No-Square Slitherlink is a variant of nikoli’s Slitherlink, original to this blog to the best of my knowledge.
A cell can be either empty or contain a number. The gameplay does not take place on the cells however; it takes place at the edges of the cells. Some of these edges must be blackened to form a loop such that each number clearly indicates the loop around it.
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.
The difference with normal Slitherlink? In this variation, the loop doesn’t contain any 2×2 square. Equivalently, the loop doesn’t contain any dot.
Form a loop that satisfies all the above conditions.
Walkthrough for the example
See the 0-3 combo. The only way the loop can extend without being stuck is if the open side of the 3 is the top one; that is, the left, right, and bottom sides are passed. This makes the right part extends up to avoid breaking the 3, and then further up because of the 1, then to the left because it’s the only way out. This also makes the left part goes left to avoid breaking the 1.
Now, note that R2C3, R2C4, and R1C4 are in the loop now, so R1C3 must not be in the loop. The upper part now goes down and left to separate out R1C3.
The game’s a bit rough now. Assume the upper part goes up instead of left. Then it’s forced to go left since it’s the only way out, and then further left because of the 2, then down since it’s the only way out again. This makes R1C1, R1C2, and R2C2 in the loop; R2C1 must be outside. So the upper part goes right and down…breaking the 1. So the upper part should have gone left instead of up.
To complete the 2, the upper part now goes up, and then left, down, and down because of the only way out, then another down to avoid breaking the 1.
Note that R2C1, R2C2, and R3C1 are in the loop now. So R3C2 must be outside. The part in the middle goes left and down to separate R3C2, and then further down to avoid the 2, and then left and up to complete the loop.