Puzzletober 2025: Murky

(Last updated ~2 hrs. post-posting: "should not exceed" -> "should not be less than")

The newcomer enters a small glade with a square-shaped lake. The lake is about 9 yards wide in each direction and its murky water hides the floor past the shore. Not too far in the distance are five people making conversation. He walks up to them. The first to notice him is a man in a dull but well-ironed coat. He slides an unprotected hand out from a long sleeve to provide a handshake and introduces himself as Victor. The newcomer says, "Are you the innkeeper?" Victor replies, "Yes. Were you looking for a room?" "My car broke down about half a mile down the road. I'm going to need a place to stay for the night." Victor thinks for a bit, looking from something to something else to the inquisitive looks from the patrons, before finally saying, "I suppose I can make an exception to the reservation rule. Welcome to the hotel. I'll get a room key for you when we return."

The others introduce themselves to the newcomer. All of them are regular visitors who have gotten to know each other well. Before the newcomer can properly introduce himself, a strong breeze picks up between the trees and tosses his hat into the center of the lake.

Rules: Find a path that should be safe to traverse from one of the slightly visible elevated sections by the perimeter to the center of the grid. The path will not be inefficient, i.e., there is not a shorter path to get to the center from an edge. A cell represents a square yard and is either entirely safe or entirely unsafe; the path must be made entirely of safe cells and cannot go diagonally. Of the grid cells on the perimeter, only the four implied at the centers of the edges are safe. You can trust what the innkeeper says in this puzzle.

Victor says, "In this situation, I suspect the patrons will either only tell the truth to help you or only tell lies to prank you. Please take what they say with a grain of salt. You ought to assume that there's a safe path."

The first patron to provide advice is a woman with a black-and-white scarf, a green pullover, and fading hints of aquamarine in her otherwise black hair. She says, "You should not enter from the south. Your first turn should be to the left. The number of steps you take from the shore to the first turn should not be less than the number of steps you take from the first turn to the second."

The next to speak is a man with a natural confidence. He appears not to have anything more than a plaid shirt around his chest but braves the cold and adequately covers his chin with a healthy beard. He says, "You should enter from the east. Your second turn should be to the left. The number of steps you take from the shore to the first turn should equal the number of steps you take from the first turn to the second."

A man with three thin layers on gives the previous patron a strange look and says, "You should not enter from the east. At one point, you will have to walk about four yards straight between two of the turns."

Finally, a woman wearing a professional suit over a casual sweatshirt adjusts her circular glasses and states with a tone of indifference, "You should enter from the north. You will have to make more than eight turns."