Here is the answer to The Tiger Problem:
Assume there is a tiger behind door 1. But then both the sign on door 1 and the one on door 3 would be true, which is not the case. Therefore there is no tiger behind door 1. This also implies that there are tigers behind doors 2 and 3, so all the signs are fake.
Since there cannot be a tiger behind door 1, you should choose door 1 for a long and prosperous life.