Please welcome the last four Sudoku puzzles for 2022!
We start with a Sudoku puzzle in progress, where it appears that there are no more obvious or not-so-obvious clues. Can you find the hidden clue in Puzzle #129?
(The answer follows the conclusion of Puzzle #132, the feature puzzle for December)
Difficult rating … 2/10 (Rating based on puzzles not requiring advanced techniques)
Puzzle #130 should be fun for you!
Impossible to solve?
About one puzzle in a thousand is “profoundly difficult”. This month we again have a rare opportunity to explore the depths of Sudoku with Puzzle #131.
Difficult rating … 4/10. (Rating based on puzzles requiring advanced techniques)
Prior to utilizing techniques 1-8, complete the 5 Steps of Puzzle Preparation …
- FILL IN DATA FROM OBSERVATIONS
- FILL IN OBVIOUS ANSWERS
- FILL IN NOT-SO-OBVIOUS ANSWERS
- MARK UNSOLVED CELLS WITH OPTIONS THAT CANNOT EXIST IN THOSE CELLS
- FILL IN THE OPTIONS FOR THE UNSOLVED CELLS
The first thing we observe is that C9R2=9 & C2R9=3.
C1R7 & C2R7 have options 4 & 8.
C3R7, C3R8 & C3R9 are limited to options 2, 6 & 9.
C3R1, C3R4 & C3R6 are limited to options 1, 5 & 7.
There is already a 5 & 7 in row 4, so, C3R4=1, C3R1=7 and C3R6=5.
In box 3, a 4 can exist as an option only in C7R1 & C7R2; thus, a 4 cannot exist as an option in C7R4, C7R6, C7R7, C7R8 & C7R9.
In box 5 a 9 can exist as an option only in C4R6 & C5R6; therefore, a 9 cannot exist as an option in C1R6 & C2R6. Indicate this by placing a small 9 in the bottom of those two cells.
In row 3 there is a hidden quad. C1R3, C7R3, C8R3 & C9R3 are limited to options 2, 3, 6 & 7; therefore, C2R3, C4R3 & C5R3 are limited to options 1, 5 & 8.
In box 2 a 7 can exist as an option only in C4R2 & C6R2; therefore, a 7 cannot exist as an option in C8R2.
Now your grid should look like Example #132.1 below:
This completes Puzzle Preparation Steps 1-4. Next, we will fill in options for all unsolved cells, giving us Example #132.2 below:
Dan recommends the following Steps to complete the puzzle.
Step 1: Sudoku Pairs, Triplets and Quads – See September 2015
Step 2: Turbos & Interaction – See October 2015
Step 3: Sudoku Gordonian Rectangles and Polygons – See November 2015
Step 4: XY-Wings & XYZ Wings – See December 2015
Step 5: X-Wings – See January 2016
Step 6: DAN’S YES/NO CHALLENGE
Step 7: DAN’S CLOSE RELATIONSHIP CHALLENGE
Step 8: AN EXPANSION OF STEP 7. Steps 1-5 are relatively common techniques and are explained in the TI LIFE articles. Steps 6-Posts 8 are covered in detail, in Dan’s book.
The first thing we notice is that there is a hidden pair in column 6. C6R2 & C6R9 are the only two unsolved cells in column 6 that can have options 5 & 7. Now your grid should look like Ex-ample #132.3 below:
That completes techniques 1-5. There are no Step 6 candidates, so we will move on to Step 7, Dan’s Close Relationship Challenge.
We will select C4R3 as our starter cell, with a sequence of 1,8. We will annotate this on the 2nd level of this cell, as per Example #132.4 below:
We annotate the unsolved cells that have a 1 as their option that are adjacent to the starter cell with “N1” indicating that those cells cannot be a 1 if the starting cell is a 1. As we track the 8 through the puzzle, if any of these N1 cells is a value other than 1, it would indicate that this cell is not a 1 regardless if the starter cell is a 1 or 8, and the 1 could be deleted as an option for that cell. We will track the 8 through the puzzle in Example #132.5 below.
However, before we perform this exercise, we will list the potential outcomes …
• The tracking of the second number of the starter cell doesn’t reach the N9 cells, and there-fore, the exercise is unsuccessful.
• The tracking of the second number goes entirely through the puzzle without a conflict, in-dicating that the 2nd number is correct for the starter cell and you have solved the puzzle.
• The tracking of the second number creates a conflict, such as a number showing up twice in a row, column or box. Or it could show up by having no cell for a particular number in a row, column or box. Regardless of how the conflict arises, it would mean the second number is incorrect for that cell, and therefore, the answer to the starter cell is the first number.
We will now track the 8 through the puzzle above on the third level of the unsolved cells to pre-serve the integrity of the original puzzle.
As you can see from example above, in tracking the 8 through the puzzle, we have reached an impasse. Look at column 4. No unsolved cell can be a 7. That is a conflict. So, now we know that C4R3 cannot be an 8; therefore, C4R3=1.
(Please note: when you track the 8 through the puzzle you may find a different conflict. Where the conflict occurs is dependent on how you track the 8.)
The puzzle is now easily solved, giving us Example #132.6 below:
May the gentle winds of Sudoku be at your back.
By Dan LeKander
Clue for Puzzle #129 … did you find the clue? If not, read on.
Check row 7. What do you see?
We see that C5R7, C7R7, C8R7 & C9R7 cannot have options 2, 5 or 7. Now, C1R7, C2R7 & C6R7 are limited to options 2, 5 & 7. Since there is already a 2 and 7 in column 1, C1R7=5.
Editor's Note: Recently someone wrote to ask how to fill them out online. Unfortunately, you need to print them yourself - but that is easy to do and I know you will have just as much fun.
And, if you have not already done so, I suggest you purchase Dan’s book: