This is the last question for the Thinking Corner, and it is an interesting one indeed. The first part requires careful thought, and the second part requires deep thought. I hope that if you have gone through the due diligence this question demands, it will be as rewarding for you as it has been for me. In particular, the second part of the question helped me understand not only the nature of information, but a lot about how society functions, and more importantly, a chance for self reflection. Here is the question:
There is a village with 100 residents. They all have extremely sharp minds, but also are very eccentric as they do not communicate with each other. Everyone has a dog, and everyone works at the sausage factory. An ongoing problem in the village is that some dogs sneak out and steal sausages when their owners are asleep. Through a bizarre arrangement, everyone has slightly different work and sleeping hours, so each resident knows exactly if everyone else’s dog is stealing, but not his own. The rule of the village is that if someone knows that his dog is stealing, he has to kick his dog out of the village the next morning; however, since nobody communicates with each other, this never happens.
One evening, the factory boss visits the village, gets everyone together and says, “There is sausage theft going on by at least one dog. That is all”. For a while, nothing happens. Sausages keep getting stolen. On a certain day after the announcement, 30 dogs get kicked out of the village.
This question has two components. The first is figuring out when and why the 30 dogs got kicked out, which is difficult enough in itself, but can be worked out with careful thought.
The second question is far more difficult. Remember that everyone already knows that dogs are stealing sausages. What the factory boss said, in fact, did not seem to impart any new information. Yet as we all know, if there is insufficient information to solve a problem, it will remain unsolvable until new information is given. Some additional information must have been given by the factory boss. What exactly is that new information?
The answer to the second question is subtle, requires deep thought and reflection, and surprisingly, reveals a lot about ourselves and human nature.