out of town, rather than phoning her workplace in the daytime hours of September 6th 1970. Was he aware that Donna Lass wasn't working on the evening of September 6th 1970, and had the day off? There can't be many other reasons why the perpetrator waited over 24 hours to phone the casino. If this was the reason, it may narrow the focus to somebody who was not only familiar with her profession, but to somebody who knew her work schedule, such as a friend or close work colleague. A person who didn't want this crime investigated as a murder and needed to make the body disappear.  

For five years, since the 340 cipher was cracked by David Oranchak, Sam Blake and Jarl Van Eycke, people have been under the misconception that the Zodiac Killer made many mistakes when encoding his 340 character message, but the reality is almost certainly different, with only eight mistakes yet to be fully explained in his cipher. I have found only four mistakes in the first 9 rows, and the same number in the second 9 rows, giving us eight mistakes in 340 operations during the encoding process, which is a success rate of 97.65%. The Zodiac Killer upped the level of difficulty from the 408 cipher to the 340 cipher, probably in response to the speed his first offering was cracked. However, no one likely expected the Zodiac Killer to ramp up the difficulty level from the first 9 rows to the second 9 rows in this one cipher. He clearly overestimated its complexity, because the message he masked behind a wall of ciphertext was of a contemporary nature, intended to be read in 1969 or 1970, not half a century later. The notion purveyed of a killer who bumbled his way through the 340 cipher, losing concentration numerous times during the encipherment process, can now be utterly dispelled. This cipher was as devious as it comes.  

The Zodiac Killer made the 340 cipher more difficult by using a combination of substitution and transposition to disguise his message, but he added a third layer in the second 9 rows of the cipher by adding 14 deliberate spelling mistakes in an organized pattern 9 spaces apart (running diagonally across the cipher). The Zodiac Killer not only hid his message by using a 9 shift (and negative 8 shift) technique shown here, but he would further complicate matters for codebreakers by baking in these spelling mistakes using the same 9 shift technique. If you thought that was the last hurdle codebreakers had to overcome you would be mistaken, because a fourth layer was added, also 9 spaces apart. The Zodiac Killer placed the phrase "LIFE IS" into his message, inserted deliberately into certain positions so that it would appear at the end of the 10th row of the original 340 cipher when the key was applied. Below are the 14 deliberate spelling errors he placed into his message, running diagonally across the grid (black rectangles). The four green circles, I believe, are the accidental errors made by the Zodiac Killer. These concepts were fully explained in the previous article No Cipher Mistakes by Zodiac. 

Below is the Zodiac Killer's encoded message with the spelling errors rectified (in brown). There is absolutely no way the Zodiac Killer accidentally made these 14 mistakes in such an organized pattern. If you add the "LIFE IS" phrase into the mix (blue rectangles), it gives us 20 deliberate "errors" by the Zodiac Killer, all organized diagonally 9 spaces apart.

This leads us to the Zodiac Killer's next "13-Symbol" cipher mailed on April 20th 1970, in which the Zodiac Killer introduced the code with the phrase "This is the Zodiac speaking. By the way have you cracked the last cipher I sent you? My name is....". If we had cracked the last cipher he sent us, we would have known that the message was encoded behind a simple combination of 9 and 8 shift techniques, which if applied to the 13-Symbol cipher encodes the message of "ME ⊕" ("ME" followed by the Zodiac crosshairs). Simply traveling 8 positions to the right of each circled 8 and cycling through the 13​-Symbol cipher, gives us the "identity" of "ME ⊕". A signature twice highlighted in the Halloween card on October 27th 1970, and given to us directly by the Zodiac Killer in the Exorcist letter on January 29th 1974. All these three communications teased us with the promise of a name, and all can easily be shown to give us the signature of "Me" in their design. The personal pronoun of "ME" was synonymous with the pseudonym "Zodiac" and his "crosshairs", hence the use of "Me-37" in his Exorcist letter rather than "⊕-37", a format he usually chose. Was the Zodiac Killer playing one big joke on us all? See here.

The Zodiac Killer's 340 cipher was broken up into 3 parts of 9, 9 and 2 rows. This was the initial key to solving the 340 cipher. If we apply the same methodology across the Z13 and cycle through the code (9th, 18th and 20th positions), we get 888, the key to solving the Zodiac Killer's 13-Symbol cipher. See here.

