100 Guards
A line of one hundred logical guards is standing before two doors. One door leads to freedom, while the other leads to a room full of angry geese.
Each guard either always lies or always tells the truth.
You're told that there are an even number of lying guards, but none of the guards know who is who.
You can ask a guard one true-or-false question. How do you find the door to freedom (and avoid the geese)?
The Greenberg variation
Through a clever solution of a slightly different problem, Adam discovered this beautiful second puzzle
Two guards stand before two doors. Again, only one door leads to freedom.
It is unknown if any of the two guards tells the truth. (But as before, guards that lie, always lie.)
You can ask each guard one true-or-false question. How do you find the door to freedom?