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 367 (Ice Walk (Hex, Bouba))

To close out the year, here's an Ice Walk on a hex grid.  This puzzle may not use loop closure that much, but the clue interactions are still surprising.  Here's to 2026 and beyond!

Rules:  Draw a loop through the centers of some cells which passes through each numbered cell. Two line segments may intersect each other only on icy cells, but they may not turn at their intersection or otherwise overlap. The loop may not turn on icy cells. A number indicates how many cells make up the continuous non-icy section of the loop that the number is on. 

Additionally, all turns must be "bouba" (i.e. all angles in the grid must be 120°.)

Puzzle 367 (Penpa)

 

Puzzle 366 (Tapa (Line))

Tapa (Line) puzzles tend to be quite difficult, because the Line restriction creates many unexpected and sometimes scary consequences.  This puzzle was specifically designed to flow nicely and be fairly easy overall.

Rules: Classic Tapa rules apply.  Additionally, no four consecutive cells in a row or column can be shaded.

Puzzle 366 (puzz.link) 

 

Puzzle 365 (Quad Tapa-Like Loop)

This is the second puzzle I made for WPC "prep".  Tapa-Like Loop is pretty cool.  Quad variants are usually pretty scary, but this one isn't too bad.

Rules: Classic Tapa-Like Loop rules apply within each quadrant.  Additionally, the contents of row / column pairs adjacent to gaps between the quadrants are exact reflections of each other, including loop segments and empty cells.  For example, the bottom row of the top-left grid is a mirror image of the top row in the bottom-left grid.

Puzzle 365 (Penpa)

 

Puzzle 364 (Kakuro (Star Battle))

This puzzle was made for WPC "prep" (the word "prep" is in quotes because I didn't attend myself).  It combines Kakuro and Star Battle in a very natural way, and I'd like to see more of the type.  That said, this puzzle is pretty tough, so beware.

Rules: Place the indicated number of stars per row and column so that no two stars touch, even diagonally. Then enter digits 1–9 into all remaining cells of the grid so that no digit repeats in any of the “words” across and down. Clues denote the sum of digits in each of the words. Cells with stars should not be counted into the sums.

Puzzle 364 (Penpa) 

 

Puzzles 362 and 363 (Slitherlink)

Here are two Nikoli-style Slitherlink puzzles on 10x18 grids.  These are always more difficult to construct than I expect.  It's pretty easy to make a puzzle with lots of easy steps, but it's much harder to create one which feels intentional.  I also tend to force linear solve paths in my puzzles, so when constructing a Nikoli-style grid, those intentions must be thrown out the window.

I think both puzzles before are successful attempts at the style, particularly the second one.

Puzzle 362 (puzz.link)

Puzzle 363 (puzz.link)

 

Puzzle 361 (Sus-Shikaku)

This puzzle is a Sus-Shikaku, a variant invented (?) by Prasanna Seshadri for last year's Puzzle Ramayan contest.  Apparently, this clue pattern was quite similar to one of the grids on the actual contest.  Regardless, this one is pretty tough.

Rules: Standard Shikaku rules, with a twist.  Divide the grid into regions so that each region contains one circle.  Regions containing black circles are still rectangular, but regions containing white circles are not rectangular.  Numbers still indicate the area of the region contained in the clue. 

Puzzle 361 (Penpa)

 

Puzzle 360 (Yajilin)

The next few posts on here will be reposts of various puzsq puzzles I've written this year.  I didn't want these posts to "dilute" the Spotlight (whatever that means), but now that the Spotlight is over, there's no reason not to cross-post them here.

First up, a Yajilin from way back in January.  At the time, I was messing with Cross+A generation, and wanted to see if it was possible to construct a symmetric Yajilin faster than Cross+A could.  The answer was "yes", although cspuz ended up being really helpful with the ending.  I'm super happy with how this one turned out.

Online interface (puzz.link)