Witness the twisted turns of this month’s Sudoku journey!
First, we will revisit the approach as discussed in my first 6 TI Life articles.
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.
See TI Life Puzzle Preparation:
Step 1: Sudoku Pairs, Triplets and Quads – September 2015
Step 2: Turbos & Interaction – October 2015
Step 3: Sudoku Gordonian Rectangles and Polygons – November 2015
Step 4: XY-Wings & XYZ Wings – December 2015
Step 5: X-Wings – 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 per above. Steps 6-8 are covered in detail, in Dan’s book.
Also see Sudoku Puzzle Challenge… February 2016, Sudoku Puzzle Challenge–March 2016, Sudoku Puzzle Challenge–April 2016, May 2016, June 2016, July 2016, August 2016, September 2016, October 2016, November 2016, December 2016, January 2017, February 2017, March 2017 , April 2017, and May 2017.
As a reminder, the basic rules of Sudoku are that the numbers 1-9 cannot be repeated in a row, column, or box, and there can only be one solution to the puzzle.
First, we will complete the 4 Steps of Puzzle Preparation …
1. Fill in the obvious answers
2. Fill in the not-so-obvious answers
3. Mark unsolved cells with options that cannot exist in those cells
4. Fill in the potential options for the unsolved cells
OBVIOUS ANSWERS … Start with the 1’s to see if there are any obvious 1-choice answers. Then navigate your way through the 2’s to 9’s.
The first obvious answer is C6R3=1 (cell in column 6, row 3). C2R3=2. C8R7=2. C5R8=2. C9R2=3. C4R1=3. C9R7=8. C6R2=8. C9R9=6. C1R7=6. C2R7=3. C6R9=3. C4R8=4. C1R8=7. C7R9=4. Now your grid should look like Example #26.1 below:
NOT SO OBVIOUS ANSWERS …
In box 8 (lower center grid of 3 x 3 cells), C4R7, C5R7 & C6R7 can only be a 5, 7 & 9. There is already a 5 & 7 in column 6; therefore, C6R7=9.
In row 8, C3R8 & C9R8 form a pair “19”. C7R7=1; therefore, C9R8 cannot be a 1 and is therefore a 9. C9R8=9 and C3R8=1. Now C3R9=9. C8R9=7. C9R3=7. Now your grid should look like Example #26.2 below:
NUMBERS IN CELLS THAT CANNOT EXIST …
In box 1, a 4 can only exist in C1R2 or C1R3; therefore, a 4 cannot exist in C1R4, C1R5 & C1R6. Indicate this by placing a small 4 in the bottom of these 3 cells, as this will be your reminder to later not include 4 as an option.
In box 2, a 4 can only exist in C5R2 or C5R3; therefore, a 4 cannot exist in C5R4 or C5R6.
In box 3, a 5 can only exist in C7R1 or C7R2; therefore a 5 cannot exist in C7R5 or C7R6 (a 5 already cannot exist in C7R4 because of the 5 in C6R4). Now your grid should look like Example #26.3 below:
FILL IN THE OPTIONS FOR THE UNSOLVED CELLS …
When we fill options for C2R1 we find that a 1 is the only option that can exist. C2R1=1. Now your grid should look like Example #26.4 below:
After considering 2 obvious pairs (C2R5 & C2R6 = 47 and C6R5 & C6R6 = 24) fill in the options for the unsolved cells and you grid should look like Example #26.5 below:
Before we begin Steps 1-8, you may have noticed that C9R4 is the only cell in row 4 that can be a 4. Why is that? Before we conclude C9R4=4 we should ensure this is true. The pair 4,7 in column 2 precludes C1R4 & C3R4 being a 4. The pair, 24 in column 6 precludes C4R4 & C5R4 from being a 4. C7R9=4 precludes C7R4 from being a 4. Finally, C8R1=4 precludes C8R4 from being a 4. There is the proof! C9R4=4. It follows that C9R6=5, C9R5=1 & C1R4=1. Now your grid should look like Example #26.6 below:
At this point, there are no Step 1-5 clues.
STEP 6: DAN’S YES-NO CHALLENGE
There are 3 circumstances that establish the potential for a Step 6 exercise:
1. Look for just 2 unsolved cells in a box that contain the same option and these 2 cells are not in the same row or column. An example is C4R5 & C5R6. Each of these 2 cells contain a 9 and are not in the same row or column.
2. Look for just 2 unsolved cells in a column that contain the same option and these 2 cells are not in the same box. An example is C3R1 & C3R5. Each of these 2 cells contain a 5 and are not in the same box.
3. Look for just 2 unsolved cells in a row that contain the same option and these 2 cells are not in the same box. An example is C1R1 & C7R1. Each of these 2 cells contain a 9 and are not in the same box.
