Cave

Rules

Shade some cells to leave behind a single orthogonally-connected group - the cave - with no enclosed shaded cells. In other words, all shaded cells must be connected edge-wise by other shaded cells to an edge of the grid. All numbered cells must be a part of the cave, with each number indicating the total count of cells connected in line vertically and horizontally to the numbered cell including the cell itself.

(Rules and example from PGP IB)

History of the puzzle

First appeared in Nikoli volume 60 (1996). Invented by ゲサク ("Gesaku"). Original title バッグ means "bag". On Nikoli this puzzle is treated as a loop puzzle (hence the name meaning numbers being enclosed), but in most instances, this puzzle is presented as a shading puzzle.

Variations

Full Cave

First appeared on WPC 2016/Round 4. "Full" variant was invented by Matej Uher (Slovakia).

Shade some (but not all) cells to get a valid Cave solution:

Leave some cells white to form a single orthogonally connected shape. Shade all the remaining cells. All shaded cells must be connected to the edge of the grid through other orthogonally adjacent shaded cells. The remaining (unshaded) numbers indicate the number of cells inside the shape that can be seen from that cell, including the cell itself. Cells do not see past shaded cells.

(Rules and example from WPC 2019 IB)

Twilight Cave

Appeared on WPC 2019/Round 8. The puzzle was written by Gabi Penn-Karras.

Shade some cells so that all unshaded cells are connected and all shaded cells are connected to the border of the grid. Cells with numbers can be shaded.

Numbers in unshaded cells indicate the total count of unshaded cells that can be seen in all four directions, including the numbered cell itself. Numbers in shaded cells indicate the size of the group of connected shaded cells they are part of. A group of shaded cells may contain none, one or several numbers.

(Rules and example from WPC 2019 IB)