The first 18 rows of the 340 cipher reads I HOPE YOU ARE HAVING LOTS OF FUN IN TRYING TO CATCH ME - THAT WASN’T ME ON THE TV SHOW - WHICH BRINGS UP A POINT ABOUT ME - I AM NOT AFRAID OF THE GAS CHAMBER BECAUSE IT WILL SEND ME TO PARADICE ALL THE SOONER BECAUSE I NOW HAVE ENOUGH SLAVES TO WORK FOR ME WHERE EVERYONE ELSE HAS NOTHING WHEN THEY REACH PARADICE - SO THEY ARE AFRAID OF DEATH - I AM NOT AFRAID BECAUSE I KNOW THAT MY NEW LIFE IS. It is clear that the first 9 rows of the cipher (in black) carried the important part of Zodiac's message, where he confirms that it wasn't him on the TV show, and he was not afraid of the gas chamber. However, the second part of his message (in blue) is pretty irrelevant drivel about "paradice" and "slaves", copying much of what was present in the 408 cipher. This may be the reason the Zodiac Killer created the first 9 rows of the cipher with less complexity and without the designed spelling mistakes present in the second 9 rows. He probably cared less about the second part of his message being deciphered. The amount of cleverness baked into the 340 cipher shows that the Zodiac Killer knew perfectly well that the design of the Z13 and Z32 codes were incompatible with normal cryptographic techniques using all the ciphertext, which is why anybody adopting this approach is quite frankly wasting their time. These two codes require a much more nuanced approach, along with an in depth knowledge of the Zodiac case spanning several years..

THE INSERTION OF THE CORRECT PLAINTEXT LETTERS BELOW WOULD RECTIFY 78% OF THE MESSAGE. ONLY FOUR ERRORS WOULD REMAIN (THE GREEN CIRCLES). 

BELOW ARE THE SECOND 9 ROWS OF THE ORIGINAL 34O CIPHER WITH THE CIPHER KEY APPLIED. THIS IS BEFORE THE PERIOD 19 SHIFT WAS USED IN AN ATTEMPT TO FIND A COHERENT MESSAGE. 

Many people have described the author of the Fairfield letter (with code) as a lazy hoaxer who just dragged two sections of ciphertext from the 340 cipher and plonked them in the Z38 code below. Not only would this be a pointless task, but if this person wanted to make the reader believe they were the Zodiac Killer, why would they adopt the approach of an obvious impersonator and imitate previous correspondence? The more realistic answer to this communication is that it was the Zodiac Killer giving us a clue to the workings of the 340 cipher. Before David Oranchak, Sam Blake and Jarl Van Eycke cracked the 340 cipher in 2020, nobody was aware that the first 4 and last 5 characters of the 340 cipher spelled "IRON" and "DEATH" when the cipher key was applied to it, yet the author of the Z38 code just happened to feature these two sections of ciphertext in their December 7th 1969 letter. Probably the most obvious thing for an impersonator to do, was to bring forth the "near Zodiac"  (ZO∆AIK) from the final row of the 340 cipher and drop it into this code, but this person snubbed that opportunity and broke it up to what we see in the second red rectangle below. An obvious feature in the 340 cipher that the impersonator failed to impersonate. This segment of code is also noticeably larger than the rest of the ciphertext, including the row it sits on.

After the cipher key was applied to the original 340 ciphertext we got the incoherent plaintext shown below. However, after the period 19 shift was applied, the word "DEATH" remained one of only three forward facing words to stay intact (the others being "WILL" and "EASY"). But "DEATH" stands out because it isn't surrounded on both sides by other plaintext, sitting in a prominent position at the end of the cipher. 

The ciphertext characters "H" and "+", not only begin and end the original 340 ciphertext, they begin and end the new ciphertext arrangement after the period 19 shift is applied to it. They also form the beginning two ciphertext characters on the first row of the new ciphertext arrangement. And begin and end the Z38 code mailed on December 7th 1969. If you apply a period 19 shift to the Z38 code above, you get the ciphertext characters "H" and "+" featuring for a fifth time. Because the cipher is 38 characters in length, if you continue the period 19 shift you will get a repeated "H+" sequence continuously. Sam Fisher, a Zodiac researcher, also pointed out that the plaintext letter "H" was represented by the ciphertext character "+" in the 148 character cipher mailed by the Zodiac Killer in May 1971.

Of course, this is all totally coincidental, created by a hoaxer who pleaded "I just need help" (not published in the newspapers) two weeks before the Melvin Belli letter arrived on December 20th 1969, stating "please help me". A December 7th 1969 letter mailed a matter of hours before somebody rang the Oklahoma City radio station KTOK, and made mockery of the Jim Dunbar TV show on October 22nd 1969, featuring attorney Melvin Belli. If we want to discover more about the Zodiac Killer, it's imperative we analyse every potential communication mailed in his name. The other option, adopted by many researchers, is to pay little heed to these communications and lazily believe what they have been fed by others in the Zodiac community, adopting an "Ignorance is bliss" type approach. Lazy individuals who believe in lazy hoaxers, who refuse to even consider that they may be wrong. 

