Problem Two: Seagull’s crisis
Sep 27th, 2006 by tony
Here’s one of my favorites:
There was an island inhabited just by seagulls. Some of them caught a lethal but non-contagious disease. The only symptom of the disease is a dark spot on the neck. The neck shows no protuberance or increased sensibility so that it is not possible for a given seagull to know whether it has one. A few months after contracting the disease, all infected seagulls die in a terrible way. Therefore, to minimize its suffering, when a seagull is sure of being infected, it commits suicide exactly at 11 pm on the day that it learns of its illness. The seagulls are highly intelligent, but they are unable to communicate with each other. They know how to count and they know the total number of seagulls on the island.
Once a day, exactly at noon, all of them meet so that they can examine all the other seagulls’ necks, but they never see the spot on their own neck or find out from other seagulls whether they have one or not. A seagull with a spot on its neck always carries the disease. During the first 39 meetings, none of the seagulls commit suicide. After 39 days and as many meetings, all of the seagulls with a spot on their neck commit suicide at 11 pm. The seagull population is constant from the first meeting until the day the suicides occur. How many seagulls commit suicide and how do they find out about their spots?
Just to clarify, the number of seagulls, and the number of infected seagulls, remains constant throughout the 39 days.
In addition, the seagulls are aware that at least one of them is infected. Remember, these are really really smart birds here.
Update: Solutions have been posted.