have some logic puzzles
Two ciphered Skyscrapers puzzles. Each letter corresponds to a distinct number.
author: aroaryan; difficulty: 1
author: Julian Schiavo; difficulty: 4
Last Fall I had discrete math honors students work with one of my puzzles; this year I had them write their own instead (and prove their solution was unique using Z3). Two students chose to have their puzzles posted here.
A ciphered Skyscrapers. Each letter corresponds to a distinct number.
I made a homework assignment out of this earlier puzzle – students had to use Z3 to a) solve the puzzle, and b) figure out some clues that could be safely removed (i.e. without allowing for multiple solutions). The puzzle here is my favorite of the smaller puzzles I found while setting this up; since the earlier one was “EASY”, this one of course must be “HARD” (but only because “medium” has more than 4 letters).
Here are some Remembered Length puzzles intended for beginners, which should perhaps be labeled with “content warning: hints”: pdf
I wrote these for Splash, an event where high-school students can attend short workshops on a variety of subjects. I ran a 50-minute “Puzzles!” class, where we alternated between students working through these puzzles in small groups, and then going over some all together to discuss the techniques used to solve them. My goal was to make it as easy as possible for solvers to discover on their own the basic toolbox used by this genre. To do that I tried something I haven’t seen elsewhere: pairs of minimalist grids where one is solvable and the other isn’t, and the only difference between them highlights the technique I want them to learn. This is where the ‘hints’ warning comes from: there aren’t any explicit/textual hints, but if you insist on discovering the genre’s secrets only from solving normal puzzles then this puzzle set is not for you.
Two Black Hole Tapas. Follow regular Tapa rules. Additionally, some shaded cells are supermassive black holes, each of which counts as M consecutive shaded cells. Each row and column contains exactly N black holes. (M and N are given for each puzzle.) [Rules source with example]
This is the 6th anniversary of the first Black Hole Tapa puzzle! Here are some 6-themed puzzles to celebrate – one very silly, the other less so. In addition, I’m also writing the brief history of the variant, and adding links to almost every Black Hole Tapa I know of (including the original, which has not previously been posted online).
History:
For a 29 May 2013 event, a friend and I created a set of puzzles themed around stars. (For any Caltech readers: this was Blacker’s “Day After Tomorrow”.) There were 4 puzzles and a metapuzzle, where each puzzle was themed on one part of a star’s life cycle and yielded a 12-letter answer. These varied widely – I forget two of them, but the Red Giant “puzzle” was literally just realizing you had to inflate the red balloon so you could read the tiny answer written on it. For the Black Hole puzzle, I came up with something a little less silly: this.
January 2016 saw the (sadly temporary) resurrection of LMI’s Tapa Variations Contest. TVC XVII’s instruction booklet included a call for new variants, so I sent in Black Hole, creating the current generalized rules in the process both to give authors more freedom and to claim a bit more territory as my invention (probably unrelated: my cousin is a patent attorney). Black Hole was included in TVC XVIII, and was well enough received (or at least the authors liked constructing them?) to make another appearance in TVC XIX. As tends to happen before these contests, a couple other puzzle writers made one for practice – I love how the newly generalized rules were quickly being used in ways I hadn’t thought of (M=0!).
Archive:
Here are (almost) all Black Hole instances I know of; if you know of any others anywhere let me know and I’ll add them to the list below.
Puzzles discussed and linked above:
| Link | Author | N (black holes per row/col) | M (black hole weight) |
| Original | me | 1 | 3 |
| Para’s TVC XVIII Practise | Bram de Laat | 3 | 2 |
| TVC XVIII | Fatih Kamer Anda | 1 | 3 |
| anderson’s #23 (TVC XIX practice) | qzqxq | 2 | 0 |
| Fatih Kamer Anda | 1 | 3 | |
| Serkan Yürekli | 2 | 4 |
More recent puzzles:
| Link | Author | N (black holes per row/col) | M (black hole weight) |
| primepuzzles #16 | me | 2 | 3 |
| primepuzzles #17 | me | 1 | ∞ |
| 9-Tapas Mashup | Tiger Eye | 1 | >1; determined by solver |
| gmpuzzles | Zoltán Horváth | 1 | 0 |
| Tapa… IN SPAAAAACE | dpad | 1 (see puzzle for special rules) | 2 |
A Slitherlink/Corral hybrid. Each clue is either (or both) a Slitherlink clue (i.e. it “indicates how many of the four potential segments surrounding that square are contained in the loop”), and a Corral clue (i.e. it is inside the loop, and “if we treat the loop as a wall, the number tells how many grid squares in the loop can be seen from the number’s square when looking vertically or horizontally, where the number’s own square is counted”).
