Curve puzzle part 2
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A follow-up the 20 piece connected curve puzzle that includes 22 additional pieces that cover all possibilities.
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These are the 22 pieces omitted from the earlier Connected curves puzzle. Unlike those 20 tiles, which each had 3 connected components, these have 1, 2, 4, and 5 components. To get a closed curve without holes, the total number of components must sum to 6, though this is not sufficient to guarantee it. You can match the 2-component pieces with 4-component pieces to form simple closed curves, while the two pieces with either 1 or 5 components must be matched with each other.
The total number of such tiles is 42, corresponding to the 5th Catalan number (the number of ways to match 5 pairs of parentheses). 20 of these have 3 components and are included in the previous printable. The remaining 22 are in this printable.
These tiles will snap together with the previous set, but you will never form a simple closed curve that way.
See the previous printable for more information. I printed these in two colors by switching the filament towards the end of the run. Alternatively, the top can be painted or you can rely on texture to tell the pieces apart.
The solution shown as the cover photo is only one of many possibilities.