On December 7th 1969 the Zodiac Killer mailed a letter and code from Fairfield just hours before he phoned the Oklahoma radio station KTOK, both times imitating the caller to the Jim Dunbar TV show on October 22nd 1969. The person who mailed the letter provided crucial information in the Z38 code that showed intrinsic knowledge regarding the mechanics of the 340 cipher and its use of the knight's move in chess. In other words, the person who mailed the December 7th 1969 letter knew how to solve the 340 cipher. They knew this because they were the Zodiac Killer. The following will show how I arrived at the plausible solution of  "TRYING TIMES. SO I NEED APPOINTMENT TO GET HELP". 

Bearing in mind that the phone call to Oklahoma and the letter mailed on December 7th 1969 to the San Francisco Chronicle, were both continuing the theme of the Jim Dunbar TV show and Melvin Belli fiasco, in which the hoax caller was pleading for help, there is a strong probability that the Z38 code may contain a message along the same lines. If it did, it would almost certainly have been something the Zodiac Killer read in the newspapers on this topic, such as the article in the Los Angeles Times newspaper on October 23rd 1969, the day after the television show.
​
In the 340 cipher message, decoded by David Oranchak, Sam Blake and Jarl Van Eycke on December 5th 2020, the Zodiac Killer used the headlines from the San Francisco Chronicle newspaper on October 24th 1969, which was titled over two pages, reading both "That Wasn't Zodiac, Say 3 Who Know" and "It Wasn't Zodiac, Say 3 Who Know". In his 340 message he stated "That Wasn't Me on the TV Show". The numerous references in the newspapers immediately after October 22nd 1969 about the caller saying "I don't want to go to the gas chamber", was replied to by Zodiac, who encoded "I am not afraid of the gas chamber". The Zodiac Killer would emphasize these two points in the first seven lines of the deciphered message.   ​

The news was abound with the failed meeting between the "Zodiac Killer" (Sam) and Melvin Belli at the Vincent de Paul thrift store in Daly City, later that day. The Los Angeles Times newspaper on October 23rd 1969 read "Attorney Melvin Belli in a phone booth at a San Francisco television station talking to caller who said he was the Zodiac Killer. Caller made an appointment but didn't keep it". This was the sort of the thing the Zodiac Killer may have mocked, after writing "I just need help" on December 7th 1969. There were two plus signs (+) together in the Z38 code, so I knew they had to represent the same plaintext letter, and gambled on the word "appointment". This would not only fill up a significant portion of the Z38 code, but would mean that the code ended with the plaintext letter "P". That was likely the last letter of "help", which also featured prominently in the Los Angeles Times newspaper and others. In fact, the title of the article was "I Want Help, Zodiac Caller Tells Attorney on Telephone". After placing "appointment" and "help" in the Z38 code, it allows us to form the word "to" immediately after "appointment" because of the double character (dotted circles). The phrase "appointment to get help" was then easy to work out. 

The first 18 ciphertext characters could then be filled in somewhat, with the dotted circle represented by the plaintext letter "T",  the circle with the single vertical line through it represented by the plaintext letter "I", the plain circle ​represented by the plaintext letter "E", the square represented by the plaintext letter "G", the triangle represented by the plaintext letter "O", and the slanted line​ represented by the plaintext letter "N". We were left with this.

The plaintext letters in blue on the top line looked like it could spell "times", followed by the word "so", thereby satisfying the double "L" ciphertext. So I took a gamble and placed the words into the message like so. 

The rest was pretty simple. After the word "so" I added the personal pronoun of "I", and "need" was the obvious next choice. The final part was filling in the blanks for the starting five plaintext letters ending in "G". Trying times" is a well-known phrase that one might experience, and necessitates the need for an "appointment to get help". This completed the Z38 code. Whether it is the correct solution I can't say for certain, but it satisfies the workings of a substitution cipher and has relevance to the contemporary events the Zodiac Killer was reading in the newspapers at the time, just like the message in the 340 cipher.

In cryptography, unicity distance is the length of an original ciphertext needed to break the cipher by reducing the number of possible spurious keys to zero in a brute force attack. That is, after trying every possible key, there should be just one decipherment that makes sense, i.e. expected amount of ciphertext needed to determine the key completely, assuming the underlying message has redundancy. For a simple substitution cipher, the number of possible keys is 26! = 4.0329 × 1026 = 288.4, the number of ways in which the alphabet can be permuted. Assuming all keys are equally likely, H(k) = log2(26!) = 88.4 bits. For English text D = 3.2, thus U = 88.4/3.2 = 28. So given 28 characters of ciphertext it should be theoretically possible to work out an English plaintext and hence the key. Wikipedia. 

• Simple Monoalphabetic Substitution Cipher: The theoretical unicity distance is about 28 characters. In practice, cryptanalysts typically need around 50 characters to perform reliable frequency analysis and achieve a definite solve.

