Reference Sandwich
(Published on 8. July 2022, 19:03 by Sktx)
==== LINKS TO SOLVE ====
F-puzzles - CtC app - Penpa+ (with answer check)
==== RULES ====
Normal Sudoku rules apply : fill the grid with digits 1 to 9 appearing each exactly once in every row, column, and 3x3 box.
Reference Sandwiches : A "crust cell" is a cell that contains a digit that is both the position of its column number in its row, and the position of its row number in its column.
- A row or column with a clue contains exactly 2 crust cells, and the clue gives the sum of the digits sandwiched strictly between them.
- A crust must always be part of at least one clued sandwich.
Negative constraint : Non-crust cells can not be valid references for both their row and column (but can be for one of the two).
==== EXAMPLE ====
In the above example, yellow cells are crusts. They reference their row number in the column, and their column number in the row (pink cells). The sum of the digits between the crusts in row 3 is given by the clue. Grey cells can not be crusts, so they can not reference both in their row and column. For instance, the 4 in R3C3 is not a crust, but it is a reference in its row. So it can not be a reference in its column.
==== ACKNOWLEDGEMENTS ====
Big thanks to Ul-Rhymm from the CtC discord server, who tested the puzzle and helped with formulating the ruleset.
Solution code: Digits from Row 8 (left to right) and then Column 9 (top to bottom). 18 digits total, no space character.
Comments
on 9. July 2022, 02:10 by marcmees
a bit confusing at first, but solves smoothly when understood.thanks
on 8. July 2022, 23:33 by JayForty
Very interesting concept! Took me some time to understand the implications of the rules, especially the negative constraint. Very clever puzzle, I really enjoyed it!
on 8. July 2022, 21:21 by Sktx
updated example
on 8. July 2022, 20:53 by Sktx
added example in a 6x6 setting with explanations
on 8. July 2022, 20:12 by Veegody
can you provide an example on a crust cell?
~~~ I just added an example in a 6x6 setting. Sorry for the obscure ruleset :x... The crust cells act like Broken 159 references, but for *both* their row and column. Other cells (non-crust) can not act as 159 references for *both*, but could act for the row or column alone.
