Have fun with the new Bonus Section following this month’s puzzle!
First, we will revisit the approach as discussed in my first six Thousand Islands 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, and June 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.
As a reminder, each row, column & box must contain all numbers 1-9.
Prior to utilizing techniques first 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 WTH OPTIONS THAT CANNOT EXIST IN THOSE CELLS
4. 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 C1R5=1 (cell in column 1, row 5). C9R9=6. C7R5=6. C2R6=6. C1R1=6. C9R5=3. C4R4=3. C9R6=9. Now your grid should look like Example 27.1 below:
NOT-SO-OBVIOUS ANSWERS …
In box 7 (lower left grid of 3 x 3 cells) a 3 can exist only in cells C3R7 or C3R9; therefore, C3R2 & C3R3 cannot be a 3. The only cell in box 1 that can be a 3 is C2R2. C2R2=3.
In box 7 a 9 can only exist in C1R7 or C1R8; therefore, a 9 cannot exist in C1R2 or C1R3. The only cell in box 1 that can be a 9 is C2R3. C2R3=9. Then C5R2=9 & C6R5=9.
In box 4 a 2 can only exist in C2R5 or C3R5; therefore, a 2 cannot exist in C4R5 or C5R5. The only cell in box 5 that can be a 2 is C6R6. C6R6=2.
In box 6 the only possible numbers for the unsolved cells are 5, 7 & 8; therefore, the only options for C8R7, C8R8 & C8R9 are 1,2 &4. In row 8 there is already a 1 & 2; therefore, C8R8=4. Now your grid should look like Example 27.2 below:
NUMBERS IN CELLS THAT CANNOT EXIST …
In box 3 a 1 can exist only in C9R2 or C9R3; therefore, a 1 cannot exist in C9R7 (a 1 cannot exist in C9R8 either but the 1 in C2R8 already precludes C9R8 from being a 1). Indicate this by placing a small 1 in the bottom of C9R7 as a reminder to not include a 1 as an option when completing the next step.
In box 3 a 2 can exist only in C7R1 or C7R3; therefore, a 2 cannot exist in C7R7 (a 2 cannot exist in C7R8 either, but the 2 in C4R8 already precludes C7R8 from being a 2).
In box 5 a 4 can exist only in C4R5 or C5R5; therefore a 4 cannot exist in C2R5 or C3R5.
In box 1 a 7 can exist only in C1R3 or C3R3; therefore a 7 cannot exist in C5R3 or C6R3.
FILL IN THE OPTIONS FOR THE UNSOLVED CELLS … Be sure to process obvious pairs as you discover them. Now your grid should look like Example #27.3 below:
There are no STEP 1 clues (Pair, triplets, quads).
STEP 2: INTERACTION & TURBOS … As you search each box for Interactions and Turbos, you immediately find an Interaction in box 1: in row 2 in box 1 either C1R2 or C3R2 must be a 2, as there are no other cells in row 2 that can be a 2; therefore, in box 1 no other unsolved cell can be a 2, eliminating a 2 as an option from C2R1, C1R3 & C3R3. Now your grid should look like Example #27.4 below:
Example # 27.4
By eliminating the 2 as an option from C2R1 we have created an obvious pair in column 2, giving us the opportunity to “look backwards” to …
STEP 1: PAIRS, TRIPLETS & QUADS. Processing the obvious pair in column 2 leads us to the conclusion that C2R5 cannot be an 8; therefore, C2R5=2. This reduces the options in C3R5 to “78”. Now your grid should look like Example #27.5 below:
Example # 27.5
STEP 4: XY & XYZ – WINGS …
Examine C2R1, C3R3 & C3R5. They form an XYZ-Wing. C3R3 is the “driver cell”. If C3R3 is an 8, then C3R2 is not an 8. If C3R2 is a 7, then C3R5=8 and C3R2 is not an 8. If C3R3 is a 4, then C2R1=8 and C3R2 is not an 8. So regardless if C3R2 is a 4, 7 or 8, C3R2 is not an 8, eliminating an 8 from C3R2; therefore, C3R2=2. We can now eliminate a 2 as an option from C1R2, C3R7 & C3R9. Now your grid should look like Example #27.6 below:
Example # 27.6
Now examine C1R2, C2R1 & C9R1. They form an XY-WING. C2R1 is the “driver cell”. If C2R1 is a 4, then C9R1=5 and C9R2 is not a 5. If C2R1 is an 8, then C1R2 is a 5 and C9R2 is not a 5. So regardless if C2R1 is a 4 or 8, C9R2 is not a 5; therefore, C9R2=1. We can now eliminate a 1 as an option from C4R2 & C9R3. Now your grid should look like Example #27.7 below:
Example # 27.7
Now note that the only choice for a 1 in box 2 is C6R3. C6R3=1. Then C6R9=8. C4R7=1. C8R7=2. C8R9=1. Now options for C3R9 & C5R9 are 34; therefore, C1R9 cannot be a 4. C1R9=2. C4R5=4.
