#153: Fire Walk

Ever since coming up with Water Walk I’ve been thinking about other potential mechanics for the “ice” patches in this class of rulesets. The most natural inversion of “can’t turn, may cross” seemed to be “must turn, may revisit a cell doing so”. I ended up deciding on a fire theme, both because of the obvious contrast with ice, but also because of an existing Firebarn puzzle by Kaz/ft029 (which only had the “must turn on every cell” rule but didn’t allow revisiting cells).

One tricky thing about trying out and publishing this genre is that the presentation requires arcing turns to disambiguate the revisited cells, but Penpa does not support those. I pitched the idea to Lennard Sprong/X_Sheep who is maintaining pzprxs (in the absence of puzz.link updates), and he kindly agreed to implement the yet-unpublished genre, so we could play around with it and spitball some possible variations on the ruleset.

After experimenting a little, we realised that there’s a bit of a uniqueness problem. There is a certain pattern which lets you flip two double-turns at the same time while maintaining a single loop in the puzzle:

Fire Walk deadly pattern

I suspect that a pattern like this would appear in most sufficiently large puzzles, and the clues provide no mechanism for disambiguating this situation. However, I believe that this only works if one double-turn is “internal” and one is “external”, and so we decided to include the slightly awkward rule that all double-turns must meet on the inside of the loop. Not the most elegant rule, and sadly not very thematic, but it seemed to be the cleanest fix to the underlying problem. That said, after constructing the puzzles in this set, I’ve already found a few nice deductions resulting from that rule, so there’s that.

Fire Walk

Rules: Draw a loop through the centres of some cells which passes through each numbered cell. The loop turns 90 degrees on every fire cell. Fire cells may be visited twice as long as the two turns in the cell do not touch, and the centre of the cell is inside the loop. A number indicates how many cells make up the continuous non-fire section of the loop that the number is on.