Kropki Arrow Sandwich (Merry Christmas PhilTheHat!)
(Published on 22. January 2025, 15:01 by RockyRoer)
This puzzle was made as a Christmas present for fellow sandwich enthusiast Phil the Hat.. He has published a few puzzles with this kropki arrow ruleset on his personal website, specifically, the kropki arrow puzzles #1, #2, and #3.
The Rules:
- [Sudoku]:Normal sudoku rules apply. Place the digits from 1 to 9 once each in every row, column, and 3x3 region.
- [Sandwich]: Numbers outside the grid must be deduced and are the sum of the digits between the 1 and 9 in that row or column.
- [Kropki Arrow]: Numbers separated by a white dot have a difference equal to the value of the white dot - which is the sum of the numbers on the arrow attached to that dot.
Numbers separated by a black dot have a ratio equal to the value of the black dot, which is the sum of the numbers on the arrow attached to that dot.
The Puzzle:
Try it on Sven's Sudokupad with a border of outside cells or without the outside border.
Solution code: Row 5
Comments
on 16. February 2025, 06:37 by Bankey
Quite a mind-twister, in a fun way. Thanks, @ RockyRoer :).
on 24. January 2025, 14:48 by MattYDdraig
Absolutely exquisite. Took a little while to get the rule straight, and kept wanting to put the arrow sum as sandwich clue for the longest time, but once understood the logic is beautiful.
on 24. January 2025, 10:42 by Aspartagcus
Awesome puzzle!
I really enjoyed the combination of those constraints, and I've got a soft spot for ambiguous outside clues. :)
Great example of a puzzle that has a novel idea and utilizes it really well.
on 22. January 2025, 21:49 by steperlich
Hi RockyRoer,
I do not understand the Kropki Arrow rule.
Could you give me an example ?
REPLY: sure.
Suppose the digits on R4c123 add to 10. Then the black circle has a value of 10. That means that R4C1 and the sandwich must be in a 10:1 ratio -- which would mean sandwiches of 10, 20, or 30 could be possible with R4C1 values of 1, 2, or 3 respectively.
Suppose R8c12 adds to 5. Then the white dot has a value of 5. R8C1 and the sandwich sum must have a difference of 5. Sandwich sums of 6, 7, 8, or 9 would be possible then with R8C1 being 1, 2, 3 or 4 respectively.
on 22. January 2025, 19:34 by Qodec
Haha I was hoping for that particular finish! Very nice!
on 22. January 2025, 18:06 by marcmees
Mindbending SW in typical RR style. thanks
