Broken Sign Blog
#021: Rail Pool (Triangular, Partial)
16 June 2022I haven’t seen a lot of loop puzzles on triangular grids. I suspect part of the reason is that triangular grids have the opposite problem of hex grids: the reduced amount of choices constrains the loop way too strongly. Also, for Rail Pool in particular, the naive way of having loops on triangular grids would give all line segments a length of 1. I think I’ve come up with a nice solution to this problem that I will be exploring with other loop genres in the future.
First, we drop the Full constraint, i.e. the loop does not have to visit every triangle in the grid (this would actually be impossible to satisfy for simple grid shapes). Second, instead of having the loop move between triangle centres, we have it move between the midpoints of edges. That way we can have straight lines of any length. And third, we allow multiple line segments in a triangle (in practice, up to 2), so the line can either move straight through, or “bounce off” the opposite edge. This gives the loop some much needed additional degrees of freedom.
These rules were somewhat based on how I handled movement in my triangular esolang Wumpus.
Rules: Draw a non-intersecting loop through the centres of all cells. Some boldly outlined regions contain number clues. If a straight loop segment visits any cells of a clued region, its length must match one of these numbers. Each number must correspond to at least one such loop segment. Question marks represent any positive integer, but numbers cannot repeat within a region.
Variant: Triangular — The grid is triangular. The loop moves straight between midpoints of triangle edges (instead of the centres of the triangles) and there can be multiple line segments within a triangle. Rail Pool clues measure the number of edge-to-edge steps in a straight line segment.
Partial — The loop does not have to visit every cell.