Broken Sign Blog
#134: Escher Skyscrapers
9 April 2024Do you also find that Skyscrapers as a genre is just not cursed enough?
I was going to use this idea for a Logic Showcase submission, but it ended up not meeting certain criteria I set myself, so that plan was scrapped. I still think this is an interesting concept though (even if the Penpa tooling is a bit lacking for these kinds of shenanigans).
I’m afraid this puzzle is going to require a little diagram for explanation:
So we’re going to be interpreting this diamond grid as an isometric projection of cubes (much like my Diorama puzzle) and we’ll be placing skyscrapers on some of the faces. These skyscrapers cannot extend outside of the NxNxN box implied by the back walls of the puzzle and no two skyscrapers can occupy the same space.
The clues outside the grid see a “ribbon” of 2N faces obtained by going through the parallel edges of each face. They only care about skyscrapers standing on their ribbon and represent the usual skyscraper counts (how many skyscrapers can be seen from the clue, with skyscrapers obscuring same-size and smaller skyscrapers; note that there’s no actual 3D perspective going on here). Also note that clues cannot see skyscrapers “hovering” over one of their faces. In particular, the red ribbon does not include the vertical grey 2-skyscraper.
There’s also no Latin square aspect to this ruleset. Any size of skyscraper can appear any number of times as long as there’s enough room for them and the clues are satisfied.
Answer check only looks for the numbers. Make sure to place them in the centre of each face. You can draw the skyscrapers using the Line > Free mode, but their projections might overlap and it gets a bit ugly in the full puzzle.
Godspeed.
Rules: The grid represents an isometric projection of stacked cubes (as well as three back walls, one for each spatial axis). Place skyscrapers with positive integer height on some faces such that no skyscraper extends beyond the bounds of the NxNxN volume defined by the back walls, and such that no two skyscrapers occupy the same volume cell.
A clue outside the grid sees a “ribbon” of 2N faces obtained by traversing parallel edges and considers only the skyscrapers placed on those faces (not skyscrapers which occupy the volume cell above the face but are placed on another face). Their value represents how many faces in the corresponding ribbon contain a larger skyscraper than all faces before it in that ribbon from the direction of the clue.