When the impossible becomes possible …
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PUZZLE #43
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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
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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 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, February 2018, March 2018, April 2018. May 2018, June 2018, and July 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.
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PUZZLE PREPARATION
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 C4R1 (cell in column 4, row 1) = 8. Next, C6R2=5.
Now your grid should look like Example #43.1 below:
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Example #43.1
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NOT-SO-OBVIOUS ANSWERS … There are none.
MARK UNSOLVED CELLS WITH OPTIONS THAT CANNOT EXIST IN THOSE CELLS …
In box 9 (lower right-hand grid of 3 x 3 cells) a 1 can exist only in C7R9 or C9R9; therefore, a 1 cannot exist as an option in C4R9, C5R9 or C6R9. Pencil a small 1 in the bottom of those three cells to indicate they cannot be a 1.
In box 4 a 7 can only exist in C1R6 or C3R6; therefore, a 7 cannot exist in C4R6 or C6R6.
Options for C5R1, C5R2 & C5R3 must be 167; therefore, a 1, 6 and 7 cannot exist in the other unsolved cells in column 5.
Now your grid should look like Example #43.2 below:
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Example #43.2
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FILL IN THE OPTIONS FOR THE UNSOLVED CELLS …
Once you fill in the options for the unsolved cells, your grid should look like Example #43.3 below:
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Example 43.3
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STEPS 1-8
We will begin with Step 1, identifying Pairs, Triplets, Quads & Quints. We will search each row, column and box. Can you spot any Step 1 clues in Example #43.3 above?
Take a close look at column 2. C2R1 & C2R7 are the only two cells in column 2 that can contain a 3 and 9 and are thus, a hidden pair; therefore, we can eliminate the other options from these two cells. (You may have detected an obvious quint with C2R3, C2R4, C2R5, C2R6 and C2R8 with options 12456. Eliminating these options from C2R1 & C2R7 gives you the same results).
Now your grid should look like Example #43.4 below:
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Example #43.4
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Can we identify any other Step 1-5 clues? No!
Looks like we have quite a challenge ahead! Impossible?
We will move to Step 6: Dan’s Yes-No Challenge.
There are 3 circumstances that establish the potential for a Step 6 exercise:
- 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.
- Look for just 2 unsolved cells in a column that contain the same option where these 2 cells are not in the same box.
- 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 8 we find just 2 unsolved cells that contain the option 3 … C8R1 & C8R4. These cells are not in the same box, thereby qualifying as a candidate for a Step 6 exercise. These cells are highlighted in yellow in Example #43.5 below:
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Example #43.5
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One of these two yellow cells must be a 3. We will consider them as “driver cells” which “drive” the exercise.
Here is the logic. We will perform two exercises. First, we will assume C8R1 is the 3 and see which other cells cannot be a 3. Then we will assume C8R4 is the 3 and see which other cells cannot be a 3.
We will mark C8R1 with a “Y” and mark C8R4 with a lower case “y” to keep track of the exercise as per Example #43.6 below.
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Example #43.6
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We will start by assuming C8R1=3. Then, C2R1 and C3R1 are not a 3 (marked with a “N”). Then, C3R2=Y, C3R7 & C3R9=N, C2R7=Y and C6R7=N.
Now we will assume C8R4=3. Then, C5R4 & C6R4=n, C6R6=y, C6R7 & C6R9=n, C5R9=y and C3R9=n.
We now see in Example #43.6 above that two cells have a “N,n” designation. What does that mean? Since we know one of the two yellow highlighted cells must be a 3 and that C6R7 and C3R9 are not a 3 regardless of which yellow cell is a 3, then 3 cannot be an option for those two cells. (Please note that if you had selected C2R1 & C2R7 as the starting cells you would have achieved the same results).
Now your grid should look like Example #43.7 below:
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Example #43.7
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We still need more clues to solve the puzzle, so we will perform another Step 6 exercise.
In Example #43.8 below we have selected C8R1 & C8R5 (highlighted in yellow) as the driver cells, as they are the only two cells in column 8 with a 9 as an option.
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Example #43.8
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Again, first we assume C8R1 is the 9. Then, C1R1=N. C2R1=N. C1R2=Y. C1R9=N. C2R7=Y. C4R7=N.
Next, we assume C8R5 is the 9. Then, C4R5=n. C5R5=n. C4R6=y. C4R7=n. C2R7=y.
We find C4R7 has a “N,n” designation, so the 9 can be removed from that cell. We also find C2R7 has a “Y,y” designation, so it is a 9 regardless of which starter cell is the 9. C2R7=9.
Now your grid should look like Example #43.9 below:
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Example #43.9
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From this point the puzzle is easily solved. C2R1=3. C9R2=3. C8R4=3 and so forth.
Your final grid should now look like Example #43.10 below:
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Example #43.10
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The “impossible” just became the possible, in this case, thanks to Step 6.
May the gentle winds of Sudoku be at your back.
Dan LeKander
Editor’s note:
Do you tackle a Sudoku on your cottage veranda, sailboat cockpit, or at a campsite? And now in June… 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 three years later and on Puzzle #43!
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. Summer is a busy time, but for the past several months… Dan sent in his puzzle long before the deadline… Thank you sir!
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