1. Answer: 1 politician
The first inhabitant will deny being a politician whether he is or not.
Therefore, the second inhabitant is not a politician because the first inhabitant did in fact deny being a politician.
If the third inhabitant is not a politician and is truthful, then the first inhabitant is a politician.
If the third inhabitant is a politician and a liar, then the first inhabitant would not be a politician
2. 49 (There was no year zero)
3. Tomorrow
4. 60 guests
5. The red door
6. Bob, Andy, Chris, Debbie, Evan
7. James was born just before Daylight Saving Time ended. John was born just after, the clock having been set back an hour.
8. 2 minutes
9. 3 cats
10. 49 steps