h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

The local spy club have a special code which allows members into the specially hidden venue. When the spy turns up he utters a random number into the speaker, say 11, the speaker replies 6, to which the spy answers 3. This special sequence allows the spy in. A foreign spy discovered the location of the club but he didn't have access to the special code. During the evening he took note of the codes used by the spies who gained access with the following results:

1, 3, 5;
27, 11, 6;
9, 4, 4.

The spy thought he had cracked the code and bravely uttered 16 into the speaker. The speaker replied 7. What was the spy's final answer?

5 (Each answer is the number of letters in the previous number)

5.
After which the spy got shot, as his first number wasn't odd.

You cannot know because the spy might have thought he cracked the code but did not! So he will give an incorrect answer.
The question 'The spy thought he had cracked the code' implies that he had not cracked the code and that he answered incorrectly meaning that the answer he gave was probably anything but 5.

If such sequences are continued indefinitely, will they always end in 4, 4, 4...?

It looks like they all will, as no other number has the same number of letters as its value, and I can't see any two (or more) numbers which could alternate in sequence.

Of course, it's all irrelavant really, 'cos these days the spy would just whip out his Q-branch mobile 'phone with built-in code-breaking function and not have to bother working anything out at all

Interesting!

Mycroft, you can also note that only one, two and three have more letters than the number they spell out, so if you're below four, you go up, and if you're above you go down. Plus, one, two and three all start a sequence that reaches four.

~Greebo claps Danny B on the back... ~

Nice one... ~grin~... a point goes to you...