Invitation: Road-test SSZ (Skyscraper Zero) Puzzles

I really like Skyscraper (SS) puzzles, so I wrote some software to generate them. In doing so, the idea for SSZ puzzles occurred to me.

In these puzzles you are placing values 0 to N-1 instead of 1 to N. A value of zero means no building at all, and this has a subtle effect on the visibility clues when they occur on the outer edges of the square.

For example, say N=6. In a normal SS puzzle, if a row in the solution has values 136245, then the visibility clue on the left is 3. In the corresponding SSZ puzzle, the row values are 025134, but the visibility clue on the left would be 2.

For this reason, SSZ puzzles tend to be trickier than their SS equivalents.

I've attached two files, the first being a sampler of gentle warmup puzzles to get you used to the idea. The second is a fairly challenging 8x8 puzzle in which the diagonals are also distinct (puzzle type SSZX). Despite the abundance of clues, including diagonal visibility clues and some given cell values, this should keep you busy for a couple of hours!

Feedback is invited!


Jim White (Mathimagics)

Ah, awesome! I've seen these very occasionally as a variant "Skyscrapers with gaps", where instead of a 0 you just leave a blank square - but they work exactly as you describe. I could include these in the Community Puzzles section of the magazine in issue 13 or 14 if you are happy for us to do so? Not all readers check the forums here, so it would get them to a larger audience. I think I'd draw them with the 0 as a gap, since it makes the idea even more obvious at a glance, if that was okay.

I'm also a fan of Skyscraper puzzles even though I find them quite difficult so it was great to see these as a variation on a theme! Having said that I found that the first 0 - 4 and the first 0 - 5 puzzles were reasonably quick to solve, but that the second of each took quite a bit longer. I'm sure it's one of those puzzles that would get a little easier with practice. As for the SSZX, that was a bit beyond me - I would have to be in the mood for a real challenge to have a serious attempt at it, but I would love to see some more of the simpler ones in print some time.

Gareth,

I'm happy to see them put in the magazine - as for 0 vs "gap", well I'll leave that up to you.

Will you print the challenger? If so, I'll email you the solution - unless you've cracked it already?

I haven't tried the challenger yet I must admit! I'll email you now.