Why can't I drag nodes freely?

The swap constraint is the whole game. Freely dragging nodes is a solved problem — you just push things apart until nothing crosses. Swapping forces you to think about which nodes are in the wrong relationship, not just which ones are in the wrong place.

Is every puzzle solvable?

Yes. Every Plet puzzle starts from a solved state that's then shuffled. The solution always exists — you're just finding your way back to it.

What's the best strategy?

Start with the most crossed node — the one where the most red lines meet. Getting that node closer to its solved position tends to clear several crossings at once. Don't chase individual crossings one at a time.

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What does Plet mean?

Plet comes from the Ukrainian word "плетіння" — a weave. That's what you're doing — untangling a weave.