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Join every pair of coloured squares. The catch is not fitting them in — it is that flows may not cross, and no flow may run alongside itself.
Drag from a coloured square to the one that matches it. Every pair has to be joined.
No square of a flow may sit beside another square of that same flow, except the ones it runs through on the way past.
Once a flow is joined, its squares belong to it. Another flow may not pass through them — it has to go around, or you have to redraw the one in the way.
Empty squares are fine. You are done the moment every pair is joined — this is not Flow Free, and leaving space is often the only way through.
Tap either end of a flow, or its chip above the board, to pull it up and redraw it. It costs a star, nothing more.