T. I. LIFE PUZZLE FOR APRIL 2018
Last month we looked at a time saving aspect of Puzzle Preparation. I have been asked to further expand on this topic, so we will present a puzzle (#36 below) and utilize this technique. At the end of this article there are puzzles for you to practice this technique.
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Puzzle #36
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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 and March 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 C7R8=5 (cell in column 7, row 8). Now your grid should look like Example #36.1 below:
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Example #36.1
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NOT-SO-OBVIOUS ANSWERS …
Before we begin this exercise, we will look for obvious Pairs, Triplets & Quads and mark the options of the cells in the top of the cells. First look at box 1 (upper left box of 3 X3 cells). You will notice that a 5 & 7 can exist only in two cells, C2R1 and C2R3, so we will mark those cells with options 57. Next, in box 7 a 4 & 8 can only exist in two cells, C2R7 and C2R8. In box 9 a 2 & 7 can only exist in two cells, C7R7 and C8R7. The only choices for cells C9R7, C9R8 & C9R9 are now 6,8 &9. Since there is a 6 in C6R7, the options for C9R7 are 89. The options for C9R8 are 689, and the options for C9R9 are 69. Now your grid should look like Example #36.2 below:
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Example #36.2
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Now we will search for Not-Obvious clues. The obvious pair “48” in C2R7 and C2R8 precludes a 4 and 8 from existing as options in the other unsolved cells in column 2. The only choice for an unsolved cell in box 4 to have a 4 is C3R5. C3R5=4. As a result, C8R6=4. Then C9R1=4. C4R2=4.
In box 8 a 7 can exist as an option only in C4R7 or C4R9; therefore, a 7 cannot exist in C4R4 or C4R6. The only cell in box 5 that can be a 7 is C6R6. C6R6=7.
We now see that C5R3=8. Your grid should now look like Example #36.3 below:
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Example #36.3
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Now we can see that the only cell in box 4 that can be an 8 is C3R4. C3R4=8.
Because of the pair 57 in C2R1 & C2R3, the only cell in box 4 that can be a 7 is C1R4. C1R4=7.
Because of the pair 27 in C7R7 & C8R7, the only cell in box 8 that can be a 7 is C4R9. C4R9=7.
Now C5R9=5.
In column 9 the only options for C9R3 and C9R4 are 13. Since there is already a 1 in C4R3, C9R3=3 and C9R4=1.
Now C5R7 = 1. Then, C6R5=1. C5R8=4. C2R8=8. C2R7=4. C9R7=8.
The only cell in row 7 that can be a 9 is C1R7. C1R7=9. C4R7=3.
In box 8 the only options for C4R8 & C6R8 are 29. There is already a 9 in column 4. C6R8=9 & C4R8=2. C5R1=9.
C9R8=6. C9R9=9. C1R8=3. C4R1=6.
In column 5 the options for C5R4 C5R5 & C5R6 are 236. Since there is already a 2 & 6 in row 6, C5R6=3.
Now your grid should look like Example #36.4 below:
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Example #36.4
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Looking further at this grid we notice that C4R6=8. C4R4=5. C8R5=5. C7R5=8. C8R2=8.
The pair 57 in C2R1 & C2R3 preclude a 5 existing as an option in C2R4, C2R5 or C2R6. The only cell in box 4 that can be a 5 is C1R6. C1R6=5.
In row 6 the only options that can exist for C2R6 & C7R6 are 19. There is already a 1 in C9R4; therefore C7R6=9 & C2R6=1. Now, C8R3=9. C2R4=9. C3R2=9.
In box 4 the only options for C1R5& C2R5 are 23. There is already a 3 in C1R8; therefore, C2R5=3 & C1R5=2.
The only options in box 6 for C7R4 & C8R4 are 36. There is already a 3 in C8R9; therefore, C7R4=3 & C8R4=6. C5R4=2. C5R5=6.
Now your grid should look like Example #36.5 below:
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Example #36.5
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MARK UNSOLVED CELLS WITH OPTIONS THAT CANNOT EXIST IN THOSE CELLS … none.
FILL IN THE OPTIONS FOR THE UNSOLVED CELLS … after filling in the options for the remaining unsolved cells, your grid should look like Example #36.6 below:
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Example #36.6
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The first thing you notice is that the only option for C3R3 is 2. C3R3=2. Then, C2R2=6. C1R2=1. C3R1=3. C6R3= 5. C2R3=7. C2R1=5. C6R2=3. C6R1=2. From this point the puzzle is easily solved, giving you the completed puzzle Example #36.7 below:
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Example #36.7
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What did you notice solving this puzzle? Actually, once we identified the obvious pairs & triplets at the beginning of the puzzle, we never got past the Puzzle Preparation phase, and no further techniques were needed!
Puzzles 37 & 38
Below are some puzzles to practice quickly identifying obvious pairs, triplets and quads. First look for obvious answers, then search for the obvious pairs, triplets & quads. Following each puzzle is the answer.
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Puzzle #37
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Obvious answers are highlighted in yellow below in Example #37.1:
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Example # 37.1
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Example #37.2
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Puzzle 38
You quickly notice that there are already a 3 and 9 in column 5, thus C5R3=6.
You may want to solve this puzzle and the two that follow.
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Puzzle #38
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Obvious answers are highlighted in yellow below in Example #38.1:
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Example #38.1
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Next search for obvious pairs, triplets & quads, giving us Example #38.2:
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Example #38.2
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Puzzle #39
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Example #39
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Obvious answers are highlighted in yellow below in Example #39.1:
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Example #39.1
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Next search for obvious pairs, triplets & quads, giving us Example #39.2:
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Example #39.2
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I hope you have enjoyed this article.
Happy springtime to you!
May the gentle winds of Sudoku be at your back.
Editor’s note:
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.
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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: Every month I say… where does he get these? How does he do it? If you see him out fishing in a month or so… stop and ask and tell me the answer. I continue to be amazed.
[See Jessy Kahn’s Book Review, “3 Advanced Sudoku Techniques…” by Dan LeKander, June issue of TI Life.
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