Yajilin – Paramesis Puzzle Blog

My first Nikoli puzzle book was Pencil Puzzle Yajilin 1, back in 2006 when the Pencil Puzzle series was available. Yajilin has always been a special puzzle type for me. It marks the beginning of that unscratchable itch that I think most puzzlers have, to relentlessly explore new puzzle types and variations and to engage with problems for which no well-trodden inventory of techniques already exists. I’m happy to return from my break with a Yajilin variation on a new tiling [33434; 3²6²; 3446; 6³].

EDIT: Following a suggestion from edderiofer, I have made the clue cells easier to distinguish.

EDIT 2: Puzzle number 3 has been corrected. The far right hexagonal clue should have been a 3.

Rules

Shade some cells and draw a loop in remaining cells such that:

Every empty cell is either shaded or part of a single loop that does not branch or intersect.
Numbers in some cells indicate the total number of shaded cells that can be seen in all directions from that cell. Lines of sight run perpendicular to the edges of a cell and terminate on the edge of the grid or at a triangular cell, counting that cell.