## 56. In Dreams or Awake?

- I, like the Black King, - confessed the Black Queen, - judge everything incorrectly in dreams, but correctly when awake. Last evening, shortly before eleven o'clock, the Black King thought I was asleep. At that very moment, I either thought he was asleep or thought he was awake.

What did I think?

Alice had to think hard about this problem, but finally, she managed to find the correct solution.

What did the Black Queen think?
56. In a dream or awake? At the given time, the King was either sleeping or awake. Suppose he was not sleeping. Awake, the King judges everything soundly. So, the Black Queen was sleeping. But in a dream, she judges everything incorrectly, so the Black Queen thought that the King was sleeping. Now suppose the King was sleeping. In a dream, he judges everything incorrectly, so the Black Queen was awake. Awake, the Black Queen judges everything soundly, so she thought that the King was sleeping.

Thus, regardless of whether the King was sleeping or awake, the Queen thought that the King was sleeping.