Heyacrazier: Big Three

Question

This is a Heyacrazier puzzle, a variant of Heyacrazy.

Rules of Heyacrazy:

• Shade some cells of the grid.

• Shaded cells cannot be orthogonally adjacent; unshaded cells must be orthogonally connected.

• When the puzzle is solved, you must not be able to draw a line segment that passes through two borders, and does not pass through any shaded cells or grid vertices.

For an example puzzle and its solution, see this question.

Rule change for Heyacrazier:

• The forbidden lines are now those that pass through three borders, instead of two. Lines that pass through only two borders are acceptable.

Answer 1

Here's my solution! While I might have written like I was case bashing, in reality there were only a few options at any one step and I did it all in my head. Not nearly as difficult as I thought it would be!

Here I let the bottom left corner be A1, label the rows with numbers and the columns with letters.

If A1 is not shaded, we have two options (modulo reflection): shade (A2, C2, D1) which allows a line through (A1, B1, B3) or shade (A4, B2, C1) which allows a line through (A1, A2, B3). Thus A1 is shaded.

We can't shade B2 and simultaneously block (B1, C2, C3), (B1, C2, D2), and (B1, D1, E1) without trapping some unshaded cells. If C3 is shaded, we can't simultaneously block (B1, D1, E1) and (A2, C2, D2) and their mirrors without trapping some unshaded cells. Thus B3 and C2 must be shaded.

D3 is obviously shaded. By similarly obvious logic, so are A4, E4, E1, F2, F5, D5, B5, D7, A7, and H7 (logic can progress in that order).