Here’s the puzzle as an interactive applet, because that’s what the cool kids are doing these days: https://puzz.link/p?slither/v:/6/6/31362dh23ag2dg22dh28121c …though since this is a variant, the “Check” button which only checks for Slitherlink logic won’t be useful.
This puzzle was my entry to Logic Showcase 3 (see Puzzle 42 for my entry to LS 2). The theme/constraint was “Make a puzzle where the goal is to construct a single non-intersecting closed loop through the centers or corners of the cells. The puzzle should use the clues and rules from exactly two established loop genres.” There were 10 official entries and I got last place. (There were also 5 unofficial, unranked entries.) Some things I could do better next time:
A Skyscrapers, with two twists. First, all possible prime clues outside the grid have been given. Second, if you shade all primes inside the grid, they form a Tapa-like wall, i.e. all shaded cells are orthogonally connected and no 2×2 group of cells is entirely shaded.
There’s a group which holds a recurring puzzle construction contest, and (uninfluenced by me) they chose as their latest theme the following constraint: “Any puzzle where the clues are numbers and only numbers. Each of the digits 2, 3, 5, 7 must appear at least once, and all other digits may not appear.” Naturally I had to participate. In the vote this puzzle got 11th place out of 18 submissions. My impression from the comments is that they generally liked the solve, but dinged it on aesthetics since 1) it has two variant rules (they seem to like one but not more), and 2) it is considered inelegant for a Skyscrapers to have any clues at all inside the grid (and compounding this issue is that the only 5 in the puzzle, required for it to be a valid contest entry, is inside the grid). I happen to be a major fan of variants, but I can also see the appeal of squeezing as many novel challenges as possible out of a simple and elegant set of rules, which layering variants definitely is not.
More info about this puzzle; solve it first then rot13: N ybg bs guvf chmmyr jnf npghnyyl pbafgehpgrq ol fbzr Clguba pbqr V jebgr, onpxrq ol gur M3 FZG fbyire. Vg gheaf bhg gur frpbaq inevnag ehyr znxrf vg rkgerzryl rnfl gb nppvqragnyyl birepbafgenva gur chmmyr, fb nsgre frireny snvyrq nggrzcgf V unq guvf pbqr perngr n inyvq svyyrq-va tevq sbe zr, naq gura pubfr gur erznvavat ehyrf naq pyhrf gb rafher n fbyir V jnf unccl jvgu. (V ebg13’q guvf orpnhfr pbzchgre-trarengrq chmmyrf ner trarenyyl ybbxrq qbja hcba, fb V jnagrq lbh gb sbez na havasyhraprq bcvavba bs gur chmmyr svefg.)
A Masyu, with a twist. Half the circles are lying – black means white and white means black. Additionally, the loop alternates between true circles and lying ones.
A ciphered Skyscrapers. Each letter corresponds to a distinct number.
Easy as 1-2-3, hopefully. It’s smaller than usual because I wrote it entirely in my head while hiking.
A ciphered Nurikabe. Each letter corresponds to a distinct number.
Wasn’t planning on using my real name here but today’s “Cipher 11ths” puzzle kinda signed itself.
A Snake. Draw a one cell wide snake in the grid. The snake is not allowed to touch itself, not even diagonally. The head and tail of the snake have been given. Numbers on the outside indicate how many cells are occupied by the snake in that row or column. [Rules source]
Additionally, the snake cannot pass through cells with an X, and the snake is 29 cells long (including head and tail).
primepuzzles 