Logic Masters Deutschland e.V.

This is my response to Scojo's setting prompt as redeemed by Dorlir, which was to use only one clue of any constraint type. I wanted to take this a step further and explore negative constraints by giving only one possible clue of certain constraint types. I created this draft, in which the negative constraint on the outside clue was only really a gimmick, but seemed to have much more potential for a fresh an interesting puzzle than the Xs and Vs.

Thank you to several testers, particularly dibble, who tested both drafts of this idea.



Normal 6x6 sudoku rules apply.

ONE AND ONLY:
• For each of the below (standard) constraints, ONE such clue has been given;
• Each clue is the ONLY possible appearance of that number as that clue type (except for the Sandwich clue, which can be trivially repeated at the other end of its row or column, but nowhere else);
• For example, if the 5 is the Hit Points clue, then 5 would not be a valid Hit Points clue in any other row/column of the finished grid;
• Clues may coincidentally work as multiple constraint types, but must be assigned to a specific type for the purpose of the One And Only ruleset.

____________
Constraints:

HIT POINTS: A clue outside the grid shows the sum of all the numbers in that row/column where the distance from the clue equals the number. For example, a row of 163425 would have a Hit Point value of 8 from the left as 1, 3 and 4 are in their "correct" positions and sum to 8, and a value of 2 from the right as 2 is in its "correct" position.

NUMBERED ROOMS: A clue outside the grid shows the digit entered in the Nth cell of that row/column from the direction of the clue, where N is the first digit seen.

SANDWICH: A clue outside the grid shows the sum of digits between the 1 and 6 in that row/column.

SKYSCRAPER: A clue outside the grid shows how many digits are visible in that row/column. Digits are visible when they are larger than all digits before them.

X-SUMS: A clue outside the grid shows the sum of the first X digits in that row/column, where X is the first digit seen.