We return to the wondrous world of Nikoli Omopa for today's genre. Balloon Box is a recent type introduced in PCN 189 which combines Shikaku-style rectangle packing with Numberlink-style connectivity. This fusion results in a unique feel that isn't seen in many other types. (Though, admittedly, I've said that phrase a lot, so maybe it doesn't mean much.)
Rules: Divide the shaded cells into rectangular balloons, and connect each balloon to a number with a string so that all cells are used by strings or balloons. Strings cannot branch, cross, or overlap each other. Every balloon is connected to exactly one number with a string, which indicates the size of the balloon. A string cannot loop back on itself and visit a cell that's orthogonally adjacent to a cell it has visited before.
Nikoli afficionados may notice that, as of Issue 190, the last rule is no longer in effect. I decided to keep it for puzz.link compatibility purposes and because it made uniqueness easier to satisfy with sparse clue layouts. The downside, though, is that constructing one of these becomes way harder with the extra restrictions on the balloons. But they're similar to the complications arising from Numberlink construction, so I'm used to them 🥲.
As usual, here are two puzzles. The first grid is designed to be smooth, while the second is significantly more meaty. Thanks to Menderbug, Rook, apiad, and Stef for testsolving.
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