Puzzles 368 - 371: Caves from Mustang Math 2025

I've continued to supply puzzles for the Mustang Math Tournament!  While MMT is primarily a math contest for middle school students (mostly written by high school students), there is one round every year which introduces a pencil puzzle genre.  In previous tournaments, we've covered Fillomino, Double Choco, and Slitherlink.  We give students an overview of the rules, a sample puzzle, and some variants, and ask them to solve as many puzzles as possible.  Some years are harder than others (the Double Choco round in 2023 was particularly nasty...) but we try to make the puzzle set accessible overall, with a few hard puzzles sprinkled in because I can't resist.

Last year, we decided to go for Cave.  We explicitly gave "no checkerboard" as a rule rather than something students needed to figure out for themselves.  Overall, the Cave round seemed to be easier than the Double Choco round from 2023, but harder than the Slitherlink round from 2024, which is not surprising.

I wrote most of the puzzles for the round, with Pranshu (a high school junior at the time) supplying the remaining grids.  Each section had a particularly tricky puzzle at the end, much harder than the rest of the set.  Here are those capstone puzzles; if you want the full set, let me know!

Puzzle 57 (Cave (Product))

Another Cave product puzzle!  This time repurposed in Penpa, because the "base puzzle type" check is pretty useless when it comes to this variant.  Thanks to Prasanna for test-solving!

Variation of standard Cave rules.  Each clue represents the product of the number of row cells visible (including the cell itself) with the number of column cells visible (including the cell itself). 

Online interface

Puzzle 56 (Cave (Product))

Originally wrote this for GMPuzzles, but decided I didn't like it enough.  This was the first time I really had to struggle to get the givens to work out given so many constraints on the geometry of the grid and the logical theme -- it felt like everything I tried broke in some way.  Thus, while I think there are some interesting ideas in here, I had to sacrifice basically all of the more interesting logic to make it work uniquely (and without stupidly easy bypasses).

Variation of standard Cave rules.  Each clue represents the product of the number of row cells visible (including the cell itself) with the number of column cells visible (including the cell itself). 

Online interface 

Puzzle 29 (Anglers Cave)

Was sufficiently interested in this variant from Grand Prix round 1 to give it a shot :)

Standard Cave rules apply. In addition, each number outside the grid represents an angler, each of whom has caught a different fish on their line. Their line is represented by a path that moves orthogonally from the angler to their fish, and the number represents the length of that line (or, the number of cells that line encounters, including the fish’s cell but not the angler). Angler’s lines may not overlap or cross each other. 

Angler’s lines must stay completely within the cave (including the fishes). It is possible for some cells in the cave to not contain an angler’s line.

Penpa interface

Puzzle 20 ("Two's a Crowd", Cave)

Here's a Cave puzzle that was (un)surprisingly difficult to set.  I think the end result is a bit easier than I would like, but I'm still happy with it.

puzz.link interface

Puzzle 19 ("Empty Space", Cave)

Haven't written a Cave in a while, so here you go.

puzz.link interface

Puzzle 15 ("Prime Diagonal", Cave)

Reuploading because puzz.link integration didn't quite seem to work last time.

Here's another Cave puzzle.  I'm really proud of this one :)

puzz.link interface