Fog of War #21 San Francisco

[Maul]

I'm stuck here. The line from R5C5 to R8C8 is clearly a renban, so no more clues there. I'm failing to prove that any or all of R3C467 are or aren't circles. The puzzle seems to be completely out of options.
https://steamcommunity.com/sharedfiles/filedetails/?id=3375635047

EDIT: And, apparently, widgets don't respect spoiler tags, because we can't have nice things.

[1810paulg]

I got stuck there for a while too. There is one digit that can be placed in box 8 if you consider one square carefully enough.

[Krest]

Originally posted by 1810paulg:

I got stuck there for a while too. There is one digit that can be placed in box 8 if you consider one square carefully enough.

This was exactly where I got stuck as well. Thank you for the very useful, but not too spoilery hint!

[Maul]

Oh, boy! How could this go past me?
Thanks a bunch.

[ZeeOcho]

I am stuck just a little bit earlier in this puzzle, and I don't know what constraint to use:

https://steamuserimages-a.akamaihd.net/ugc/27684734850192343/E0015815C1963D6FB6823B3901A26BFA5ABB8799/?imw=5000&imh=5000&ima=fit&impolicy=Letterbox&imcolor=%23000000&letterbox=false

Excuse my pencil-Mark-ings, but otherwise I will miss plain sudoku stuff^^.

I don't recognize any further constraints on the lines that I have discovered so far, so I don't see that I could put a number anywhere there.

I see the circle of a new line (containing 24567), but I feel I cannot really get anything out of that. If that is the beginning of a german whisper line, any of the numbers feel possible? Because then it could be a lot longer that 9 digits.

Also, the hints are really not helping me.

I feel I don't really get a good grasp of this one. I appreciate any hints on this.

[Krest]

Originally posted by ZeeOcho:

I am stuck just a little bit earlier in this puzzle, and I don't know what constraint to use:

https://steamuserimages-a.akamaihd.net/ugc/27684734850192343/E0015815C1963D6FB6823B3901A26BFA5ABB8799/?imw=5000&imh=5000&ima=fit&impolicy=Letterbox&imcolor=%23000000&letterbox=false

Excuse my pencil-Mark-ings, but otherwise I will miss plain sudoku stuff^^.

I don't recognize any further constraints on the lines that I have discovered so far, so I don't see that I could put a number anywhere there.

I see the circle of a new line (containing 24567), but I feel I cannot really get anything out of that. If that is the beginning of a german whisper line, any of the numbers feel possible? Because then it could be a lot longer that 9 digits.

Also, the hints are really not helping me.

I feel I don't really get a good grasp of this one. I appreciate any hints on this.

I always start by pencil marking the entire grid as well, I'm really bad at seeing the numbers, so I need the highlighting.

You can do more with your german whispers line. The 3 in r6c8 means that there are 3 uneven numbers on the line. You already have 3, 9 and 9, so all other numbers have to be even.

[ZeeOcho]

Originally posted by Krest:

Originally posted by ZeeOcho:

I am stuck just a little bit earlier in this puzzle, and I don't know what constraint to use:

https://steamuserimages-a.akamaihd.net/ugc/27684734850192343/E0015815C1963D6FB6823B3901A26BFA5ABB8799/?imw=5000&imh=5000&ima=fit&impolicy=Letterbox&imcolor=%23000000&letterbox=false

Excuse my pencil-Mark-ings, but otherwise I will miss plain sudoku stuff^^.

I don't recognize any further constraints on the lines that I have discovered so far, so I don't see that I could put a number anywhere there.

I see the circle of a new line (containing 24567), but I feel I cannot really get anything out of that. If that is the beginning of a german whisper line, any of the numbers feel possible? Because then it could be a lot longer that 9 digits.

Also, the hints are really not helping me.

I feel I don't really get a good grasp of this one. I appreciate any hints on this.

I always start by pencil marking the entire grid as well, I'm really bad at seeing the numbers, so I need the highlighting.