FURTHER READING: "IRON" AND "DEATH" FEATURED IN TWO CIPHERS   

On October 22nd 1969 Will Stevens published an article in the San Francisco Examiner, in which Professor Donald C. B. Marsh urged the killer to contact him in code, stating "The killer wouldn't dare, as he claimed in letters to the newspapers, to reveal his name in the cipher to established cryptogram experts. He knows, to quote Edgar Allan Poe, that any cipher created by man can be solved by man. Zodiac has not told the truth in his cipher messages to the Examiner, the Chronicle and the Vallejo Times-Herald. Zodiac has not done this, because to tell the complete truth in relation to his name - in cipher code - would lead to his capture. I invite Zodiac to send The American Cryptogram Association a cipher code - however complicated - which will truly and honestly include his name"

Professor Donald C. B. Marsh, by invoking the name of Edgar Allan Poe, was probably hoping that the Zodiac Killer was going to use techniques mentioned or used by Poe, making any future offering by Zodiac easier to solve. The next two ciphers/codes mailed by the Zodiac Killer can be linked to Poe's 1841 essay "A Few Words on Secret Writing" from the July edition of Graham's magazine. The scytale method of decryption featured by Poe can solve the 340 cipher. The immediate next passage of  A Few Words on Secret Writing further describes cryptographic techniques, showing the splitting of the alphabet into ABCDEFGHIJKLM and NOPQRSTUVWXYZ, creating two portions of thirteen letters. The Zodiac Killer's April 20th 1970 communication was a 13-Symbol cipher beginning with A and ending with M. Edgar Allan Poe then describes a cipher wheel that can be used to give a credible answer to the Z13 code. But of course, it doesn't end there.

Not only did the Zodiac Killer use the encryption techniques described by Edgar Allan Poe, he may have embedded two of Edgar Allan's poems in the mechanics of the 340 cipher. Notable words from these two poems were visible when the cipher key was applied to the 340 cipher (before the period 19 shift was used to acquire the message). The presence of the second Edgar Allan Poe poem in the 340 cipher (after the key was applied) was highlighted by the author of the Z38 code mailed from Fairfield on December 7th 1969, who was undeniably the Zodiac Killer.

But let us deal with the first poem that was plainly visible in the deciphered 340 message, that read: I HOPE YOU ARE HAVING LOTS OF FUN IN TRYING TO CATCH ME - THAT WASN’T ME ON THE TV SHOW - WHICH BRINGS UP A POINT ABOUT ME - I AM NOT AFRAID OF THE GAS CHAMBER BECAUSE IT WILL SEND ME TO PARADICE ALL THE SOONER BECAUSE I NOW HAVE ENOUGH SLAVES TO WORK FOR ME WHERE EVERYONE ELSE HAS NOTHING WHEN THEY REACH PARADICE - SO THEY ARE AFRAID OF DEATH - I AM NOT AFRAID BECAUSE I KNOW THAT MY NEW LIFE IS LIFE WILL BE AN EASY ONE IN PARADICE DEATH.

"To One in Paradise" was written by Edgar Allan Poe. This poem was first published as part of the short story titled "The Visionary" (later retitled as "The Assignation"). The poem was also published under the names "To lanthe in Heaven" and "To One Beloved". The title "To One in Paradise" was used in the February 25th 1843 edition of the Philidelphia Saturday Museum. This poem was written after the death of Poe's wife. He writes that she was his life and he lived for her and now he looks forward to the future where they will be together again in death. link. Now let's look for the second poem by Edgar Allan Poe. When the Zodiac Killer mailed the Z38 code on December 7th 1969, he repeated two notable segments of ciphertext from the 340 cipher. The first four ciphertext characters, and the last five ciphertext characters (shown below). 

This may not seem significant, until you consider that when the original 340 cipher was changed using the key, it created the words "IRON" and "DEATH" in these two exact positions (see below). Are we are expected to believe that when the author of the Z38 code selected these four and five sections of ciphertext from the 340 cipher, taken from the beginning and end of the cipher, he chose two legible words created by the 340 key by accident, which he should have had no knowledge of unless he was the Zodiac Killer. No hoaxer should have been aware of this fact and had the foresight to highlight these sections in the Z38 code. The person who created the Z38 code broke up the "Zodiac-like" pseudonym (ZO∆AIK) from the last row of the 340 cipher to create the word "death", something that would not have been expected from a hoaxer. The person who did this knew exactly what they were doing, because they created the 340 cipher.

It must be remembered that Edgar Allan Poe wrote "To One in Paradise" upon the death of his beloved wife, Virginia Eliza Poe. But how can "IRON" and "DEATH" introduce a second Edgar Allan Poe poem into the equation? Edgar Allan Poe wrote "To One in Paradise" about the death of his wife, but this wasn't the only poem written by Poe about the death of Virginia. The inspiration for the second poem, "The Bells", was reported as coming from his friend, Marie Louise Shew, who likened the sound of the Fordham University bell made of "iron", to "death".