We have now created an Interaction in box 2. The only cells in column 4 that can be a 5 are C4R1 & C4R2. The other unsolved cells in box 2 cannot be a 5.
Now C5R3 & C7R3 have options 28, eliminating an 8 from C1R3 & C3R3.
Now your grid should look like Example #27.8 below:
Example # 27.8
Can you now locate another XY or XYZ-Wing?
Check out C2R1, C3R3 & C3R5 (were those cells previously an XYZ-Wing? Yes!) This is an XY-Wing. Again, C3R3 is the driver cell. If C3R3 is a 4, then C2R1=8 and C2R4 is not an 8. If C3R3 is a 7, then C3R5=8 and C2R4 is not an 8. Regardless if C3R3 is a 4 or 7, C2R4 is not an 8. C2R4=4. From this point the puzzle is “unlocked” and easily solved.
Let’s assume you missed this clue and went on to Step 6: Dan’s Yes-No Challenge. When you scan the eights, you find only 2 unsolved cells in row 2 that are not in the same box, meeting one of the conditions to possibly have a successful Step 6. If C4R2=8, then C4R6 is not an 8, then C5R5=8 and C3R5 is not an 8. If C1R2=8, then C1R7 & C1R8 are not an 8, then C3R7=8, and then C3R5 is not an 8. So regardless of which cell in row 2 is an 8, C3R5 is not an 8. C3R5=7. And again, the puzzle is easily solved from here.
You will find this time and time again; there are usually multiple ways to solve a Sudoku puzzle!
Puzzle 27 is about as difficult of a puzzle to solve as you will find in print.
Please see Example 27.9 below, which is the completed puzzle:
Example # 27.9
BONUS FOR JULY
If you like to “race the clock”, below is a puzzle to time your abilities. You will notice two unusual aspects of this puzzle …
1. There are 17 given answers. If you count the given answers of Sudoku puzzles you find that there are usually 21-30, whereas the puzzles usually get more difficult as there are fewer given answers. Of course, there are many exceptions to this observation. This puzzle has 17 given answers, which is extremely rare!
2. Most Sudoku puzzles have the given answers in cells such that the placement in the opposite boxes form a mirror image. Many Sudoku purists agree that this must be a condition for a valid Sudoku puzzle. I am not sure who made this rule, but a minority of people who publish Sudoku puzzles do not agree. This puzzle is of this nature. Just compare the placement of the given answers of this puzzle with Puzzle 27.
You may surmise by the bonus puzzle that with 17 given answers, this puzzle is extremely difficult. Interestingly it is not that difficult. Here is a clue: think Puzzle Preparation and specifically “not-so-obvious answers”! Give it a go and rate your performance.
I have taken the liberty of classifying personal progress. For this puzzle …
Accomplished 30 minutes
Expert 20 minutes
Master 13 minutes
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.…
THANKS Dan and THANKS to his better half, Peggy LeKander, who helps make sure the article is correct and reads well. What a team! Please keep it up….
Enjoy. May the gentle winds of Sudoku be at your back!
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.]
Do you have suggestions for future articles or do you want any Step 1-8 techniques explained further? You can post on this article or contact me directly at firstname.lastname@example.org.