Mrs. Hudson path deduction example #2
In puzzle 4A #43, here's the state of the puzzle:
There's a clue that says that "It is 4 steps from the Pig to the Puppy." The Hint that the program provides is that there can NOT be a path going EAST from the 2C intersection. Huh?
It's a matter of visualization. You have to be able to imagine that the hypothesized path is there (in this case), and then see what that does to all remaining possibilities. Here's what the program does:
In this first example, it places the hypothetical path that the hint tells us can't be there.
Now, in ALL cases the path south of the Pig can NOT continue due south to the Puppy, because that would connect them in 2 steps, so that segment is ALWAYS out, not possible. That leaves two directions for that Pig-southerly path to go, east or west. If it goes east (the red line), then we have:
In this case, there are three other possible segments that can be removed because the path is already entering and leaving the street or intersection, and the Pig has no way of reaching the Puppy in 4 steps. If the Pig-southerly path goes west (the red lines), then we have:
In order to reach the Puppy in 4 steps, the path would have to turn south, at which point it runs into the path from Mrs. Hudson, so it would be unable to turn into the Puppy. And also in that case, the Pig-east path also can't reach the Puppy in 4 steps, because if it turns south it will run into our hypothesized path. So, with our hypothesized path in place, we've eliminated all possible ways for the Pig-south path to reach the Puppy in 4 steps. That leaves only the Pig-east path as a possibility. But the only way for it to reach the Puppy in 4 steps would be to turn immediately south, and then it would run into our hypothesized path, preventing it from reaching the Puppy in 4 steps:
That's a lot of words to explain what the program goes through to figure out that the hypothesized path can't be there. The way I (or you) as the player would probably approach it is to look for the ways that the Pig CAN reach the Puppy in 4 steps. There are exactly two, as shown here:
Note that in both cases, the completion of the path forces the proto-path going east from intersection 2C to NOT be a path. Much quicker and easier to see, once you get used to looking for it. Of course, the path directly south from the Pig to the Puppy is also not possible in both cases.