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Here's how you brute force the sky as efficiently as possible without testing the same piece twice
>Get the edge pieces surrounding the sky in place
Step 1
>Get a pile of untested sky pieces ready
Step 2
>Pick a piece from the untested pile
Step 3
>Pick an end of the piece (could be male or female) and test it with every single slot of the opposite end type along the inside edges
>If no placement is found, pick a new end and test it with every single slot. Make sure to test against the ends of any new piece that has been placed.
>Repeat step 3 until the piece either fits or every end of the piece has been tested against the edge
Step 4
>Go through every piece in the untested pile until every single one is either in a slot of the no-fit pile
>The no-fit pile now becomes the new untested pile. Repeat from Step one
It's boring and robotic but it's the fastest way to get a shitty, monotone part of a puzzle done