You can do more with your german whispers line. The 3 in r6c8 means that there are 3 uneven numbers on the line. You already have 3, 9 and 9, so all other numbers have to be even.

Thank you so much! I knew I forgot some rule / restriction, I totally forgot the even/odd part!

[Kristian]

Struggling to understand how you were able to place the 4 and 5 on the bottom left line - and how can you prove that there aren't circles hiding along the line behind the fog? Also, how do you know the 4/5 goes on those squares and not the other way around?

[Maul]

Originally posted by Kristian:

Struggling to understand how you were able to place the 4 and 5 on the bottom left line - and how can you prove that there aren't circles hiding along the line behind the fog? Also, how do you know the 4/5 goes on those squares and not the other way around?

1 hidden circle in R7C4:

• If R7C4 was a circle and R8C5 wasn't, R7C4 and R5C5 would have to sum to 3, and R7C4 and R8C8 would have to sum to 7.
  
• Therefore R5C5 would be 1 and R7C4 would be 2.
  
• But at the same time, R8C8 would be 5, and 5 can't exist on a German Whispers, so the line would have to be a Renban.
  
• But that's not possible, because the circles of a Renban must be consecutive.

2 hidden circles in R7C4 and R8C5:

• If R7C4 and R8C5 were both circles, then R5C5 and R8C5 would both have to be 1, breaking the puzzle.

1 hidden circle in R8C5:

• If only R8C5 was a circle. Both lines would have to have a length of 5, so whatever R8C5 would be, R5C5 and R8C8 would have to be equal.
  
• R8C5 could now only be from 134, so the other two circles would be from 124.
  
• Of those digits, R8C8 can only be 4, so it and R5C5 would have to both be 4 and R8C5 would have to be 1.
  
• Because circles on a Renban have to be consecutive, both lines would have to be German Whispers.
  
• But then, both, R6C5 and R9C7 would have to be 9 due to the 4s, and neither can be.

No hidden circles:

• Therefore the line has a length of 9, there are no hidden circles, and both circles must sum to 9.
  
• The only options for that are 36 and 45 with R5C5 being from 345 and R8C8 being from 456.
  
• On a Renban the digits in both circles must be consecutive, so, if it was 36, the line would have to be a German Whispers.
  
• But then both circles would have to have the same parity due to the odd length of the line.
  
• Therefore it's 45.
  
• 5 can't exist on a German Whispers line, so it must be a Renban.
  
• On a Renban of length 9, each digit from 1 to 9 must be featured exactly once.
  
• 45 are already in the circles. Therefore 45 cannot exist anywhere else on the line.
  
• Due to 45 in R28C8, R9C8 can't be 45 either.
  
• This leaves only one position for 4 in box 9: R8C8.
  
• Therefore R5C5 is 5.

[Xantrias]

I am really struggling with the rules of parity bridge. The rules state that line segments have circles at their endpoints, one even, one odd. In the first hint, it says that because each line has one odd and one even circle, the length of the line must be odd. Well, if I have two line segments on the line and it goes: odd--line segment--even--line segment--odd, this would give me an even length count. Can someone clarify because it is impossible for me to even attempt it. A line can consist of different line segments. Every line segment is identified through a starting circle and an end circle. One circle is odd, one is even. The digits in those circles give the total count of digits of their respective parity on the LINE. If more than one line segment exist on the same line, the line segments share one or more circles. Is this correct?

[Krest]

Originally posted by Xantrias:

A line can consist of different line segments. Every line segment is identified through a starting circle and an end circle. One circle is odd, one is even. The digits in those circles give the total count of digits of their respective parity on the LINE. If more than one line segment exist on the same line, the line segments share one or more circles. Is this correct?

The digits in the circle give the total count in the line SEGMENT, not the total line. So if a line segment goes:
circle, line space, line space, line space, circle
Then there are 5 numbers on that line segment, and the number on circle 1 + number on circle 2 equals 5.

If circle 2 1, then there the rest of the numbers on the line segment are even. If circle 2 is also connected to a second line segment, then the rest of those numbers on that line are also even.