This idea of min/max cave clues has been explored and refined several times over with the help of people on the Skunkworks server, namely : SeveNateNine, wisty, zzw, and chilly.

Big thanks to wisty, who authored the majority of the ruleset. I'm fairly certain my attempt would have been messier and much longer.

I have also added an example puzzle with images of a empty grid followed by a solution, so that the ruleset can be examined against a solved grid.

Big thanks to wisty, who authored the majority of the ruleset. I'm fairly certain my attempt would have been messier and much longer.

I have also added an example puzzle with images of a empty grid followed by a solution, so that the ruleset can be examined against a solved grid.

**Cavernous Chaos Construction :**

Divide the grid into nine regions and place a digit from 1-9 in each cell such that digits do not repeat in any row, column, or region.

In each region, place exactly two cave clues. A cave clue counts the number of cells seen in the four orthogonal directions, including itself, where region borders obstruct view.

For each region, one placed clue equals the maximum value any cave clue in that region could have, while the other equals the minimum.

Minimum clues for all regions must be the same digit, however the maximum clue across all regions will vary.**Truly Terrifying Sandwich Sums :**

Consider the placed cave clues as crust cells.

Outside clues are sorted into TWO GROUPS, one representing sums between two crust cells, and the other representing the sum of cells between a crust cell and the edge of the grid.

For any row or column with clues, all such sums are given.

However, the GROUP containing the smallest sum is listed first, followed by THE OTHER GROUP. Groups containing multiple sums always list their sums lowest to highest.

Rows/columns without an outside clue indicates that there are not enough crust cells to have a sum between.

(? = a single-digit sum ; ?? = a double-digit sum)- SudokuPad link - link to solve 6x6 example puzzle
- SudokuPad link - link to solve 9x9 below

Below is an sample puzzle, along with the starting and finished grids.

To better demonstrate the outside clues, the clues with a green circle around are a grouped set,

but whether they are crust or sandwich sums can not yet be determined.

The clues with the red circle are not a grouped set since the 9 is larger than the 4.

Lösungscode: Row 1 followed by Column 6

Zuletzt geändert -

Gelöst von Chilly, zakkai, nuzzopa, Raz, gfoot, tonald, jkuo7, SeveNateNine, marcmees, MxTery, henrypijames, ONeill

Zuletzt geändert am 12. Mai 2024, 19:24 Uhr

**am 12. Mai 2024, 02:48 Uhr von ONeill**

Awesome puzzle, I can’t imagine how long it must’ve taken to create as it seems there are endless opportunities for the puzzle to break. I wish my solve would’ve got it rated. Thanks!

-----

Thanks for checking this one out as well ONeill.. This one was very tough to set. Region shapes/placement was quite elusive and the ruleset went through a few changes/variations. Glad you enjoyed it, appreciate the feedback.

Zuletzt geändert am 7. Mai 2024, 04:24 Uhr

**am 6. Mai 2024, 19:38 Uhr von henrypijames**

This might've been a personal record of how many mistakes I've made in a puzzle - many of them over and over again. Finished on the third complete redo only.

-----

Ack! Sorry this one tripped you up but the perseverance is admirable. Thanks for the feedback and giving this one a try.

Zuletzt geändert am 21. April 2024, 20:16 Uhr

**am 21. April 2024, 08:10 Uhr von MxTery**

There's some really beautiful reasoning in this puzzle that it took me an embarrassingly long time to see. I'm absolutely glad that I stuck with it (and that I did the 6x6 - getting some practice with the rules was a big help).

-----

First off, congrats for conquering this beast, and don't be embarrassed as this really hasn't been explored that I know of, so at least some of the logic is reasonably new. Second, I'm relieved that I didn't create and provide an example puzzle for no reason, really glad it is proving to be useful. Thanks so much for the kind feedback and the solve.

Zuletzt geändert am 12. April 2024, 16:26 Uhr

**am 11. April 2024, 13:08 Uhr von marcmees**

Put this exceptional puzzle aside for a while as it looked too scary. It eventually solves really nice with some great logical deductions. Thanks.

-----

Congrats marcmees, and admire the perseverance, as well as appreciate the solve and feedback.

Zuletzt geändert am 7. April 2024, 22:44 Uhr

**am 7. April 2024, 21:08 Uhr von gfoot**

What a brilliant puzzle, I didn't find it as hard as it looked, and it was fascinating the way the different aspects worked together!

-----

Appreciate the compliments and the solve. The test solves all required multiple hours to complete, and the feedback was that the difficulty was pretty high. It will be interesting if it gets knocked down a notch to four stars.

-----

Interesting, I am not generally very fast and often spend an hour or two on even 3-4 star difficulty puzzles. But I never felt stuck here, though I did make careless mistakes twice and had to backtrack a bit each time to correct them.

Zuletzt geändert am 6. April 2024, 01:45 Uhr

**am 6. April 2024, 00:34 Uhr von zakkai**

incredible setting!

-----

Thanks for taking the time to give this one a go. And I really appreciate the kind words.

Zuletzt geändert am 6. April 2024, 01:44 Uhr

**am 6. April 2024, 00:01 Uhr von Chilly**

Easiest puzzle I ever did ... just joking. That was really hard for me. But very nice.

-----

Really appreciate the discussions/solves on this one, as the idea really hasn't been explored as far as I'm aware, but I think there is much more to be discovered around this min/max cave constraint.. Cheers!