How I procedurally generated puzzles in "makenines"

In this video, I go behind the scenes to the daily puzzle generation of 'makenines'. i.e. how are the puzzles generated. What are the parameters? What is the logic process? What issues are there with it? How could it be improved? Let's find out!
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Background Music by Monomoon:
(as featured in makenines!)

[@toddzircher6168]

Always nice to see how the sausage (or puzzles) is made. :-)