Adjacent 3s

How it works

1. Two 3s sharing an edge. A 3 has exactly one blank side, so each of these cells is one X away from being fully drawn.
2. Suppose the left 3's OUTER edge were that blank side. Then it takes its top, its bottom, and the edge it shares with its neighbour.
3. Now the dot at the top of the shared edge already has two lines meeting at it — the left 3's top, and the shared edge itself. A dot never carries more than two, so everything else there is blank, including the right 3's top. The dot at the bottom kills the right 3's bottom the same way.
4. That strands the right 3 with only two sides available: the shared edge and its own outer edge. It can't reach 3.
5. So the left 3's outer edge is a line — and by the mirror image, so is the right 3's. Both are forced without ever deciding the shared edge.
6. The shared edge is a line too, but that needs a different argument: leaving it blank gives each 3 its other three sides, which closes a tiny rectangle. Only Loop Avoidance (or a Quad Window against the board's border) can rule that out.