Logic Masters Deutschland e.V.

This puzzle was created for the Secret Satan event hosted by Gliperal. My victim was James Sinclair, who gave me authorization to publish the puzzle here.

I advice you to read carefully the rules and to pay attention to the given examples.

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Rules:

Sudoku: Within the thick-bordered 9x9 grid, place the digits 1 to 9 in every row, column, and 3x3 box.

In Order: A digit from 1 to 9 must be placed in each dashed-line cell outside the grid. Digits in those cells give the order in which those digits must appear in the corresponding row or column, but not necessarily next to each other.

Partial Cave: Shade a set of digits from the entire grid such that every instance of those digits is shaded and every instance of other digits is unshaded. Shade the digits in such a way that if you limit the grid at the 9x9 that does not contain the last three columns (i.e. the 9x9 composed of the dotted columns and the six leftmost columns of the thick-bordered grid), all shaded cells are connected orthogonally by other shaded cells to the edge of that 9x9, and the remaining unshaded cells form one orthogonally connected area.

Counting arrows: Digits with arrows give the number of different digits that appear in straight lines in unshaded cells in the indicated directions combined inside the 9x9 denoted above.

Double Japanese Sums: Numbers in the upper side of the puzzle indicate the sums of the digits in groups of shaded and unshaded cells in the corresponding column, in order.

A single ? represents a single digit from 1 to 9. Combined with other digits, it can also be 0, as long as it is not the leading digit. ?? represents some number which is greater than 9. * represents any number of sets of consecutive cells with arbitrary sums including no cells at all.

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Arrows to the gates of hell is also available online on CTC-App.

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Some clarifications about the rules.

This in an example of how digits in dotted cells work:

The puzzle is made of two overlapping grids. The one at the left is the one in which all unshaded cells are orthogonally connected. The one at the right is the sudoku.


The shading of the cells applies to the entire 9x12 grid, even if Cave restrictions apply only at the 9x9 at the left. Sums above the grid refer to the entire 9x12 grid. Dotted cells refer to the 9x9 sudoku grid. Arrow digits refer to the 9x9 at the right.

So for example this 3 with two arrows means that in the highlighted cells combined there are exactly three different unshaded digits. Of course they can be repeated as many times as possible, if they don’t break the other rules.

Please notice that the arrows stop before entering the grey area.

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Have fun solving. I'm sure you'll find your way through the gates of hell! And please leave a comment after you solve!