Build Your Own Killer: The Empty Box
(Published on 18. November 2022, 18:52 by Playmaker6174)
Estimated difficulty is around 4/5, but for someone already being familiar with the rule set it may be lower. I hope you enjoy!
For previous entries of the concept, check out Number 1; Number 2; Number 3.
Rules:
- Normal Sudoku rules apply: every row, column and 3x3 box contains digits from 1 to 9 each once.
- A given one-cell killer cage is used to construct a real killer cage that starts from that cell and goes straight horizontally, vertically or diagonally in the direction of the given arrow in it, the length of each cage is to be deduced (the limit one can reach to is the 9x9 grid borders). Once a cage is finished, digits within that cage mustn't repeat and they sum to the small number written in that cage.
- There are two types of color: red and blue.
+ If a red cage has the length of N cell[s] then that red cage must contain digit N (which can be anywhere within the cage).
+ If a blue cage has the length of N cell[s] then that blue cage must not contain digit N.
Note: there can be some occasions where a cage is one cell long, and some cages can overlap each other regardless of their colors.
(The gray box in the middle is for aesthetic purpose only)
Some of the examples in the following image:
(+) For red cage, the 20 red cage can be 3 cells long or 4 cells long with configurations like in the image.
(+) For blue cage, the blue 8 cage can be only 1 cell long (contains only digit 8, which is possible), can be 2 cells but mustn't contain digit 2 in it.
The blue 10 cage can't be 1 cell long because 10 is not a single digit, and can't be 4 cells long because the only way it works is with 1+2+3+4 cage, but it contains a 4 and is a blue cage so it's not valid.
The blue 12 cage can only be 2 cells long or 3 cells long because of how close it is to the border.
Puzzle:
Good luck and have fun solving!
Solution code: Row 2 (left to right) and column 8 (top to bottom), 18 digits long with no space
Comments
on 11. January 2024, 23:10 by Mad-Tyas
Beautiful puzzle! So many satisfying deductions. Towards the end I hit a massive wall and stared at the grid for about 10 mins without making any progress. Then I realizied that there was one cage where I had an option pencilmarked that wasn't valid for the whole time :-D
on 28. January 2023, 14:04 by Cheburashechka
Beautiful, both the start and ending were great, love the ruleset
on 27. January 2023, 19:58 by Mr.Menace
Very nice puzzle with this great ruleset! thanks so much!
on 17. January 2023, 01:52 by Piatato
Very nice! Cool twist with the diagonal clues, it seems like it made for a slightly easier puzzle. :-)
on 23. November 2022, 08:16 by Playmaker6174
Thank you all for the lovely feedback, @lerroyy, @Elliott810, @Niverio, @cdwg2000! I’m glad to hear the enjoyment from all of you :)
on 20. November 2022, 08:33 by cdwg2000
Very nice and smooth.
on 19. November 2022, 18:53 by Niverio
Easiest of the bunch, but definitely just as fun!
on 19. November 2022, 01:08 by Elliott810
Very nice puzzle with a beautiful break-in! Thanks:)
on 18. November 2022, 22:19 by kjholt
So the cages are always 1 cell wide? If not, can the two adjacent clued 15s be a single cage? Also cages must be able to overlap right? Otherwise I'm confused as to how the 18 arrow can point upwards.
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Each cage is independent of each other, and in the direction of the arrow you have to create a ‘true’ cage for each of them and determine its length (for example, with the 18 cage R9C1, it may be 3 cells wide R9C123 or 4 cells wide R9C1234, etc). So, no those two 15 adjacent cages are independent of each other and don’t form a single cage, also cages may overlap each other as in the note says.
Thank you! I should clarify I meant "wide" as the opposite dimension of length (i.e. that each cage would be 1x1, 2x1, 3x1, etc).
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Ah I was a bit confused as well, but yes every cage is one cell wide like how you understood :)
on 18. November 2022, 20:04 by lerroyy
Very nice puzzle with a smooth solve! thanks