​Edgar Allan Poe's poem "The Bells" uses different types of bells (silver, gold, brazen, iron) as powerful metaphors for the stages of human life, from the joy and playfulness of childhood (silver sleigh bells) through the harmony of youth and marriage (golden bells), to the panic and chaos of maturity (brazen bells), culminating in the inescapable melancholy and terror of death (iron bells). Written at the end of his life, the poem's shifting sounds and increasing length mirror the journey from youthful delight to the despair and inevitability of mortality, exploring the passage of time and its emotional toll. Edgar Allan Poe's poem "The Bells" was inspired by the sounds of bells from Fordham University's church while he lived nearby in the Bronx, New York, capturing the changing emotions of life, from youthful joy (silver bells) to despair and death (iron bells), a reflection of his own grief after his wife Virginia's passing.. Inspiration for the poem is often granted to Marie Louise Shew, a woman who had helped care for Poe's wife Virginia as she lay dying. One day, as Shew was visiting Poe at his cottage in Fordham, New York, Poe needed to write a poem but had no inspiration. Shew allegedly heard ringing bells from afar and playfully suggested to start there, possibly even writing the first line of each stanza.

I always wondered why these two prominent English words began and ended the 340 cipher after the key was applied to the original 340 ciphertext, and then highlighted by Zodiac in the Z38 code. The poems "The Bells" and "To One in Paradise" were written about the grief Edgar Allan Poe experienced upon the death of his wife, with "IRON", "DEATH" and "PARADISE" instrumental to both - which just happened to be present at the beginning and end of the Zodiac Killer's 340 cipher after the key was applied (although "one in paradice" was reversed at this point). Throw in the essay A Few Words on Secret Writing by Edgar Allan Poe, containing a technique that can solve Zodiac's 340 cipher (and a further technique that possibly influenced the design and solution of the Z13), and we have a story steeped in history. 

FURTHER READING: THE MECHANICS OF THE Z38 CODE 

Thanks to the brilliance and determination of David Oranchak, Sam Blake and Jarl Van Eycke, the 340 cipher was finally cracked after 51 years on December 5th 2020. However, with the exception of a few people, little has been done to find the inspiration for a killer who created a cipher that required the knight's move in chess to reconfigure the ciphertext and allow the message to be broken using homophonic substitution. The 340 cipher needed a one down, two across system to make the cipher easier to crack, with the Zodiac Killer's errors creating a further roadblock. Ciphers are mathematical, relying on algorithms, modular arithmetic, and complex equations for encryption and decryption, evolving from simple letter shifts to advanced concepts in number theory and abstract algebra for modern digital security. They use mathematical procedures to transform readable text (plaintext) into unreadable text (ciphertext) and back, making them a core part of cryptography, which sits at the intersection of math and computer science.

Radians, chosen by the Zodiac Killer for us to discover the location of his hidden (likely pretend) bomb, are fundamental to mathematics, serving as the standard unit for measuring angles, especially in calculus and physics, because they simplify formulas by relating angles directly to the circle's radius, making calculations for arc length, sectors, and trigonometric functions much cleaner than using degrees. Radians are essentially a unitless count of "radius units", making them a natural fit for mathematical expressions. This was another of Zodiac's puzzles that lay unbroken for 51 years until Zodiac researcher, Druzer, filled in the blanks on December 27th 2020. But what is another form of mathematics that may have inspired the Zodiac Killer to fashion the 340 cipher the way he did? A form of mathematics that Zodiac mentioned in his letters?​  

On July 19th 1978, a deeply controversial communication, that is almost certainly genuine Zodiac material, was mailed to the Los Angeles Times. It read: "I am the ZODIAC and I am in control of all things. I am going to tell you a secret. I like friction tape. I like to have it around in case I need to truss someone up in a hurry....I have my real name on a small metallic tape. You see, while you have it in your possession, I want you to know it belongs to me and you think I may have left it accidentally. I am athletic. It could be swim fins, or a piece of scuba gear. But maybe you play chess with me. I have several cheap sets in closets all over. I have my name on the bottom of the lid with the scotch tape....My tape is waiting for me all over California. Do you know me? I am the ZODIAC and I am in control". This letter probably formed the basis of Robert Graysmith's mentioning of Zodiac's crimes as an "outdoor game of chess".

Chess is deeply mathematical, relying on logic, patterns, probability, and combinatorics, even though it's not about traditional arithmetic; it's a game of finite states and algorithms with a vast solution space, making it a practical application of mathematical thinking. While you don't need advanced math skills to play, the underlying principles of strategic calculation, geometry, and problem-solving connect it directly to mathematics. Coming the day after the opening game in the World Chess Championship between Anatoly Karpov and Viktor Korchnoi on July 18th 1978, this letter told of a person who had "chess sets all over California" and suggested that David Toschi, who had been demoted to pawn detail, play a game of chess with him.

