#A61: Balloon Box (Revised)
This genre reminds me a bit of Pencils but might be closer to Shikaku. It's interesting how it tries to counterbalance the relatively rigid logic in the shaded cells with the relatively loose logic in the unshaded cells.
In addition to not knowing what the original ruleset was before the revision, I'm also not entirely certain what the current ruleset is supposed to be. The default pzprxs implementation differs from the Puzzle Square JP rule tab in that a numberless looped string is valid, but enabling the "Strings cannot loop back on themselves" checkbox also differs because it causes a string that passes next to itself to be invalid. The shared example solution isn't open enough to differentiate and all three versions of the ruleset pose different kinds of nuance.
The following puzzles use the version of the rules where strings may snake near themselves but loops aren't allowed.
https://pzprxs.vercel.app/p?balloon/v:/a/5/5/hphjhg12n1g1n25g
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