After examining the 1-8’s we find no Step 6 clues. Now we will focus on the 9’s. We find only 2 unsolved cells in column 4 that contain a 9 as an option but are in different boxes, which are highlighted in yellow, in Example #26.7 below:
The two yellow highlighted cells are the “driver” cells. Hopefully they will reveal which unsolved cell(s) in the puzzle cannot have a 9 as an option.
We will first assume that C4R3 is a 9 and mark it as a “Y”, as per above example. It then follows that if C4R3 is a “Y”, then C1R3, C5R2, C5R3 & C8R3 are a “N” (not a 9). In box 3, if C8R3 is a “N”, then either C7R1 or C7R2 is a Y. Then C7R5 & C7R6 are a “N”, and C8R5 is a “Y”.
Next, we will assume that C4R5 is a 9 and mark it with a lower case “y”. It follows that C7R5 & C8R5 are a “n”. Then C7R6 is a “y”. Then C7R1 & C7R2 are a “n”. Then C8R3 is a “y”. Then C1R3 & C5R3 are a “n”.
Ok, what have we discovered? If a cell has a “N, n” designation it cannot be a 9. Why? One of the two yellow driver cells must be a 9. Regardless of which driver cell is a 9, the “N, n” designated cells are not a 9; therefore, we can eliminate the 9 as an option from cells C1R3, C5R3 & C7R5, giving us example #26.8 below:
When you find a clue, and can eliminate options from cells, it often benefits you to look back at previous steps. Can you detect any Step 1-5 clues as a result of eliminating the option 9 from 3 unsolved cells?
What is particular about row 5? By eliminating the 9 from C7R5 and reducing the options of that cell to “2,7”, we have created a Step 1 Triplet, with cells C2R5, C6R5 & C7R5. These 3 cells have a monopoly on the numbers 2,4, & 7 in row 5, so we can eliminate those numbers from any other cell in row 5. Now options for C3R5 are “5,6” and options for C4R5 are “6,9”.
Now your grid should look like Example #26.9 below:
Next, notice the 6 yellow highlighted cells in the example above. If C7R6 was neither an 8 or 9, its options would be 2,7. This would create a Step 4 Gordonian Polygon, in which there would be 2 equally valid answers to the puzzle. Since one rule of Sudoku is that there can only be 1 valid answer, C7R6 must be an 8 or 9, eliminating the 2 & 7 from C7R6. Now your grid should look like Example #26.10 below:
Now look at column 7 in the example above. Can you find a Step 1 hidden pair? C7R4 & C7R5 are the only two cells in column 7 that have both options “2,7”, eliminating the 8 from C7R4. Now your grid should look like Example #26.11 below:
The previous clue, eliminating the 8 from C7R4, sets up a potential Step 2 Turbo in box 6, with cells C7R6 & C8R4 as highlighted in yellow, in the example above. There is only 1 other cell in column 7 that contains an 8 as an option, which is C7R1, highlighted in blue. There is only 1 other cell in row 4 that contains an 8 as an option, which is C3R4. In the cell where the 2 blue cells intersect, an 8 cannot be an option, eliminating the 8 from C3R1. C3R1=5. From this point, the puzzle is easily solved, giving us the completed puzzle as per Example #26.12 below:
In the beginning of this article, I purposely did not mention that this is an extremely difficult puzzle. To easily solve this puzzle and other very difficult puzzles, it is imperative to have a total grasp of Steps 1-5. If you need assistance with Steps 1-5, you can review my previous articles in the TI Life as mentioned earlier.
Thank you for your interest. May the gentle winds of Sudoku be at your back.
(Photo above… Sudoku is for everyone… you’re never too young to start!)
Do you tackle a Sudoku on your cottage veranda, sailboat cockpit, or at a campsite? TI Life is taking full advantage of Dan LeKander, from Wellesley Island, who is a Sudoku expert and author of “3 Advanced Sudoku Techniques – That Will Change Your Game Forever!”
In January 2016, we published a final article in his original series – but many of us enjoy using “Dan’s Steps,” so when he asked if we would like a puzzle to solve every month … this editor said an enthusiastic… Yes, please!
I suggest you try this relatively difficult puzzle and that you also purchase Dan’s book, “3 Advanced Sudoku Techniques, That Will Change Your Game Forever!”
Most importantly, I ask that you leave comments on any part of his series and throughout the year. Remember when your teacher said – no such thing as a silly question – as we can all learn together.
Dan’s book is available online, amazon.com and on ebay.com.
Purchase of a book includes a 50-page blank grid pad, 33 black and two green tokens, to assist with Step 6.…
Now, with the new year well underway, I want to say THANKS Dan and THANKS to his better half, Peggy LeKander, who helps make sure the article is correct and reads well. What a team!
Do you have suggestions for future articles? You can post on this article or contact me directly at firstname.lastname@example.org.