​If the Zodiac Killer really had an avid interest in chess and puzzles, he would very likely have known about the knight's tour challenge, a mathematical problem where you have to move a knight around a chessboard (8 X 8 grid) and visit all 64 squares without landing on a square more than once. The Knight's Tour is very well-known, recognized as a classic, over-thousand-year-old mathematical puzzle and graph theory problem, first appearing in 9th-century Sanskrit texts and later analyzed by Leonhard Euler, becoming famous for its complexity and links to magic squares, popularizing it through chess history and computer science as an illustration of algorithms. 

Ciphers are essentially algorithms (or sets of rules/steps) used for encryption and decryption, transforming readable text (plaintext) into unreadable ciphertext and back again, using keys to control the process. So did the Zodiac Killer use a knowledge of chess and the well-known puzzle of the knight's tour, and create a more complex 340 cipher that required the very same move to begin decoding his message on November 8th 1969? 

FURTHER READING: A PAWN IN A GAME OF DEATH   ​

Oak Shores Day Use Area is a free public recreation site managed by the Bureau of Reclamation on the western shore of Lake Berryessa. Nestled in the blue oak woodlands east of Napa Valley, the area provides beach access, swimming, shoreline fishing, picnicking, and wildlife viewing opportunities. Oak Shores and Smittle Creek are two separate but nearby day-use areas at Lake Berryessa, connected by scenic trails, including the 2.6 mile Smittle Creek Trail, offering hiking, and lake access; you can drive between them or hike the trails, enjoying oak woodlands and creek views. This is an unmaintained single track path that travels along the western edge of Lake Berryessa. ​One (or parts) of these trails could have been used by the Zodiac Killer after possibly encountering the three Pacific Union College girls from Angwin, before the attack on Bryan Hartnell and Cecelia Shepard on September 27th 1969. He could have trawled the hillsides and trails looking for more potential victims, until he reached the location of Bryan and Cecelia just under a mile south.

After the suspicious man had been observed by the three girls for about 55 minutes, he apparently returned to his vehicle at about 4:25 pm, which was not in the parking lot at 4:30 pm when they decided to drive home. My initial belief was that the three girls were at a beach area of Smittle Creek slightly north of Coyote Beach, but now have concluded they were 450 meters south at Coyote Beach itself, which the excellent work of Gorillatrain on Discord highlighted several months earlier. The girls stated that they "parked their vehicle at a location two miles north of the A & W Root Beer stand on Knoxville Road" (located at 5100 Knoxville Road). The Coyote Beach parking lot is exactly 2 miles north of the A & W Root Beer stand (1.8 miles by crow), and is a recreation spot in the Smittle Creek area. 

Obviously one of the major factors for shifting their encounter marginally south, is the girls mentioned a parking lot area in the police report, which wasn't conveniently situated near the location of the beach I had previously identified at Smittle Creek. More importantly, one of the girls stated that she saw "the subject go into the parking lot to the south. Subject went past their vehicle and backed up so their rear bumpers were nearly touching". Below I have shown the likely parking lot with north and south sections. The road leading from Knoxville Road to the parking lot joins the parking lot on its south edge, which is what the girl said when recollecting that the man entered the "parking lot to the south". The man then probably took the right turn into the parking lot and passed their vehicle, before reversing as she described. The journey to the beach (by the cluster of trees) is just over 760 feet. One of the girls noticed the man watching them from the edge of the trees about 40 or 50 feet away. Another stated that he was standing on the bank about 45 yards away (135 feet). From the red circle below to the front of the beach is 135 feet. After the encounter the man walked back up the hill. That area is sloped upwards from right to left. They stated that from the man's vantage point when he was initially in his vehicle, it was very doubtful he could observe them on the beach. Of course, I cannot say for sure the exact location they were sunbathing, but this stretch of beach ticks all the boxes,  

Gorillatrain has identified an area where he believes Dr. Rayfield and his son spotted the man on the hillside later that day (6:30 pm). If correct, the man would have been just 1,000 feet from the northern edge of the Coyote Beach parking lot, where his car was parked about 2 hours earlier (4:25 pm). According to a friend of Zodiac researcher, Dion Walker, the location of Dr. Rayfield's vehicle on September 27th 1969 at 6:30 pm, remembered by David Rayfield in later years, places it at the location shown in the image on the left.

The police report stated that they "went down to the beach when David noticed a white male subject walking in the area, described as 5'10", heavy build, wearing dark trousers, a dark shirt with red in it, long sleeves. The subject was walking alongside the hill area about halfway between the road and the lake". David stated the subject was about 100 yards away. The parking location of the Rayfield's vehicle shown in the accompanying image is 8/10ths of a mile from the Karmann Ghia of Bryan Hartnell, as described in the police report. They made no mention of leaving their vehicle in a parking lot, or directly referred to Coyote Beach, so the location depicted on the map is a distinct probability. There is a convenient turnout 250 feet from the red Google marker.

The recollection of David Rayfield was given many decades after the events at Lake Berryessa, which must be taken into account, but the location he identified does match the police report and this area of Smittle Creek - an area that both Gorillatrain and I have previously calculated to be the location of the Rayfield sighting based on measurements and descriptions given by investigators.

