Psychology experiment interrupted by the alarm
So I thought (well, I don't know if this entire thought formed while I was having my dream but it came to me all at once when I woke up) that this would be interesting: if the puzzle turned out to be a real English phrase (it comprised four words) then that had to mean my brain knew the answer - but then whoever was guessing didn't know the answer! So there's some kind of divide between what you're dreaming of and what the character you're playing is thinking. To put it another way, there's a sort of conscious unconscious - the one playing the puzzle, who didn't know the answer - and the unconscious unconscious, which set the puzzle.
Unfortunately, I had just guessed the second letter (e, which turned up in _ _ _ E E _, the third word of the four) and I was going through words it could be (career, exceed...) when the alarm rang and the dream instantly dissipated. Dash and bother. Oh well, it wouldn't have been a real experiment anyway - no way to repeat it. I suppose this is what's called the introspective method.