The creator of one of the world’s most famous mysteries is giving obsessive fans a new clue.

Kryptos, a sculpture in a courtyard at the headquarters of the Central Intelligence Agency in Langley, Va., holds an encrypted message that has not fully yielded to attempts to crack it. It’s been nearly 30 years since its tall scroll of copper with thousands of punched-through letters was set in place.

Three of the four passages of the sculpture have been decrypted (the first, though unacknowledged at the time, was solved by a team from the National Security Agency). But after nearly three decades, one brief passage remains uncracked. And that has been a source of delight and consternation to thousands of people around the world.

Kryptos. Courtesy of Jim Sanborn

The sculptor, Jim Sanborn, has been hounded for decades by codebreaking enthusiasts. And he has twice provided clues to move the community of would-be solvers along, once in 2010 and again in 2014.

Now he is offering another clue. The last one, he says.

It is a word: “NORTHEAST.” (More on that later.)

Why do people care so much about a puzzle cut into a sheet of copper in a courtyard after so much time? It’s not just that the piece itself has a kind of brooding, powerful beauty, or the fact that it has been referred to in novels by the thriller writer Dan Brown. It is something deeper, something that involves the nature of the human mind, said Craig Bauer, a professor of mathematics at York College of Pennsylvania and a former scholar in residence at the N.S.A.’s Center for Cryptologic History.

“We have many problems that are difficult to resolve — intimidating, perhaps even scary,” he said. “It gives people great pleasure to pick up on one that they think they have a chance of solving.”

Three Deciphered Passages

The message of Kryptos, and a partial guide to its solution, is contained in the panels of the sculpture. Mr. Sanborn devised the codes that he used for the passages with the help of Edward Scheidt, a retired chairman of the C.I.A.’s cryptographic center. The passages follow a theme of concealment and discovery, each more difficult to decipher than the last. The first reads: “BETWEEN SUBTLE SHADING AND THE ABSENCE OF LIGHT LIES THE NUANCE OF IQLUSION.” (The misspelling was intentional, Mr. Sanborn has said, to make it more difficult to decode — or, as he put it, “to mix it up.”)

Tap to flip.

The second includes the location of C.I.A. headquarters by latitude and longitude, and asks: “DOES LANGLEY KNOW ABOUT THIS? THEY SHOULD: IT’S BURIED OUT THERE SOMEWHERE. X WHO KNOWS THE EXACT LOCATION? ONLY WW.” The “W.W." is a reference to William Webster, who headed the C.I.A. when the sculpture was unveiled. Mr. Sanborn provided him with a key for deciphering the messages.

Mr. Webster, who left the C.I.A. in 1991, declined a request for an interview.

The third passage paraphrases, again with a bit of misspelling, the account by the Egyptologist Howard Carter of opening King Tut’s tomb:

With spacing and punctuation added, the text reads: “SLOWLY, DESPARATLY SLOWLY, THE REMAINS OF PASSAGE DEBRIS THAT ENCUMBERED THE LOWER PART OF THE DOORWAY WAS REMOVED. WITH TREMBLING HANDS I MADE A TINY BREACH IN THE UPPER LEFT-HAND CORNER. AND THEN, WIDENING THE HOLE A LITTLE, I INSERTED THE CANDLE AND PEERED IN. THE HOT AIR ESCAPING FROM THE CHAMBER CAUSED THE FLAME TO FLICKER, BUT PRESENTLY DETAILS OF THE ROOM WITHIN EMERGED FROM THE MIST. X CAN YOU SEE ANYTHING? Q”

The Final Clue

The fourth section is shorter than the others, it’s just 97 characters, a fact that “could, in itself, present a decryption challenge,” Mr. Scheidt said in an exchange of emails. Common solution methods rely on the frequency of the most common letters, like E, T, A, O, I and N. In addition, he said, the last passage uses what is known as a masking technique, a further level of obfuscation.

The clues Mr. Sanborn has offered so far are in the form of a “crib,” which is a word or phrase that appears in the decrypted text. The 2010 clue was the word BERLIN, in the 64th through 69th positions of that final passage. In 2014 he revealed the word CLOCK in the next five, 70 through 74.

While the response was a frenzy of activity among enthusiasts, the result, in cryptographic terms, was bupkis.

So now, Mr. Sanborn, at 74, is giving the world another shot: the word NORTHEAST, at positions 26 through 34. Will it be enough?

Why Now?

Did we mention Mr. Sanborn is 74?

Holding on to one of the world’s most enticing secrets can be stressful. Some would-be codebreakers have appeared at his home.

Many felt they had solved the puzzle, and wanted to check with Mr. Sanborn. Sometimes forcefully. Sometimes, in person.

Elonka Dunin, a game developer and consultant who has created a rich page of background information on the sculpture and oversees the best known online community of thousands of Kryptos fans, said that some who contact her (sometimes also at home) are obsessive and appear to have tipped into mental illness. “I am always gentle to them and do my best to listen to them,” she said.

Mr. Sanborn has set up systems to allow people to check their proposed solutions without having to contact him directly. The most recent incarnation is an email-based process with a fee of $50 to submit a potential solution. He receives regular inquiries, so far none of them successful.

The ongoing process is exhausting, he said, adding “It’s not something I thought I would be doing 30 years on.”

Kryptos, which includes petrified wood, a swirling pool and slabs of granite, at C.I.A. headquarters. Courtesy of Jim Sanborn

But time is passing. And while he makes no claims to mathematical accomplishment, he can do basic arithmetic. “For the past few years I have been trying to figure out how to have this ‘system’ survive my death,” Mr. Sanborn said, “and it has not been easy.”

He has decided that if the code is not broken when he dies, the secret will be put up for auction. He might even do it in his lifetime. “I do realize that the value of Kryptos is unknown and that perhaps this concept will bear little fruit,” he said. The buyer could reveal the secret or perpetuate the mystery and maintain the system for submissions.

The money raised, he said, would go to funding climate science. Why that particular cause? “Seemed like a no brainer to me,” he said. “We live on an island!” The National Oceanic and Atmospheric Administration has found that the Chesapeake Bay, where he lives, has some of the worst relative sea level rise in the country, at 3.4 millimeters a year, or about twice the global rate.

If you would like to try to solve Kryptos yourself, start with Ms. Dunin’s encyclopedic site and read the work of Kim Zetter at Wired. Dr. Bauer goes into a detailed description of how the first three passages were decrypted in his book, “Unsolved!: The History and Mystery of the World’s Greatest Ciphers.” And this earlier article might help, too.

Ms. Dunin suggested that the fourth passage could turn out to be unsolvable; “Maybe he did something really weird,” she said.

But still, these several additional letters might be enough for the current community of Kryptos fans, or some gifted newcomer, to tease out the plain text of that final passage.

And it will not be the end of the mysteries of Kryptos: The full text contains a riddle.

Dr. Bauer put it this way: “There will be yet another mystery that the four passages together have a meaning that’s greater than their individual pieces and there’s something more to figure out.” The sculpture is more than its copper scroll; there are scraps of Morse code scattered through elements around the piece, as well as a pillar of petrified wood, a swirling pool, slabs of granite and more. The full mystery of Kryptos could involve the broader assemblage of pieces and their relationships to each other.

“This,” Dr. Bauer said, “is the sculpture that keeps on giving.”