The artist who created the enigmatic Kryptos, a puzzle-in-a-sculpture that has driven code breakers to distraction since it was installed 24 years ago in a courtyard at C.I.A. headquarters in Langley, Va., has decided that it is time for a new clue.

By 1999, nine years after it went up, Kryptos fans had deciphered three of the sculpture’s four messages — 865 letters punched through elegantly curved copper sheets that make up the most striking part of the work. (In fact, cryptographers at the National Security Agency cracked those messages in 1993, but kept the triumph to themselves.) The fourth and final passage, a mere 97 characters long, has thwarted thousands of followers ever since.

Jim Sanborn, the sculptor, having grown impatient with the progress of the fans and their incessant prodding for clues — and the misguided insistence by some that they had actually solved the puzzle — provided a six-letter clue to the puzzle in 2010. The 64th through 69th characters of the final panel, when deciphered, spelled out the word BERLIN.

Since then, the fans, many of whom keep up a lively online conversation, have come up empty-handed. And so Mr. Sanborn has decided to open the door a bit more with five additional letters, those in the 70th through 74th position.