So firstly, I would like to press home the notion that the Zodiac Killer's 340 cipher was nothing more than a ruse, designed to stick two fingers up to the challenge laid down by Professor D.C.B. Marsh of the American Cryptogram Association (ACA) on October 22nd 1969, when he "invited Zodiac to send The American Cryptogram Association a cipher code - however complicated - which will truly and honestly include his name." The Zodiac Killer would eventually reveal the workings of the 340 cipher just over a year later when he mailed the rather cryptic Halloween card on October 27th 1970, revealing the trick, not treat, he had perpetrated on his challengers. The killer couldn't have been any more obvious when he actually wrote "sorry no cipher" on the envelope inner.
There are only two identical characters (the "+" sign) in the 9th column along the first 10 rows, and we know the letter "A" is center of the bisecting "Paradice" and "Slaves" on the Halloween card. It is then a simple task of placing the "R" of "Paradice" and "LV" of "Slaves" into position, to exactly mirror the Halloween card formation. It is then not difficult to find the word "By" in all four quadrants of the 340 cipher, again mirroring the Halloween card. See here for visual.
The second clue may have also come from the envelope, when the Zodiac Killer underlined the 'LAV' of the misspelled Paul Avery on the address side. The three letters 'LAV' bisected the center point of the 340 cipher. What are the odds of "sorry no cipher" mimicking the "Paradice" and "Slaves" formation on the Halloween card, which then mimicked the 340 cipher, along with the three alphabetical letters 'LAV' being integral to both.
The words "Paradice" and "Slaves" were decoded in the 408 cipher and featured prominently in the Halloween card, so what are the chances they were an integral part in the design of the 340 cipher as well? So much so, they may have formed crosshairs, bisecting the cipher at its midpoint? If none of the above was an intentional creation by Zodiac and it all fell out by accident, then he is certainly one hell of a fortunate designer.
In the words of Thomas Horan, the 340 cipher was certainly the "Great Zodiac Killer Hoax of 1969".
When the Zodiac Killer mailed his trinity of July 31st 1969 communications he withheld his identity or pseudonym, but beginning on August 4th 1969 with his 'Debut of Zodiac' letter through to his March 13th 1971 'Los Angeles' letter, every single letter the Zodiac Killer mailed began with "This is the Zodiac Speaking" (excluding cards). So why should the 340 cipher message be any different - which was effectively a letter within a card.
A negative photocopy inverts the colors of the document when creating a photocopy, resulting in letters that appear white on a black background instead of black on a white background. Negative photocopies of old or faded documents sometimes produce documents which have better focus and are easier to read and study. Wikipedia. To invert something is to put upside down or in the opposite position, order, or arrangement. Synonyms of invert, are to turn upside down, upturn, upend, turn around, turn about, turn inside out, turn back to front, reverse, flip (over) or transpose. Therefore, was the designer of the 'American Greetings' card hinting that we should "invert the key" or "flip the key". In other words, the key to the 340 cipher is to "invert" or "flip" it on its head in order to read it. The "sorry no cipher" arrangement on the Halloween card envelope was equated with "Paradice" and "Slaves", but could have been written with the 'vertical' "sorry no cipher" running downwards. Could this imply that "Paradice" was meant to be flipped on the 340 cipher, running from bottom to top?
The correspondence before the Halloween card was the October 5th 1970 '13 Hole' postcard. It too contained a cross and flipped text, stating "There are reports city police pig cops are closeing in on me. Fk I'm crackproof. What is the price tag now?"
Wouldn't it be nice if "Fk" meant "Flipped key" as well, and the '13 Hole' postcard was the third member of the trinity of solutions to the Zodiac Killer's unbreakable 340 cipher.