Logic Masters Deutschland e.V.

Place the digits 1 to 9 exactly once in each row and column of the grid, and some cells in the grid are to be shaded such that the final shading of the grid resembles a valid cave (All unshaded cells are orthogonally connected and all shaded cells are orthogonally connected by other shaded cells to an edge of the grid).

Outside clues are Japanese sum clues. "?" is a stand in for any digit 0-9, but for a double digit number, the first digit may not be 0. Each distinct letter represents some unique digit from 0 to 9.

Clues to the left of the grid are Japanese sum clues for either shaded or unshaded groups of cells, where each group needs at least one of the other (shaded or unshaded) to separate the groups. Clues to the top of the grid are Japanese sum clues for the OTHER of shaded or unshaded. (That is, if it turns out clues to the left indicate sums of unshaded blocks, clues to the top indicate sums of shaded blocks). Either all or no outside clues are given for each row and column.

Variant:

Clues to the right and bottom of the grid are Sisyphos clues, which is a constraint type invented last year by Phistomefel. A Sisyphos clue indicates how many cells a rock rolls from the adjacent square to the outside clue. Each number represents a hill of the corresponding height, and the rock only ever moves from a higher to a lower hill and then rolls towards the smallest orthogonally adjacent hill. If the two smallest adjacent hills are the same size, the rock rolls straight ahead.

However, all unshaded cells are of a lower height than all shaded cells. Specifically, for the 9x9 grid, there are 18 distinct levels of elevation: the unshaded 9 is lower than the shaded 1. Likewise, for the 7x7 example, there are 14 distinct levels of elevation.

I highly recommend first acquainting yourself with the example puzzle before attempting the 9x9 grid.

Play on Penpa+!

Answer check is enabled with blue sudoku digits.

Example puzzle