This month we are going on a journey, to add the finishing touches to Puzzle Preparation. You might say that this is the extreme of “not-so-obvious clues.” Spotting these clues will save you significant time, in solving a puzzle. We will look at Puzzle #35 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.
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, March 2016, 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, May 2017, June 2017, July 2017, August 2017, September 2017, October 2017 , November 2017 , December 2017, January 2018 and February 2018.
As a reminder, the basic rules of Sudoku are that the numbers 1-9 must be contained and cannot be repeated in a row, column, or box, and there can only be one solution to the puzzle.
Prior to utilizing techniques first complete the 4 Steps of Puzzle Preparation …
- 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
OBVIOUS ANSWERS …
Start with the 1’s to see if there are any obvious 1-choice answers. Then navigate the 2’s through 9’s.
The first obvious answer is C2R7=4 (cell in column2, row 7). Then C3R9=2. C8R5=6. Now your grid should look like Example #35.1 below:
NOT-SO-OBVIOUS ANSWERS …
Here is another approach to this phase of Puzzle Preparation. Let’s look for obvious Pairs & Triplets, while searching for not-so-obvious answers. Look at box 4 (middle left box of 3 x 3 cells). There are 2 cells in box 4 that could be a 38, which are C1R5 & C2R5. Therefore, this is Pair and we will mark them with a small “38” in the upper part of the cells as their only choice for options as per Example #35.1 below:
C1R5 & C2R5 have a monopoly in box 4. These 2 cells also have a monopoly in row 5; therefore, no other cell in row 5 can have a 3 or 8 as an option. Now you can clearly see that the only cell in box 5 that can be a 3 is C5R6. C5R6=3. Now the only cell in box 5 that can be an 8 is C4R6. C4R6=8. Now look again at row 6. The 7 in box 6 prevents C7R6, C8R6 & C9R6 from being a 7; therefore, the only remaining unsolved cell in row 6 that can be a 7 is C3R6. C3R6=7. Then C1R2=7, C8R1=7 & C9R9=7. Now your grid should look like Example #35.3 below:
We are still in the Puzzle Preparation phase, but incorporating Step 1: Pairs, Triplets & Quads. Let’s look for other Pairs or Triplets. The only choice in box 6 for options 45 are C9R4 & C9R5, which is another obvious Pair. Then, the only possible options for C7R1, C8R1 & C9R1 are 129. The only possible options for C1R7, C1R8 & C1R9 are 169. Mark those 8 cells with their only possible options and your grid should now look like Example #35.4 below:
Now you note that the only cell in column 9 that can be a 3 is C9R2. C9R2=3. Then C2R1=3. C2R5=8 & C1R5=3. Now your grid should look like Example #35.5 below:
From here you can see that the only 2 options for C1R3 & C1R4 are 58. Since there is an 8 in row 4, C1R3 must be the 8 and C1R4=5. Now C9R4=4 & C9R5=5. Now C2R4 must be a 2. Now the only 2 choices for option in C2R2 & C2R3 are 19. Since there is a 9 in C4R2, C2R2=1 & C2R3=9. Also, fill in the obvious Pair in column 3, box 4 and the Triplet in column 3, box 1. Now your grid should look like Example #35.6 below:
We can now see that C6R3=1. C7R1=9. The only options for the 3 unsolved cells in column 9 are 289. Since there already an 8 & 9 in row 3, C9R3=2. Then C9R6=9 & C9R8=8. Then C6R9=8. C6R7=3. C8R9=3. C7R2=8. C5R1=8. C7R3=6. Now the only cell in row 9 that can be a 9 is C1R9. C1R9=9. C1R7=1 & C1R8=6. C4R7=7.
Then C4R9=6 & C7R9=1. C7R6=2 & C8R6=1.
The only options for C7R7 & C7R8 are 45. Since there is already a 4 in row 7, C7R7=5 & C7R8=4.
Now your grid should look like Example #35.7 below:
Now look at row 4. The only possible options for the 4 unsolved cells are 1679. There are already a 679 in column 4; therefore, C4R4=1. C3R4=9 & C3R5=1. Then C5R8=1. Now the only cell in row 4 that can be a 7 is C6R4. C6R4=7. C5R4=6. Now your grid should look like Example #35.8 below:
Look at box 8. The only cell that can be a 5 is C4R8. C4R8=5. Now the only options for C4R1 & C4R5 are 24. Since there is already a 2 in row 1, C4R1=4 & C4R5=2. The only cell in column 5 that can be a 5 is C5R2. C5R2=5. Now the only options for C5R5 & C5R6 are 49. Since there is already a 4 in column 5, C5R5=9 & C6R5=4. Then, C5R7=2, C6R2=2 & C6R1=6. C6R8=9. C8R7=9. C8R8=2. C3R1=5. C3R3=4. C3R2=6. C8R2=4 & C8R3=5, giving us the final puzzle as Example #35.9 below:
Well, what just happened here? By recognizing Pairs & Triplets while performing “Not-So-Obvious Clues in the Puzzle Preparation phase, we can sometimes successfully complete a puzzle that appears very difficult.
May the gentle winds of Sudoku be at your back.
Do you tackle a Sudoku on your cottage veranda, sailboat cockpit, or at a campsite? And now in MARCH… how about the beach!
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 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! Now we are two years later and on Puzzle #34!
I suggest you purchase Dan’s book, “3 Advanced Sudoku Techniques, That Will Change Your Game Forever!”
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.…
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.
As always, I want to thank Dan…and his proof reader… Peggy! what a lot of work they put into our TI Life articles.
By Dan LeKander, Wellesley Island
Dan LeKander and his wife Peggy, have been seasonal residents of Fineview, on Wellesley Island, NY, since 1983. In addition to being a Sudoku addict, Dan explores the 1000 Islands to enjoy the wildlife, beauty and of course, Catch-and Release bass fishing.
Editor’s Note: Wow; Number 34! How many have you completed?
[See Jessy Kahn’s Book Review, “3 Advanced Sudoku Techniques…” by Dan LeKander, June issue of TI Life.]