Solve five Slitherlinks, each with a unique solution.
Please say a word regarding (or show an image depicting) each solution method.
I looked at other people's answers for the first four grids, and got the solutions from those. However, here's what I think the fifth grid is (minor spoilers for the other four grids):
Place the four tetronimoes from the solutions to the first four grids together into a 2×2 square, without rotating them. There's only one way to do it:
|?|? 2 ?|
| +-+-+ |
| +-+ +-+
+-+ +-+ |
|3 ? ?|?|
It has a unique solution:
This is copied directly from my notes; I was using
+for an intersection the line definitely went through, and
.for an intersection or edge it definitely didn't go through. The main observation is that the only way to get a line through a pair of 3s is to zigzag it past; if you zigzag it the other way, the 2 forces it to get stuck in the top-left corner, so the only possible path for the line goes round like this.
I've found four slitherlink solutions, but I'm not certain how to construct the fifth...
I initially thought the items in the tetrominoes were potential values for that square in a 2x2 Slitherlink, but there's no way to make that work without rearranging the squares. (ex. 3/3 on the right side is a contradiction, and 3/1 would force a 1 at the bottom left, which only has options for 3 or 2.)