Equality Cages 132: Equally Colored Lines: Let's Solve this Ambiguous Sudoku

#sudoku #SudokuSleuth
Today's Puzzle:
More Equality Cages from gUBBLOR it’s another ambigious puzzle for us to determine and solve!
It’s more approachable than it may seem initially 😉
Link to Play:
Equality Cages 132: Equally colored lines by gUBBLOR
tinyurl.com/SudokuSleuthEqual...
Rules:
Normal Sudoku rules apply. Place the digits 1 through 9 in each empty cell. Digits must not repeat within the same row, column, or box.
Equality cages: Cages must have an equal number of low (1,2,3,4) and high (6,7,8,9) digits AND an equal number of even (2,4,6,8) and odd (1,3,7,9) digits. Equality cages can never contain 5. Digits may not repeat in a cage.
Kropki dots: A black dot between cells indicates cell values with a 2:1 ratio. Not all dots are shown.
X: Adjacent cells connected with an X must sum to 10. Not all X's are shown.
Ambiguous lines: There are lines of four different colors in the puzzle, and four different line constraints. It's up to the solver to deduce which color is paired with which constraint. Each color has only one constraint it identifies as, but lines are allowed to act as more than one constraint. The lines could be any of these four;
1. Thermometers - Digits along each thermometer must increase starting from the bulb end. Bulbs are always at the end of the line, but which end must be deduced by the solver.
2. Arrows - The digits along each arrow must sum to the digit in the circled cell. Circled cells are always at the end of the line, but which end must be deduced by the solver. Digits may repeat on arrows.
3. Dutch Whispers - Adjacent digits along each Dutch Whisper line must have a difference of at least 4. Digits may repeat on the line.
4. Shifter Lines - Adjacent digits within the same box on a shifter line share both parity (even/odd) AND polarity (low/high). Whenever the line enters a new box either the parity OR the polarity shifts, never both. Shifter lines can never have 5 on it. Digits may repeat on lines.
Chapters:
00:00:00 Intro
00:02:29 Rules
00:10:08 Solve
00:40:02 Outro
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/ sudokusleuth

[@gubblor2545]

Very nice, I'm really enjoying disambiguation like this, more like this is probably coming soon! Great solve!

[@SudokuSleuth]

Thank you for the puzzle gUBBLOR, I mean Sinclair 😉 Sorry about the mixup!

[@gubblor2545]

@@SudokuSleuth all good, it made me giggle a bit! 😊

[@anaayoung9142]

Somehow I knew this was my country's flag, but it was weird!! 😂 I need to confess, it was fun but messy! At the end I did the green line at boxes 7 and 8 by luck, because I was thinking that it was a thermo!! I don't know how it worked (it was the other way). I only saw this at the almost end when I need to place the bulb in the others 😅 Great! It is important that it solved 😂 Thank you! 😊

[@GillesGouaillardet]

At 18' you rule out red being an arrow because R2C6 is not a 3. But what if it is a 9? Did I miss something?

[@samueldeandrade8535]

You are absolutely right.

[@SudokuSleuth]

Oooh, good point!

[@SudokuSleuth]

Ok got it If you have a 9 in the equality cage, you’re forced to put 24 on the blue shifter line That doesn’t work as 13 and 68 are not available in box 3 I missed a step there

[@samueldeandrade8535]

It turns out the 9 don't work because of the Blue/Shifter line above. If Red is Arrow, then it is 9, the cell above would be 24, making the Blue/Shifter line in Box 2 a 24 pair, so the other side in Box 3 can't be completed, because it would be 13 or 68, contradicting the 36 Kropki dot. It is the reasoning he does later.

[@ryuuguu01]

I agree with you. he put 9 as a pencil mark a little later. it is not until 22:08 that he can say it thermometer because the 8 in R1C6 rules out a 9 in R2C6. Oops, I now see that he used that green is an arrow line to get the 26 pair that forced the 8. It can shown that it is a 68 not a 24 on the blue shifter. A 24 would need a 13 or 68 on the other side, and 3&6 are already in box 3.

[@samueldeandrade8535]

Oh my Euler!!! This puzzle is so FUN!

[@psiphiorg]

I'm generally hesitant about disambiguation puzzles, but this one was one I could wrap my mind around. My time was 28:47, solver number 158.

[@SudokuSleuth]

I'm with you. Ambigigiouty are usually my nemesis. There are definitley puzzles that I don't enjoy and don't post as a result.

[@jdyerjdyer]

Got bogged down twice and had to back track once. Still, 66 minutes isn't too bad, I don't think?

[@SudokuSleuth]

I agree, nicely done!

[@samueldeandrade8535]

It is written "James Sinclaire" in the video's description. It is "Sinclair", isn't it?

[@SudokuSleuth]

Thank you, fixed!

[@samueldeandrade8535]

@@SudokuSleuth :D

[@gubblor2545]

@@SudokuSleuth Sinclair had nothing to do with the puzzle at all though :P