Villagers and sick dogs
There are 50 villagers in a village and each villager has a dog,while some of them are sick dogs.Every day,they will meet together once and only once with their own dogs. All the villagers know the axiom:There is at least 1 sick dog among the dogs.
Since they love their own dogs,each person can easily tell whether the others' dogs are sick or not ,however,they would assume their own dog isn't sick first unless they confirmed their own dog is sick just by looking at the other dogs .If they confirmed their own dog is sick one day,they will kill their own dogs with their own gun on that day.They can't tell others whether the dogs are sick or not,and they can only kill their own dogs with their own gun.The villagers are clever and they can always figure out whether their own dogs are sick or not.
On the first day,there is no gunshot. On the second day,there is no gunshot. On the third day,gunshot is heard in the village.
How many sick dogs are there in the village?
The answer is 3.
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1 solution
Let's assume there is 1 sick dog (the wrong answer I chose casually in my first try):
Day 1: Villagers with healthy dogs can see 1 sick dog. Villager with sick dog can tell no other dog is sick, so he concludes that his own dog must be sick and kills his own dog on Day 1.
If there are 2 sick dogs:
Day 1: Villagers with healthy dogs can see 2 sick dogs. Villagers with sick dogs can tell 1 dog is sick (except their own dog, obviously), expect them to be killed by their owner and in conclusion, everyone waits for a gunshot but nothing happens.
Day 2: Villagers with healthy dogs can see 2 sick dogs. Villagers with sick dogs can tell 1 dog is sick (except their own dog, obviously), but is still not killed so they assume the other sick dog must be their own. Gunshot(s) is/are heard.
If you let this pattern slide a little bit, I don't not feel the need to tell you that the number of dogs must be 3 as gunshot(s) is/are heard on Day 3.