Skyscrapers by Ashish Kumar
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Theme: Twos
Author/Opus: This is the 51st puzzle from our contributing puzzlemaster Ashish Kumar.
Rules: Standard Skyscrapers rules.
Difficulty: 2 stars
Time Standards (highlight to view): Grandmaster = 1:00, Master = 2:00, Expert = 4:00
Solution: PDF; a solution video is also available here.
Note: Follow this link for classic Skyscrapers puzzles and this link for variations on Skyscrapers puzzles. If you are new to this puzzle type, here are our easiest Skyscrapers Puzzles to get started on. More Skyscrapers puzzles can be found in The Art of Puzzles, in our beginner-friendly collection Intro to GMPuzzles by Serkan Yürekli, and in the e-book Skyscrapers by Ashish Kumar.
Skyscrapers authorship has always been super interesting to me because, I mean, there’s gotta be a limit on the number of unique, interesting 5×5’s, right? Not even counting those that are rotations or reflections of each other. Have I solved this exact 5×5 before? I’ve certainly seen quite a few “only use one digit” themes before.
None of that is to detract from the puzzle itself which was enjoyable.
One would expect 5×5 skyscrapers puzzles to not be particularly versatile, but that isn’t quite the case in my experience. For example, I have solved a considerable number of interesting 5×5 skyscrapers puzzles consisting of only 3 clues. Goes to show how great a genre it is!
There are “only” 2^20=1048576 ways you can arrange 2’s around the outside of a 5×5 Skyscrapers. Multiply that by 5 for all of the single-digit themed puzzles. Most of these arrangements are not valid puzzles, but the number seems small enough that you could have a computer enumerate all possible valid 5×5 Skyscrapers that use the “only one digit” theme. I might do that on a rainy weekend sometime…