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guess,” responded Henryk. “The inscrutable six tell recipients the correct setting for that specific message.
    “You mean,” asked Jerzy, “they not only send the three-letter settings for the wheels, but then repeat them?”
    “Exactly,” replied Henryk. “They send them twice so the recipients can be sure they've gotten them right. Otherwise, if they made a mistake, the message would be gibberish."
    Jerzy puffed at the stub of his cigar, with a skeptical frown. "But the three letters aren't repeated. He glanced down at the messages. “DSI FDR, in Anna's message, for example. And there seem to be no repeats in the other messages, either.” He leafed through the papers in front of him.
    Anna spoke. "The Germans have a cipher machine. Why should they send the wheel settings in the clear? If they did, then anyone who captured one of their machines, or anyone who already has one," she smiled as she glanced across at the machine, "could read the message. Just as Henryk read my 'Merry Widow' the other day. Instead, why not use the machine to encrypt them?"
    "In other words," said Henryk, “there are two settings. The first we might call the basic setting, indicated by the discriminant—Blue in this case. Anyone with access to the Blue codebook can look up the basic wheel setting currently in use. Using this setting, the signalman receiving the message reads the inscrutable six. That gives him the three letters to reset the wheels, to read the body of the message—what we might call the message setting.”
    “Now we can see why they call it an Enigma machine,” observed Jerzy. “A puzzle within a puzzle."
    "And so," said Henryk with finality, tapping his pencil on the table, " we can't really break the enigma machine. That's impossible. All we can do is read specific messages, or, at the best, figure out the basic wheel setting—for Blue messages, for example. It will be good only for a fraction of the Enigma traffic, and only until they change the setting."
    All eyes turned to Marian. He had been sitting silently stroking his beard, deep in thought.

5
Anna's Idiots:
The Opposite of Genius
    Gentlemen do not read each other's mail.

Secretary of State Henry Stimson, expressing shock when shown deciphered Japanese communications in 1929.
(Stimson had the “unethical” decoding shut down, but it was soon revived.)
     
    "T hings aren't quite so bad.” Marian broke his silence, lightening the gloom. "I think we're just about there. If Henryk's right—if the inscrutable six represent a repeat of the message setting—we've got the key to unlock the basic setting, the one which all Blue operators start with. We can find it by working backward, through trial and error. Let's use brute force to find the wheel setting that translates the inscrutable six—DSI FDR in Anna's message—into the setting for her message, QRT QRT. When we do, we should have the basic Blue setting. Then we should be able to decode all the Blue traffic. I'll have the staff work on this. Any questions?"
    As they broke up, Henryk glanced toward Anna and raised his index finger, a sign that he wanted to talk to her. When they got to his office, her eyes were again drawn out the wide window. The earlier cold, crisp snow had been softened by warming air; the moist snowflakes were now ideal for packing. Young boys were engaged in a glorious snowball fight. Off to the north, a young couple, surrounded by their entranced children, were leaning against a snowman, struggling to raise the head to its rightful place. For a fleeting moment, Anna wondered if she would pay too high a price for her challenging new job.
    "Now that you've proven yourself—even faster than I expected—I want to talk about your role. We're dividing our operation into two groups. One will look at ways to deal with brute force problems: how to go through the multitude of possibilities quickly. Marian Rejewski will be working with me in this group. He has some very promising