Broken Sign Blog
#045: Rail Tool
12 October 2022I’ve been fascinated by this concept since seeing a Twopa puzzle for the first time and finally got around to applying it to Rail Pool. This took quite a while to construct. I had a first working version early on, but it was already unique after adding just a couple of clues on the right-hand side, which felt very unbalanced. So I had to go back to the drawing board and try again.
If you want to solve this on puzz.link, you’ll have to open the link in two separate tabs or windows and check the distinct-solutions constraint yourself. If you’re solving this with Penpa, when you think you’ve found the break-in, you can shade the corresponding clue cell to see which solution goes into which grid for the answer check.
And just in case you haven’t seen this idea before, I want to clarify that, yes, there is a unique pair of solutions that satisfies the constraint, and there is a clean solve path for finding those solutions.
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: Divergent — The puzzle is non-unique. Find two solutions such that no question mark represents the same number in both solutions. If a region has multiple question marks, they all have to differ. E.g. a 1–?–? clue could become 1–2–5 in one solution and 1–3–4 in the other (but not 1–2–3 and 1–3–4, respectively).