Mrs. Hudson path deduction example #1
The number of possible deductions involving paths are almost uncountable. I won't try to cover all of the basic ones, but I'll try to spotlight a few that might help you get started.
In the above example, notice the currently highlighted clue that indicates that the Wine is to the left across the street from the Steak and what the path looks like in the street between them. You can immediately remove ALL of the Wines and Steaks from the top row of the puzzle, because the path must go NORTH out of the street between those two images. The two matched-pairs of blocks circled in green can also not be the Wine on the left nor the Steak on the right because the path cannot go NORTH in the street between them. Since we're focusing on the path deductions, I won't go into any of the image-only deductions.
Similarly, notice the currently highlighted clue that indicates that the Pig is NORTH across the street from Mrs. Hudson and there is NO path in the street between them. The two matched-pairs of blocks circled in green can not be the Pig on the top nor Mrs. Hudson on the bottom because the path DOES go through the street between them.
Here's another really basic path deduction that you have to watch out for. We have the clue "From the Wine, it is 6 steps along the path to the Steak." At first, you might think that this is only telling us how far apart those two images are. But there's actually another VERY important piece of information implicit in that clue: the path DOES go THROUGH both the Wine and the Steak, as otherwise, how could they be any number of steps apart along the path? When we look at the puzzle, we see that the location of the Wine is known, and it has no known path segments going in/out of it and only two proto-path segments. That means that, in order for the path to go through the Wine, both of those (green-circled in this example) proto-paths HAVE to be actual paths and can be marked as such.
In fact, you can often tell a great deal about which images are and are not ON THE PATH just by examining the clues. Looking at this set of clues, I've put together a diagram showing which images HAVE TO BE on the path (circled in green) as well as one (the Mouse) that I know can NOT be on the path. ANY image appearing in a STEPS-APART or STOP-NUMBER clue HAS TO BE on the path. Any clue that appears in a BLOCK-PATHS clue (all but the first two vertical clues in this example) HAS TO BE on the path if green paths are shown going in/out of them and CAN'T be on the path if there are NO green paths going in/out (only red 'paths'). With the ACROSS-THE-STREET-WITH-PATH-BETWEEN clues, if the clue shows a green path turning in towards one of the images, then that image HAS TO BE on the path. If there's a green path running between the two images, then BOTH images HAVE TO BE on the path. Of course, Mrs. Hudson is ALWAYS on the path. Don't forget these pieces of information. They're not always "in your face obvious," but they can often help you make quick deductions in otherwise sticky situations. But be careful: don't fall into the trap of thinking that just because there's no clue indicating that the path goes through a particular image, that the path DOESN'T go through that image. That's NOT a valid assumption, and it's guaranteed that it will sometimes be a faulty assumption.
Going back to the clue "From the Wine, it's 6 steps to the Steak," we can make a few more easy path deductions. First, the proto-path circled in RED can NOT be a path because that would connect the Wine to the Steak in only 4 steps. Second, removing that RED-circled proto-path leaves only one remaining direction for the path out of the Wine to go: straight NORTH into the block above it (circled in GREEN). Third, the proto-paths circled in BLUE have to be paths, as that is now the only remaining way for the path from the Wine to reach the Steak in 6 steps.
And the deductions just keep on a rolling! The RED-circled Mouse can't be there, because the paths in/out of that block don't match the clue. Also, in the upper-left corner, we see a section of proto-paths and a block that are connected to the rest of the known paths by just a single proto-path. That doesn't allow for the path to get in AND out of that area, so NONE of the proto-paths in that area can be a PATH. Next, remember what I said about Mrs. Hudson ALWAYS being on the path (because the path starts at and returns to her home). Her location is known, there are only two proto-paths connected to her, so they both have to be PATHS. Finally, the block in the bottom-right corner can NOT be on the path. If it were, both proto-paths connected to it would have to be paths, and that would form a small isolated loop in that corner. So both of the proto-paths connected to that block can be removed.
Here we use the "From the Tea, it's 8 steps to the Mouse" clue to remove a couple of more possibilities. The Tea in the upper-left can't be there because the path doesn't go through that block. The Mouse in the lower-left corner can't be there because none of the possible Tea locations can reach that block in 8 steps, following any of the known and possible path segments.
Since the Egg is stop #1, theh path from Mrs. Hudson must pass through the Egg before it passes through ANY other blocks. Therefore, the RED-circled proto-path MUST be a path, because if the path went NORTH instead, it would have to go through the Puppy, Cake or Tea first.
Finally, the path from the Mouse can NOT go through either the Drumstick or Blondie. The Mouse is stop #4 and the Cat is stop #5, so there can't be any additional stops in between them.