Rail Pool by Martin Ender

This puzzle style was created by Martin Ender (first example here), and was one of the “new generation” of puzzles at the 2022 World Puzzle Championship. While it won’t be in our upcoming Loop Variety Collection 2, we are planning to have some more Rail Pool in GMPuzzles projects in the future.

Rail Pool by Martin Ender


or solve online (using our beta test of Penpa-Edit tools in default linex mode where left-click+drag draws line and right click marks X’s)

Theme: Tetris

Author/Opus: This is the 1st puzzle from guest contributor Martin Ender.

Rules: Draw a single, non-intersecting loop that passes through the centers of all cells, including clue cells. Clues represent all of the different lengths of the straight line segments that pass through all cells within the region, either partially or fully contained by that region. Each number within a region must be represented by at least one line segment. Each “?” represents a positive integer; if a clue cell has more than one “?”, all numbers and “?”s in that clue must be different from each other.

Also see this example:

Rail Pool Example by Serkan Yürekli

Difficulty: 2.5 stars

Time Standards (highlight to view): Grandmaster = 1:30, Master = 2:45, Expert = 5:30

Solution: PDF and solving video.

Note: Follow this link for other Loop/Path puzzles.

  • Almost says:

    The description of the rules was confusing to me. I had to read it a few times to realize that the clue contains all of the distinct lengths of line segments passing through the region. The same length can occur multiple times in a region, but only the clued lengths are possible in that region.

    • Avatar photo drsudoku says:

      Thanks for this feedback. This is certainly a harder style to grasp all the rules for, and we’ll continue to think about how to show this better in pictures than words; once you understand how the rules work together there is a very interesting puzzle space for this style.

  • Almost says:

    Yea, after I figured out the rules I quite enjoyed the puzzle and would be happy to see more.

    • Avatar photo drsudoku says:

      I think a lot about rule sets (most puzzle genres are actually combinations of rule sets) and I didn’t have a lot of time in this week to try to perfect all of the styles, but I wonder if you or other solvers would accept/make this kind of connection: Rail Pool has an “all cell loop” type rule which you see many times, and then a “numbers affecting loop” property. It is a bit more involved than Geradeweg, but in some ways if you view all the Geradeweg circles as one-cell regions, they are all Rail Pool clues. Admittedly when numbers stack together to have 2 in a one cell region or 2 or more in a two+ cell region you then have further emergent properties but the start of “numbers equal confined loop lengths whether passed through straight or turning” is an element of Geradeweg that is a simplified beginning of the less familiar concept of Rail Pool.

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