In a revised Lake Berryessa timeline we have the possibility of the Zodiac Killer signing 6:30 on the car door of Bryan Hartnell at approximately 6:07 pm. The journey time walking 0.8 miles north from the car of Bryan Hartnell to the Coyote Beach area, traversing the hillsides, would take approximately 25 minutes. This would place the Zodiac Killer passing the location of Dr. Rayfield and David at about 6:32 pm, almost matching the estimate of 6:30 pm given by the Rayfields. There is a turnout and small roadway just beyond the Rayfield's location shown above.

We have the accounts of the Rayfields and the three girls placing "a man they deemed worthy enough to report to police", possibly within 1,000 feet of one another, either side of the brutal stabbing of Bryan Hartnell and Cecelia Shepard on September 27th 1969. Everything occurring in a three hour window, from the 3:30 pm time the three girls first noticed the suspicious man, to the David Rayfield observations at 6:30 pm. Not forgetting that one of the girls described a white belt around his back, and thought that it may have been a tee shirt hanging out. ​Many have considered this observation significant, because the Zodiac Killer when he later approached Bryan Hartnell & Cecelia Shepard at around 6:00 pm, had some cut lengths of white clothesline cord seated in the rear of his trousers.

Of course, there is no way to know for certain whether the Zodiac Killer walked to the area where he stabbed both Bryan Hartnell and Cecelia Shepard, or drove to this location, but this doesn't change the fact we have two sightings of a man in virtually the same location, that necessitated five people to contact the police and recount what they saw that day. And is it reasonable to conclude that the Zodiac Killer drove to Lake Berryessa on September 27th 1969 and immediately found his victims at the first attempt at 6:00 pm? Or was he likely scouring the shores of Lake Berryessa for several hours until a suitable and safe opportunity arose? I will let you decide.

On September 27th 1969, three girls from Pacific Union College in Angwin, California noticed a suspicious man at approximately 3:30 pm at Smittle Creek, close to the shoreline of Lake Berryessa. They had left Angwin at 2:45 pm. They told investigators that the man had pulled up behind their vehicle in what they described as a late model silver blue Chevrolet with California license plates, and assumed the man had remained in his vehicle for about 30-45 minutes, before heading to their location and watching them sunbathing from a distance, for another 30-45 minutes. One of the girls described a white belt around his back, but thought that it may have been a tee shirt hanging out. ​Many have considered this observation significant, because the Zodiac Killer when he later approached Bryan Hartnell & Cecelia Shepard just after 6:00 pm, had some cut lengths of white clothesline cord seated in the rear of his trousers.

​The approximate times given by the three girls has the man departing Smittle Creek at anywhere between 4:30 pm and 5:00 pm. However, the time given in the police report for the girls leaving that area was 4:30 pm, with the man's vehicle gone from the car park. So if this was the Zodiac Killer, he likely left the area shortly before 4:30 pm. He may have seen the girls packing up their belongings and decided to abandon what intentions he had envisaged. The journey time from Angwin to Smittle Creek is about 45 minutes, so this tallies with their initial departure time of 2:45 pm, to arrive at Lake Berryessa at 3:30 pm. 

One of the girls advised the responding officer (see above) that "she and her two girlfriends parked their vehicle at a location two miles north of the A & W Root Beer stand on Knoxville Road" (located at 5100 Knoxville Road). But why had they clarified the position of their location with respect to the A & W Root Beer stand and not any other significant area? Knowing that they were going sunbathing on a pretty hot day (about 75 degrees Fahrenheit), did they briefly stop off to pick up some cool drinks at the Sugar Loaf Park general store at 5100 Knoxville Road, selling  A & W Root Beer, refreshments, sandwiches, hamburgers, fishing tackle and an array of other items? It would have added barely 2 minutes to their journey - and explained why they mentioned the A & W Root Beer stand to interviewing officers.

If the Zodiac Killer had traveled by car to Lake Berryessa from either Vallejo (40 miles) or San Francisco (70 miles), knowing that he was going to trawl the hillsides on a hot day looking for victims, he may have thought exactly the same as the three girls. As he was passing the Sugar Loaf Park general store, he had the option to stop off and purchase several cool A & W Root Beers or any other bottled soft drink, These specific Root Beers were usually manufactured in a brown bottle, but I have been unable to confirm if this product was also manufactured using green glass in the 1960s. Regardless, on a hot day, it is certainly plausible that the Zodiac Killer chose to enter this general store and purchase some fluids (which may have been a combination of beer and soft drink).

