Here we are in the middle of January and the first month of a brand-new year. May all your Sudoku wishes come true. This is an activity where you can keep learning. May you learn and grow with Sudoku.
Clueless?
As a bonus each month we 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 #98?
(The answer follows after the conclusion of Puzzle #99, the feature puzzle for January)
Feature Puzzle
If you have been following my November and December 2021 articles, you may have a much easier time with the following “impossible” puzzle this month, Puzzle #99 . . .
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 C2R5=2. Next, C8R2=5 & C7R1=7. We now know that C9R1, C9R2 & C9R3 can only have options 249. We now know that C9R4, C9R6, C9R7 & C9R9 can only have options 1368. The only unsolved cells in Box 4 that can have a 9 as an option are C3R4, C3R5 & C3R6; therefore, C3R1, C3R2 & C3R3 cannot have option 9.
These clues give us Example #99.1 below:
This concludes Puzzle Preparation steps 1-4, but before we complete step 5 by filling in the options for all the unsolved cells, we will look at the puzzle and ask if there are any good Step 6 potentials. As in previous articles, we determined a particular number was a potentially successful Step 6 exercise if that number appears as a given answer in 3 separate boxes, such that the boxes are not side-by-side, nor over each other. Which numbers are good candidates? Yes, 3 and 6.
We will first pick the number 3 and perform the exercise. At this point at your home, you would put green tokens on two starter cells that are 3’s and black tokens on all unsolved cells that could have the option 3. For purposed of illustration, in Example #99.2 below we will highlight two starter cells in green, and the unsolved cells that could be a 3 in yellow (vs black).
Now we will perform the exercise. We will use C5R2 and C5R6 as our starter cells. One of these 2 unsolved cells must be 3. We will start with C5R2 and assume it is the 3. Then we can see that C1R2 & C3R2 cannot be a 3, then C3R1=3, C3R7 cannot be a 3.
Next, we assume that C5R6 is the 3. It follows that C7R7 & C9R7 cannot be a 3, then C7R5=3, then C7R7 &C7R8 cannot be a 3, then C9R7=3, then C1R7 & C3R7 cannot be a 3, then C1R8=3, and C1R2 cannot be a 3. So regardless of which starter cell is a 3, C1R2 & C3R7 cannot be a 3. This exercise eliminates two cells from being a 3, but does not give us further clues.
Now we will pick the number 6 and perform the exercise. We will color code the 2 starter cells in green and the unsolved cells that cannot be 6 in yellow, giving us Example #99.3 below:
We will begin with starter cell C1R3 and assume it is the 6. Then, C4R3 & C5R3 are not a 6, C4R1=6, C4R4 & C4R5 are not a 6, C5R4=6, C8R4 & C9R4 are not a 6, C8R5=6, C8R8 & C8R9 are not a 6, C9R9=6, and C3R9 is not a 6.
Now we will assume C1R8 is the 6, and right away we know that C3R9 is not a 6. Regardless of whether C1R3 or C1R8 is a 6, C3R9 is not a 6; therefore, in box 7 only C1R8 can be a 6. C1R8=6.
From this point it is all downhill. The 6’s are soon dispatched, followed by the 3’s and followed by the 1’s, leading to a rapid conclusion per Example #99.4 below:
A Step 6 exercise may not lead to a clue, but when a Step 6 leads to a conclusion, it produces accurate results 100% of the time. It is much easier to use props such as the green or black plastic tokens, or by labeling the cells with a Y or N (as done in previous articles). In either case, doing this exercise prior to filling in the options for the unsolved cells can often lead to a much faster solution.
May the gentle winds of Sudoku be at your back.
Dan LeKander
Clue for Puzzle #98 … did you find the clue? If not, read on.
Let’s look at column 2. We see that C2R3 & C2R4 are the only unsolved cells in column 2 that can have options 1 & 7, so fill in these options. This leaves C2R2 as the remaining unsolved cell in column 2 that can have a 4 as an option. C2R2=4. Now in box 3 the only unsolved cells that can have options 147 are C7R1, C8R1 & C9R2.
Editor's Note: January 2022!
Dan's fishing season has moved to the sunny south, but you can see from Puzzles #98 & #99 he is still creating puzzles for TI Life readers. Thanks Dan and your wonderful proofreader (and, as they say, better half) Peggy, once again you have given us a nice challenge.
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: