On the first day, everyone checked. If someone checks that the other 29 people are not sick, then they can be sure that they are sick and will shoot. But on the first day, no one made a move, which means that everyone has at least one sick dog, which means that there are at least two sick dogs (if there is only one sick dog, the owner of the sick dog will check 29 healthy dogs and then go back to kill his own dog. ) So I knew on the first day that at least two dogs in the village were sick.

The next day, if someone checks out 28 healthy dogs and 1 sick dogs at this time, then because there are at least two sick dogs, he will know that his dog is sick and will shoot his dog, but no one will do so, which means that at least three dogs will be sick.

On the third day, someone made a move, that is, when he knew that at least three dogs were sick, because a hunter only checked two sick dogs, he could determine that his dogs were sick. So there are three sick dogs.