As we approach fall, it is difficult to believe the St. Lawrence River summer season is coming to an end. Maybe next season the water levels will behave a bit better!
The Sudoku puzzle for August was a scorcher! You rarely encounter a puzzle that difficult. But if you have faith in the 8 Step approach and practice it for a period, you will someday be able to solve any Sudoku puzzle, regardless of how difficult it appears.
Puzzle #29 below, is a barrel of fun, and again Step 6 proves its worth! Print it out and give it a go!
First, we will revisit the approach, as discussed in my first T. I. 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, May 2017, June 2017, July 2017 and August 2017.
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 through the 2’s through 9’s.
The first obvious answer is C5R8 (cell in column 5, row 8) =1. C6R7=7.
NOT-SO-OBVIOUS ANSWERS … In box 8 (lower center grid of 3 x 3 cells) C4C9, C5R9 &C6R9 can contain only the digits 2, 4 & 5; therefore, a 2, 4 & 5 cannot exist in the other unsolved cells, in row 9. The viable options for C1R9, C2R9, C7R9 & C8R9 are now 3689. Note; in column 2, you’re already given answers of 368; therefore, C2R9=9. In column 7,you’re already given answers of 36; therefore, C7R9=8.
NUMBERS IN CELLS THAT CANNOT EXIST …
- In box 1, a 1 can only exist in C1R2 or C1R3; therefore, a 1 cannot exist in C1R4, C1R5 & C1R6.
- In box 1, a 2 can only exist in C1R2 or C1R3; therefore, a 2 cannot exist in C1R7, C1R8 & C1R9.
- In box 6, a 2 can only exist in C9R5 or C9R6; therefore, a 2 cannot exist in C9R7 or C9R8.
FILL IN THE OPTIONS FOR THE UNSOLVED CELLS …
Be sure to take into account the above step. The first clue we should note is that the only options possible for C1R2 & C1R3 are 12. Now your grid should look like Example #29.1 below:
STEPS 1-8 …
STEP 1 … PAIRS, TRIPLETS & QUADS
The first item we notice is in row 1. Can you spot this? The only 2 unsolved cells in row 1 that can have options 36 are C5R1 & C9R1. This is a hidden, versus obvious, pair. You may now change the options for those 2 cells to 36.
The second Step 1 we notice is in row 4. Can you spot this? The only unsolved cells in row 4 that can have options 36 is C1R4 & C5R4, another hidden pair. You may now change the options for those 2 cells to 36.
As a result, we now have an obvious pair with C5R1 & C5R4, eliminating the 3 & 6 as options from any other unsolved cell in column 5.
We also have an obvious pair with C1R4 & C1R9, eliminating the 3 & 6 as options from any other unsolved cell in column 1.
Your grid should now look like Example #29.2 below:
STEP 2 … INTERACTION & TURBO
Can you spot the Interaction in box 6? The only 2 cells in row 5 that can be a 1, are C8R5 & C9R5. One of these 2 cells must be a 1; therefore, a 1 cannot exist in any other unsolved cell, in box 6. Your grid should now look like Example #29.3 below:
There are no other Step 1-5 clues. On to Step 6.
STEP 6 … DAN’S CLOSE RELATIONSHIP 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 where these 2 cells are not in the same row or column.
2. Look for just 2 unsolved cells in a column that contain the same option where these 2 cells are not in the same box.
3. Look for just 2 unsolved cells in a row that contain the same option where these 2 cells are not in the same box.
In column 3 we find just 2 unsolved cells that contain a 3 as an option, and these 2 cells are not in the same box, which meets our criteria.
These 2 cells are highlighted in Example #29.4 below:
One of the 2 yellow highlighted cells must be a 3, and we will consider them our “starter cells”. We will give each of these 2 cells a chance to be a 3 to see if there is a cell or cells that cannot be a 3 regardless of which starter cell is truly a 3.
First, we will assume C3R7 is a 3 and mark it with a “Y” for “yes” (in pencil). If C3R7=3, then C8R7 & C9R7 cannot be a 3, so we will mark them as “N” for “no”. If this is true, then the only other cell in box 9 that can be a 3 is C8R9 and we will mark it with a “Y”. Then C8R2 is a “N”.
Next, we will assume C3R5 is a 3 and mark it with a lower-case “y” for “yes” to differentiate from the upper-case “Y” that we marked C3R7. Then C6R5 is a “n”. Then C5R4 is a “y”. Then C5R1 is an “n”. Then C6R2 is a “y”. Then C8R2 is a “n”. Then C9R1 is a “y”. And finally, C9R7 is a “n”.
We have arrived at 2 cells that have a “N,n” designation: C8R2 & C9R8. These 2 cells are not a 3 regardless of which “starter cell” is a 3; therefore, C8R2 & C9R8 cannot be a 3, eliminating a 3 as an option.
Now your grid should look like Example #29.5 below:
Now there is only 1 cell in box 3 that has a 3 as an option. C9R1=3. It follows that C5R1=6. C5R4=3. C1R4=6. C1R9=3. C8R9=6. C9R8=5. C8R8=4. C7R8=2. C2R8=7. C1R8=8. C3R9=6.
Now, your grid should look like #29.6 below:
- The only cell in box 2 that has a 3, as an option, is C6R2. C6R2=3.
- The only cell in box 3 that has a 6, as an option, is C9R3. C9R3=6.
- The only cell in box 4 that has a 3, as an option, is C3R5. C3R5=3.
- The only cell in box 9 that has a 3, as an option, is C8R7. C8R7=3.
- The only cell in column 2 that has a 2, as an option, is C2R7. C2R7=2.
- The only cell in column 7 that has a 4, as an option, is C7R4. C7R4=4 and C2R4=1.
- The only cell in row 4 that has a 7, as an option, is C8R4. C8R4=7.
Now your grid should look like Example #29.7 below:
Next, examine column 6. You find an obvious pair 24, eliminating the 2 & 4 from C6R3 & C6R6. C6R3=8. C6R6=6.
- The only cell in row 1, with an 8 as an option, is C3R1. C3R1=8.
- The only cell in row 6, with a 1 as an option, is C4R6. C4R6=1.
- The only cell in column 4 that has an 8, as an option, is C4R4. C4R4=8. C9R4=9. C9R7=1 and C7R7=9.
Now your grid should look like Example #29.8 below:
Continuing, C9R5=2. C9R6=8. C8R6=5. C8R5=1. C6R5=4.
At this point you can easily solve the balance of the puzzle, giving us the completed solution per Example #29.9 below:
In essence, one Step 6: Dan’s Yes-No Challenge, broke the puzzle wide open, illustrating the sheer power of this advanced Sudoku technique. I sincerely hope you enjoyed this puzzle.
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 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.…
THANKS Dan and THANKS to your better half, Peggy LeKander, who helps make sure the article is correct and reads well. What a team! Please keep it up….
May the gentle winds of Sudoku be at your back.
By Dan LeKander
Editor’s Note: You can see this is Puzzle #29…. Can #30 be far behind? I certainly hope so. We want to know how many you have completed.
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.
[See Jessy Kahn’s Book Review, “3 Advanced Sudoku Techniques…” by Dan LeKander, June issue of TI Life.]