Battlefield Sudoku #2
(Published on 2. June 2020, 02:21 by Big Tiger)
Standard Sudoku Rules apply to the final numerical layout.
The Battlefield Basics: On this ancient battlefield, 36 armies fought: 9 from each horizontal direction, and 9 from each vertical direction. Each army advanced X cells, with X being the first number at their end of their row or column, and counting the first cell as part of their advance.
Where two opposing armies overlapped, there was a bloody battle and resulting casualties. Where two opposing armies ceased advancing and declared a truce before a battle could ensue, lives were thankfully spared.
The Numbers outside each row and column indicate the sum of either the casualties or the lives spared, but do not indicate whether it was a battle or a truce.
On the puzzle grid, Red Cells indicate all the fields where both a row and a column engaged in battle. Green Cells indicate all the fields where none of the four armies from that row or column ever entered.
*****
Setter's Diary :: June 2, 2020 :: As an amateur logic puzzle fan, I was delighted that my experiment with the Battlefield idea generated a rating in the high 90's and at least one other setter using it to create a puzzle almost immediately. (In fact, in chronological order, his may actually be Number Two.)
This second one seemed easier to solve in the testing phase, so you may find it less challenging. I'll start experimenting with variations I create a third one.
Someone noted that this seems to be a variation on the idea of X-sums: Yes, that notion was at the foundation of my experimenting to come up with something new and hopefully intriguing. I'm happy to see people enjoying it.
Solution code: Row 5 then Column 5.
Comments
on 15. July 2020, 05:08 by MatthewDonovan
Another great puzzle, thanks!
on 13. July 2020, 08:41 by Richard
@Big Tiger, Nylimb and SirWoezel: thanks! I got it now.
I meant: after correcting my miscalculated sum of 24/26 in the middle row. :-)
on 11. July 2020, 13:46 by Nylimb
@Richard: Consider the green cell at R6C2. This means that in row 6 there's a gap which includes this cell and in column 2 there's a gap which includes this cell. So R9C2 can't be what you said because then the gap in column 2 wouldn't include R6C2.
Similarly a red cell means there's an overlap in its row which includes the cell, and there's an overlap in its column which includes it.
on 11. July 2020, 12:10 by Richard
All right, then I think I don’t fullt understand the meaning of the colours. Thanks for answering!
on 11. July 2020, 12:01 by SirWoezel
Well, R9C2 can never be what you say it must be as it would mean that army goes somewhere it may not go
on 11. July 2020, 12:00 by Richard
Sorry, I mistyped. Meant gap clue at step 5. Does that change anything?
on 11. July 2020, 11:38 by SirWoezel
@Richard I think step 5. Look at the colour of R6C2
on 18. June 2020, 21:49 by Big Tiger
For minimal numbers, you could fairly easily lock down 1's and 2's like Nylimb's "Border Crossing" only in reverse. But yes, you'd need a FEW of the "mutual battle" and "mutual truce" squares in the grid to get that going.
on 18. June 2020, 17:24 by Nylimb
@Realshaggy: Thanks for the link. I wonder how the program that proved this works. Offhand I can't think of a way to reduce the search space to make it practical, so the programmers must be cleverer than I am.
on 18. June 2020, 14:13 by Realshaggy
See this post, but it's rather a claim to have proofed it with exhaustive search rather than providing a proof. (And also the pattern is much bigger while still preventing any valid puzzle).
http://forum.enjoysudoku.com/investigation-of-one-crossing-free-patterns-t30977.html#p224617
I once tried to construct something like that and failed, and that was the reason for some "research" where I found this thread.
on 18. June 2020, 13:04 by Nylimb
@Realshaggy: I'd like to see the proof of that. Do you know where I can find it?
on 18. June 2020, 10:39 by Realshaggy
I thought about doing one that is mostly based on the colored cells. But this has to either have some givens in the grid or some outside clues. The colors only influence the "border" of the grid, and it has been proofed, that a Sudoku can't be unique by just giiving the border completely.
on 18. June 2020, 03:36 by Nylimb
I've created a puzzle which uses only 3 numeric clues, in addition to the colored squares. I'll publish it after I do some final testing.
I wouldn't be too surprised if a puzzle with just 2 numeric clues is possible.
on 13. June 2020, 23:19 by Big Tiger
Nylimb: Christoph Seeliger made one that left out a FEW of the side numbers, but I don't imagine a way to leave them ALL out without its becoming something other than "Battlefield" methodology.
on 13. June 2020, 06:30 by Nylimb
I thought that I'd solved this soon after it was published, but somehow I missed it. I'm too slow a solver to keep up with all of the new ones.
Anyway, it's another good one!
I wonder if it's possible to make a puzzle like this without the numbers along the edges, that's solvable just using the red and green squares.
P.S.: Probably not. Without the sums, the red and green squares only give information about the numbers on the edges of the grid. I don't think that's enough to complete the solution. (But I'm not sure of that.)
on 6. June 2020, 18:11 by ch1983
Very nice - I also like the story, in my opinion the sudoku gets more lively with the armies in mind!
on 6. June 2020, 11:57 by Mody
Super konstruiert :)
on 4. June 2020, 21:08 by Big Tiger
Altered a few words in the instructions based on user feedback.
on 4. June 2020, 20:40 by Big Tiger
SirWoezel and Madmahogany - many thanks! For someone who is "just a guy" and will probably never be a "real" puzzle setter like Phistomofel or Mr. Seeliger, it is a very rewarding feeling to have created a puzzle type that people are enjoying.
on 4. June 2020, 20:02 by Madmahogany
I am really loving this series! Looking forward to the next one!
on 4. June 2020, 17:25 by SirWoezel
Great puzzle, and in my opinion quite a lot harder than your first Battlefield-sudoku
on 4. June 2020, 08:32 by Statistica
Nice idea and nice puzzles. But I prefer the name "XY-sandwich sudoku" (as in #3KI). In my opinion the name "Battlefield Sudoku" is too martial.
on 2. June 2020, 02:49 by Big Tiger
Added icons.
