# Sheep and Wolves

Sheep and Wolves Example

Sheep and Wolves is a puzzle type invented by Dave Tuller, though the inspiration comes to me independent from that. It is a modified version of Slitherlink.

Cell types

Besides the original Slitherlink that a cell can be either empty or contain a number, a cell can also contain a black or a white diamond. A black diamond must be inside the loop; a white diamond is outside.

Interaction

First, the loop never crosses itself, and no, the loop doesn’t branch. Not even touching itself at a point. A number tells how many loop segments (or blackened edges) are around that cell.

As the name suggests, the loop must contain all black diamonds (“sheep”) and must not contain any white diamond (“wolves”).

Objective

Form a loop that satisfies all the above conditions.

Walkthrough for the example

Begin with R1C4. It’s obviously outside the loop (if it’s inside, there must be at least two segments adjacent to it), so R2C4 is also outside the loop. So the first lines are drawn by separating the sheep from the wolf and the zero; the top, left, and right segments of R3C4 must be passed. This makes the right part goes down, left, then left again. To the upper part, it can only go left, which in turn makes the lower part must go another left.

If the lower part goes around the 1 now, it needs two segments (bottom and left). So the lower part must goes up and then another up due to the 1, which makes the right part goes up twice.

The left part needs to go around the 3 to the left, otherwise it’s stuck between the 3 and the 1. Now, just complete by putting an edge above the 2.