Some logic puzzles about the Isle of Dreams, based on those found in "The Lady or the Tiger?" by Raymond Smullyan.

I once dreamed there was a certain island called the Isle of Dreams. The inhabitants of this island dream quite vividly; indeed, their thoughts while asleep are as vivid as while awake. Moreover, their dreamlife has the same continuity from night to night as their waking life has from day to day. As a result, some of the inhabitants sometimes have difficulty in knowing whether they are awake or asleep at a given time.

Based on their thoughts, attempt to determine if the islanders are diurnal or nocturnal, awake, or asleep. In some cases you may not be able to determine everything about the islanders. In some cases, the particular combination of thoughts might not be possible.

There are 4 laws that can be deduced concerning the inhabitants of the island.

1. An islander while awake will believe they are diurnal.
2. An islander while asleep will believe they are nocturnal.
3. Diurnal inhabitants at all times believe they are awake.
4. Nocturnal inhabitants at all times believe they are asleep.
Try to convince yourself of each rule, and apply them to the thoughts of the islanders in the puzzle.