I searched for x wing and the bone. Im thinking colors but not sure.
5
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3$\begingroup$ Look at all the left 3x3 blocks. All of them are missing 3s, but the top left and bottom left blocks can only have 3s in the left or center column. This means that for the middle left block, 3 must be in the right column. $\endgroup$– votbearNov 21, 2017 at 6:15
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1$\begingroup$ From this you can deduce the position of 5 for the middle left block, and the rest will come from there. $\endgroup$– votbearNov 21, 2017 at 6:16
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$\begingroup$ Which is the original problem? The one with black numbers or the one with the blue numbers? It seems it is partially solved / attempted to solve a sudoku, which is abandoned due to an initial faulty start/middle game. $\endgroup$– Mea Culpa NayNov 21, 2017 at 10:30
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$\begingroup$ Black is the original puzzle. You are correct. Either my blue entries were made in error or I overlooked something simple such as the 3's being isolated to column 3 $\endgroup$– TS79Nov 21, 2017 at 14:21
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$\begingroup$ Related: Techniques to Solve Sudoku Puzzles. $\endgroup$– Kevin CruijssenNov 21, 2017 at 17:51
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4 Answers
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3
I found a chain:
If R9C9 is a 5, then R2C9 must be a 4, R4C9 must be a 3, R4C2 must be 5, R4C5 must be a 4, R1C5 must be a 5, R1C8 must be a 4, R2C9 must be a 5 and R9C9 must be a 3.
This is a contradiction, so the initial 5 was wrong and R9C9 must be a 3.
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$\begingroup$ Thank you. I have always tried to avoid using this method (chain?) due to suspicions I must be missing something if I am reduced to playing out 2 possible solutions. Is this considered a valid technique for Sudoku - are there puzzles which require this method which are not solvable with other methods? No criticism intended - I am simply wondering if there was any merit to my assumption. $\endgroup$– TS79Nov 21, 2017 at 14:35
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$\begingroup$ In light of the found 5 by VotBear and boboquack it seems your solution is the only way to move forward. $\endgroup$– TS79Nov 21, 2017 at 14:42
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$\begingroup$ @TS79 "Is this a valid technique?" Yes. Anything that can logically reduce the candidates is a valid technique. "Are there puzzles which require this method which are not solvable with other methods?" I don't think that any specific technique is "required". There is more than one way to reduce candidates. But there are puzzles that cannot be solved by "easy" techniques only, like naked subsets. $\endgroup$– Dennis_ENov 21, 2017 at 14:47
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Take the:
Third column
And observe that:
There must be a 3 in the middle group of 3
So:
The top-middle box of the middle cell cannot contain 3, and must be 5
Image:
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Look at the...
First (leftmost) column. You have a Triple: 1, 3 and 5. That triple exists in the top left and bottom left group. This means you can strike the potential 3 and 5 in the middle left group.
This leaves a Single 5 in the middle left group. Write that in and strike potential 5's in the corresponding group, row and column
Now you have a...
Deadly Pattern of 1's and 3's. These are in the top left group, and bottom left group. The only odd square out is the one that contains a 5. You must write that 5 or you have a dual solution to the puzzle.
After you write that 5, everything else solves itself trivially.
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Start with:
Column 9 Row 9 right bottom cell
You have only two choices 3 or 5
Starting with 5 in the right bottom cell will end with error
Start with 3 and all will follow logically
The Solution:
