13. Rosa wants to start at the arrow, follow the line, and get out at the other arrow. Which piece, if placed in the middle, cannot produce this? Note the piece CAN be rotated. In order to exit, there needs to be a path from this upper curve in square 4 to the lower curve in square 4, and that's because if we just trace this down, that's where we get in from this arrow, then we trace this arrow back, this is where this lower curve comes from. So that's what we need to do. We need to have some path that goes from here to here inside of this square. OK, so both A and C have this small curve right here that allows for that to happen. In A, we basically go straight from here down here, and then that's it. We've completed our path. C, if we rotate this 180 degrees so that this is now on the left-hand side, then it basically does the same thing as A, where you go straight from here down to here, and that's it. We're done. Now, B and E have horizontal lines, so these horizontal lines follow from this upper curve all the way to this side, to square 6, and then you can turn on to square 6 and then come back into square 5 and then reach this curve, and that also brings us back to the map. So that's evident here in B, these two lines, and then here in E, either of these two sets of parallel lines works. So D, on the other hand, doesn't really have a path. You can take a look, all of D's paths kind of end up going elsewhere, and in fact, these two are just never connected in them, so as a result, D must be the correct answer.

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