The obvious approach lets you
reduce to the case of a size-3 triangle
at which point
there are WLOG only three options for your single non-sunny line, and you can pretty much draw the diagrams and say “behold!” but even writing out longhand why you can’t cover what’s left in any of those cases with two sunny lines isn’t too painful.
The obvious approach lets you
reduce to the case of a size-3 triangle
at which point
there are WLOG only three options for your single non-sunny line, and you can pretty much draw the diagrams and say “behold!” but even writing out longhand why you can’t cover what’s left in any of those cases with two sunny lines isn’t too painful.