Toroidal Sandwich
(Published on 20. November 2020, 22:27 by PrimeWeasel)
Normal Sudoku and Sandwich Rules apply. A grey square contains an even digit.
All digits outside the grid are the sum of the digits sandwiched between 1 and 9 for that row or column.
However, Sandwich clues for the rows are also Sandwich clues for the digits sandwiched between 2 and 4 toroidally, which is also a negative constraint in the sense that the Sandwich sum on a row between 1 and 9 is not the same for the Toroidal sum between 2 and 4, if there isn't a clue given outside the grid.
Sandwich clues for the columns are also Toroidal clues for the sum between 2 digits, which can be different for every column. This is also a negative constraint in the sense that the Sandwich sum in a column between 1 and 9 can not be summed toroidally between any 2 digits, if there isn't a clue given.
Example 1: a 19 Sandwich clue for a row could result in, for instance: 187496523 for the 1-9 Sandwich would be 8+7+4=19 and the Toroidal 2-4 Sandwich would be 8+7+1+3=19.
Example 2: No Sandwich clue for a column could result in, for instance: 879314562 for the 1-9 Sandwich is 3 and there is no way to toroidally get to 3.
f-puzzle link
Solution code: Row 1, column 7, 18 digits, no spaces.
Comments
on 25. July 2022, 20:40 by Vebby
Very nice! 4/5 difficulty imo.
on 20. March 2022, 01:41 by jgreenfield
Just for clarity, is a toroidal sum a positive constraint (i.e. it *must* wrap around the puzzle), or does it just mean that the toroidal sum *may* wrap around the puzzle?
Furthermore, do both of the two digits involved in the toroidal clues for the columns need to be digits other than 1 and 9, or can you re-use one of them?
If these are questions intentionally left for the solver to determine, that's completely fair -- I've only put about an hour into the puzzle thus far, so it's entirely possible that I'll discover how the rules work eventually, but it would be nice to confirm that I'm not missing something that was supposed to be clear from the instructions.
~Hi there, thanks for trying it on. Regarding your first question, the toroidal sum must indeed wrap around the puzzle, for the rows the sum between 2/4 has to occur in a wrapped way, so it is a positive constraint. If there is a clue, there is both a normal sandwich and a toroidal sandwich.
As far as I can remember, for the columns the 1 and 9 can be used again, but I'll have to either resolve it myself again or have a deep dive into my files. This is a fair question and I should have made a remark about it, although stating that it could be any two digits, makes me think that it's definitely the case.
on 6. January 2021, 09:24 by PrimeWeasel
Changed difficulty
on 21. November 2020, 14:11 by marcmees
thanks. very nice.
~ You're welcome
