Araf (Skyscrapers) by John Bulten

Araf (Skyscrapers) by John Bulten


or solve online (using our beta test of Penpa-Edit tools with a composite mode for line/edge drawing and a composite mode for coloring.)

Theme: City Knights

Author/Opus: This is the 86th puzzle from our contributing puzzlemaster John Bulten.

Rules: Standard Araf rules. Also, numbers outside the grid show the number of separate region segments visible in that direction. A segment of length N in a given direction is taken as a building of height N. Buildings of height N block the view of all buildings behind them of equal or lesser height.

See also this example:

Araf (Skyscrapers) example by Serkan Yürekli

Difficulty: 4.5 stars

Time Standards (highlight to view): Grandmaster = 7:15, Master = 15:30, Expert = 31:00

Solution: PDF; a solution video is also available here.

Note: Follow this link for more Araf puzzles on this website. If you are new to this puzzle type, here are our easiest Araf Puzzles to get started on. More Araf puzzles can be found in the ebook Araf by Serkan Yürekli.

  • david glasser says:

    Hmm, the example doesn’t make this explicit — if a region appears on a row or column twice (like the second row) those segments can count as separate buildings, right?

  • mathgrant says:

    Row 2 of the example makes it explicit. Yes.

  • mathgrant says:

    The rules of this example seem to be, “Erase the given internal boundaries to make an undivided grid.”

  • david glasser says:

    mathgrant: I disagree since the two region pieces aren’t ever “compared” against each other (the one in the middle blocks), but seems clear the answer should be yes, yeah.

  • zmaj says:

    Difficult, but I enjoyed it!

  • D says:

    keep notice myself, two orthogonal 2 cells region may not be the same region. But still missing this, struggling for this mistake for 20 mins.

  • David says:

    19:45 after about twenty restarts. Oooof.

  • mathgrant says:

    david glasser: If the question you’re asking is “does a building block the vision of another building of the same size?”, a question that normally doesn’t come up in Skyscrapers puzzles because building sizes aren’t duplicated within rows and columns, then the answer is a resounding “yes”. See the leftmost column of the example, in which the clues at the top and bottom would both be 3 if a building of size 2 didn’t block the vision of another building of size 1. This has been the case in all Skyscrapers variants of other puzzles (including Nurikabe and Tapa) posted on this site.

  • David Glasser says:

    Nah my question was just whether seeing the same building twice counts, but fortunately the answer was pretty clear. Good puzzle.

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