​It is at this location that the Zodiac Killer possibly crossed paths with the three girls, trailed them to Smittle Creek and pulled up behind their vehicle (bumper to bumper). Later, with the clothesline firmly nestled in his back pocket or waistband, he may have considered an attack on the three girls a little risky, and ultimately departed the scene when he saw they were packing up for the day. Two hours later, Bryan Hartnell and Cecelia Shepard were brutally stabbed just 0.8 miles south. A green bottle, determined by investigators to have two latent fingerprints of value, was found near the stump of a tree, close to the crime scene. Obviously, this green bottle could have been disposed of by anybody visiting the lake that day, but there also remains a possibility that it was purchased by the Zodiac Killer at the Sugar Loaf Park store at approximately 3:25 pm, when he latched onto the three girls several hours earlier. If only they had CCTV in 1969.

On September 13th 1973, the San Jose Mercury reported on the September 10th 1973 murder of Yellow Cab driver Roland J. Canfield (41) of 551 Manor Drive, Pacifica, who was shot behind his right ear at 4:00 pm while parked at the intersection of 27th and Noe streets in San Francisco. The wallet of Roland J. Canfield, although empty, was still in his back pocket, with investigators concluding that robbery appeared not to be the motive. The taxicab strongbox was described as undisturbed. Homicide inspectors David Toschi and William Armstrong, investigatng the case, indicated a lack of evidence to form a Zodiac Killer connection to that of Paul Stine on October 11th 1969. However, a lack of evidence to form a Zodiac link, doesn't mean there wasn't one.

​Somebody had phoned the Yellow Taxicab Company and requested a pick up at 27th and Noe streets in Noe Valley, a family-friendly, wealthy, upper-middle-class neighborhood in central San Francisco, known for its charming Victorian homes and vibrant 24th Street with local shops and restaurants. The caller had clearly given this location to the Yellow Cab Company operator, but had provided a non-existent address. When Roland Canfield arrived at the intersection he was immediately flagged down by a lone male walking on the street, who apparently entered the rear of the taxicab and shot the driver behind the right ear. Witnesses nearby heard the shot and saw a man enter a vehicle and leave the scene.   

It is virtually impossible to dismiss the notion that the phone caller and murderer were the same individual. On first look, it is safe to conclude that the taxicab driver was deliberately lured to this location for the sole purpose of murder. The fictitious address (likely a house number) probably designed to keep Roland Canfield at that location temporarily as he radioed back to headquarters to notify them that the address didn't exist and he was available for hire once again. This information was obviously given to police by the Yellow Cab Company, who were likely informed by Canfield shortly after his arrival at the intersection. This short window of time would have given the eventual murderer, who "just happened to be walking" in close proximity to the taxicab, the opportunity to wave down the taxicab driver, who was probably grateful he hadn't wasted a journey. If the phone call, fictitious address and murder happening within a few minutes of one another was just a coincidence, then it's an unlikely one. 

After the Zodiac Killer's "Monticello" postcard on July 13th 1971, over two years had elapsed before a mini revival in "Zodiac" activity, beginning on August 1st 1973 with the arrival of the Albany letter, mailed to the Albany Times Union newspaper in New York, with the Zodiac Killer threatening he was "going to start killing again". Just under six weeks later, Roland Canfield, a taxicab driver, was killed at an intersection in San Francisco by an unknown assailant - seemingly directed to a location for nothing more than murder. Eight days later, on September 18th 1973, the Zodiac Killer surfaced in San Jose, removing the tombstone (of likely Kathie Snoozy) from the Oak Hill Memorial Park & Cemetery at 300 Curtner Avenue, where Kathie Snoozy (15) was buried. The tombstone being placed at the front gate of the cemetery with the pseudonym "Zodiac" written on it in crayon.

​A cemetery located in the Monticello neighborhood of San Jose, which the Zodiac Killer referenced in his "Monticello" postcard after claiming the murder of Kathy Bilek, who "in the woods died April" (stabbed on April 11th 1971). Less than four months would pass, when on January 11th 1974, somebody claiming to be the Zodiac Killer phoned the police and newspapers stating he had killed a woman and placed her body in a Daly City church in San Mateo County. Only 18 days later, the Zodiac Killer mailed the "Exorcist" letter to the San Francisco Chronicle on January 29th 1974, threatening that if his latest letter wasn't published in the newspaper he would "do something nasty" which everyone knew he was capable of. We have five actual events, three of which can be proven to be Zodiac activity, in the space of six months. Question marks obviously remain regarding September 10th 1973 and January 11th 1974. 

The Albany letter mailed on August 1st 1973 was the only communication since the Paul Stine letter on October 13th 1969 to carry small crosshairs on the address side of the envelope, despite the Paul Stine envelope not having been released to the public, so it's uncanny that the next event to be associated with the Zodiac Killer was the murder of Roland J. Canfield on September 10th 1973, the following month. There is limited information on the Roland Canfield murder in the newspapers to forge any substantial link to the Zodiac Killer, but the mere fsct he was mentioned in connection to the murder, may have been the catalyst that drove him to the Monticello neighborhood in San Jose on September 18th 1973.