Once again, after August, the River has become really quiet. Boat traffic is a fraction of summertime levels. September and October as well as May and June are my favorite months for enjoying the grand St. Lawrence River.
Clueless?
As a bonus each month this year we will start with a Sudoku puzzle in progress, where it appears there are no more obvious or not-so-obvious clues. Can you find the missing clue in Puzzle #92?
(The answer follows below after the conclusion of Puzzle #93, the feature puzzle for October)
Feature Puzzle # 93
This “impossible” puzzle was chosen to illustrate the importance of taking your time when you think you have all obvious answers and not-so-obvious answers filled in and it is time to fill in the options for the unsolved cells. Finding that really not-so-obvious clue can possibly save you an immense amount of time in solving the puzzle. We will see this in our feature puzzle #93 below . . .
DAN’S 8-STEP APPROACH TO SOLVING ALL SUDOKU PUZZLES
Once you have completed the puzzle, to the extent that you have filled-in all obvious answers and have written all potential options across the top of the unsolved cells (PUZZLE PREPARATION), 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 7Steps 1-5 are relatively common techniques and are explained in the TI LIFE articles above. Steps 6-8 are covered in detail, in Dan’s book.
PUZZLE PREPARATION
Prior to utilizing Steps 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
We will complete all of the first 4 steps in the order we observe them, until we conclude all Puzzle Preparation Step 1-4 clues.
The first thing we observe is that C6R1=9 and C1R8=4. That is it for obvious answers.
In box 2 a 4 can only exist as an option in C4R2 or C6R2; therefore, a 4 cannot exist as an option in C2R2, C7R2 or C8R2. Indicate this by placing a small 4 in the bottom of those two cells
In box 4 a 1 can only exist as an option in C2R5 or C3R5; therefore, a 1 cannot exist as an option in C7R5 or C9R5.
In box 6 a 9 can only exist as an option in C7R4 or C7R5; therefore, a 9 cannot exist as an op-tion in C7R7 or C7R8.
In box 6 an 8 can only exist as an option in C9R4 or C9R5; therefore, an 8 cannot exist as an option in C9R7, C9R8 and C9R9.
In box 7 a 3 can only exist as an option in C1R9 or C2R9; therefore, a 3 cannot exist as an option in C6R9, C8R9 and C9R9.
In box 7 a 6 can only exist as an option in C3R7 or C3R8; therefore, a 6 cannot exist as an option in C3R1, C3R3, C3R4 and C3R5.
Now your grid should look like Example #93.1 below:
Now the magic question arises! What are we missing here? See if you can figure this out on your own before reading further.
If you figured this out, great. If not, please look at row 2. What do you see? Yes, a hidden pair. The only unsolved cells in row 2 that could be a 2 and 5 are C1R2 & C7R2. We will mark our grid as such, giving us Example #93.2 below:
This completes puzzle preparation, so we will fill in the options for the unsolved cells, giving us Example #93.3 below:
Steps 1-5
I always check to see if there are any possibilities of a potentially lucrative Step 6 exercise, to give a fast conclusion to the puzzle. If you recall from previous articles, look for a number 1-9 where three cells have that number as an answer, and the three cells are not in the same row, column or box! Looking at the puzzle above, we see that numbers 2 and 5 fit that description. So, we will now proceed to Step 6: Dan’s Yes-No Challenge with Example #93.4 below:
As you can see above, column 3 has just two unsolved cells with a 2 as an option, meeting our criteria for a Step 6 exercise. We call them our starter cells, and one of the these two cells must be a 2. We will first assume C3R1 is a 2 and see which other unsolved cells can or cannot be a 2, and mark them with a “Y” for “yes” or an “N” for “no”. If C3R1=2 (Y), then C1R1, C1R2 & C9R1 =N. Then, C7R2=Y and C7R7=N.
Next, we will assume C3R4 is a 2 and mark it with a “y”. Then, we will mark which other cells can and cannot be a 2 with a “y” or “n”. Follow the markings above.
Cells with a N,n designation indicate that those cells cannot be a 2 regardless of which of the two starter cells is a 2, and the 2 can be dropped as an option for those cells.
The cells with a Y,y designation indicates that that cell is a 2 regardless of which starter cell is a 2; therefore, C7R2=2. It follows that C1R2=5. Then C3R5=5, C6R6=5.
The 5’s are quickly retired, then the 1’s and 2’s retire and the puzzle is a downhill bike ride from there, giving us the completed puzzle in Example #93.5 below:
And Puzzle #92?
Clue for Puzzle #92 … check out box 8. What do you observe?
In box 8 a 2 can exist as an option only in C4R7 or C5R7; therefore, a 2 cannot be an option in C3R7. Now focus on column 3. A 2 can only exist as an option in C3R9. C3R9=2, and then C3R6=6.]
May the gentle winds of Sudoku be at your back.
By Dan LeKander
Editor's Note: October 2021!
Dan, when not out fishing, and his proofreader (and, as they say, better half) Peggy, give us a new challenge each month. This month we have 92 & 93 = getting very close to 100. So stay tuned as we will certainly have a celebration.
It was back in January 2016, when we published a final article in Dan's Series of Steps to learn the logic of Sudoku – he asked if we would like a puzzle to solve every month … this editor said an enthusiastic… Yes, please!
If you have not already done so, I suggest you purchase Dan’s book: