You spoke, and I listened. Many thanks to those of you who indicated the step-by-step guide was very helpful, but more detail is needed. The article this month provides detailed steps for solving the puzzle. So regardless of your Sudoku level of expertise, you have a comprehensive blueprint to solve this difficult puzzle.
First, we will revisit the approach as discussed in Dan’s first six TI 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, and December 2016
Puzzle # 21
Decision time. Do you want to print Puzzle #21 and solve it prior to following the steps below; or do you want to waltz through the steps with me as we utilize Dan’s 8 Step Approach?
As a reminder, the basic rule of Sudoku is that numbers 1-9 cannot be repeated in a row, column, or box. And there can only be one solution to a puzzle.
First we will complete the four steps of Puzzle Preparation …
1. Fill in obvious answers
2. Fill in the not-so-obvious answers
3. Mark the unsolved cells with options that cannot exist in those cells
4. Fill in the potential options for the unsolved cells
OBVIOUS ANSWERS … Start with the 1’s to see if there are any obvious 1-choice answers (a 1-choice answer means that there is only one number of numbers 1-9 that will work in that cell). Then move on to the 2’s through 9’s.
The first obvious answer is C9R6 (cell in column 9, row 6) = 3. Then C3R9 = 6, C6R3 = 6, C5R4 = 6, C9R5 = 6, C7R7 = 6, C5R1 = 8, C8R3 = 8, C7R6 = 8, C6R5 = 8, C7R4 = 5, C8R5 = 1, and C9R2 = 5.
NOT SO OBVIOUS ANSWERS … Look at box 2 (top, middle box of 9 cells). The 9 in C5R7 precludes C5R2 from being a 9. The 9 in C9R3 precludes C4R3 from being a 9. Therefore, in box 2 a 9 must exist in cells C4R1 or C4R2. Therefore, a 9 cannot exist in C4R4, C4R5, or C4R6. C1R6 is a 9, therefore C5R6 and C6R6 cannot be a 9. Therefore the only cell in box 5 (middle box) that can be a 9 is C6R4. Therefore, C6R4 = 9.
Now your grid should look like Example 21.1 below …
Puzzle # 21.1
NUMBERS IN UNSOLVED CELLS THAT CANNOT EXIST … In box 3 a 1 cannot exist in C7R2 or C8R1. Therefore a 1 must exist in C7R1 or C9R1. Therefore a 1 cannot exist in C2R1 or C3R1. We will mark those two cells with a “1” in the lower part of the cells as per example 21.2 below.
In box 2 a 3 must exist in C4R1 or C4R2. Therefore a 3 cannot exist in C4R7. We will mark C4R7 with a 3 in the lower part of that cell. Now your grid should look like 21.2 below.
Puzzle # 21.2
FILL IN THE OPTIONS FOR THE UNSOLVED CELLS … you will find the best place to start is the column, row, or box that has the fewest unsolved cells. In 21.2 above you see that column 9 has only two unsolved cells, missing a 1 and 7. As you can see the 7 in C1R7 precludes C9R7 from being a 7. Therefore C9R7 = 1. Then C9R1 can only be a 7.
Next look at box 3. The only numbers missing are now 1,2 & 4. Looking at column 8, you see a 1 and 4 in that column. Therefore C8R1 must be a 2.
Now the only missing numbers in box 3 are 1 & 4. The 1 in C6R2 precludes C7R2 from being a 1, so therefore C7R2 = 4, and then C7R1 must be a 1.
In box 2 the missing numbers are 2,3,4 & 9. Look at C5R2. You see a 4 in C7R2, a 3 in C5R5, and a 9 in C5R7. Therefore C5R2 can only be a 2.
Now the missing numbers in box 2 are 3, 4 & 9. Now look at C4R3. You see a 3 and 9 in row 3, so C4R3 can only be a 4.
In column 7 the missing numbers are 2 & 7. The 2 in C2R8 precludes C7R8 from being a 2, and therefore it must be a 7. Then the only choice for C7R9 is a 2.
Now look at box 8. A 7 can only exist in C6R9.
After filling in the options for the unsolved cells, your grid should now look like Example 21.3 below.
Puzzle # 21.3
This completes the Puzzle Preparation phase. You will note that we have yet to employ a Step 1-7 technique. Much was accomplished in the Puzzle Preparation phase by just following the basic rules of Sudoku.
STEPS 1-7 … I suggest exploring Steps 1-7 in the order of 1 through 7. Please also keep in mind that when you discover a clue it may then require you to look at previous steps for other clues (such is the case below).
• PAIRS, TRIPLETS & QUADS (Step 1). As you examine the grid, you find no Step 1 clues.
• INTERACTIONS & TURBOS (Step 2). In examining the grid, we find that there are three unsolved cells in box 4 that have a 4 as an option. Upon further examination, we find that the only choice for a 4 in row 5 are cells C1R5 or C2R5, which sets up an Interaction. Since one of those cells must be a 4, C3R6 cannot be a 4, and we can eliminate the 4 as an option from that cell, leaving its options as 12. But now notice in column 3 we have two unsolved cells with options 12, which is a pair.
• PAIRS, TRIPLETS, QUADS (Step 1). Since we noticed the pair in column 3, we go back to Step 1 to take advantage of this clue. The pair in column 3 allows us to delete a 1 or 2 from any other unsolved cells in column, therefore eliminate the 1 from C3R4 and C3R8.
• INTERACTIONS & TURBOS. Now we go back to finish our search for Step 2 clues. In column 4 either C4R4 or C4R6 must be a 1, therefore a 1 cannot exist in C5R6, and can be eliminated as an option from that cell.
• That concludes clues from Steps 1-5. Now your grid should look like 21.4 below.
Puzzle # 21.4
• There are no clues for Step 6 (DAN'S YES-NO CHALLENGE), so we will move on to Step 7.
• DAN’S CLOSE RELATIONSHIP CHALLENGE (Step 7). As in previous puzzles, you pick a 2-digit unsolved cell to explore those two digits with the unsolved cells in the same box, column, and row. We will pick C4R5, use the sequence 2,7, and mark C4R5 with”2,7” on the second level of the cell. If C4R5 is a 2, then neither C4R6 nor C4R7 can be a 2, so we will mark them as N2 on the second level of those cells. Now your grid should look like 21.5 below.
Puzzle # 21.5
Now we will “track” the 7 through the puzzle to see what the values of C4R6 and C4R7 will be. We start with C4R5 = 7 (highlighted in green above), and put the tracking numbers in the 3rd level of the unsolved cells. Then C4R4 = 1, then C1R4 = 3, C3R4 = 7, C2R5 = 4, C1R5 = 2, C3R6 = 1, C3R3 = 2, C1R9 options become 15 and C1R3 options become 15. Then C1R8 becomes a 4 (its options are 1, 3, 4 & 5. The pair in column 1 eliminate the 1 & 5. C1R4 is a 3, leaving 4 as the the only possibility for C1R8). Then C6R8 = 3. Then C3R8 = 9. Then C8R8 = 5. Then C5R8 = 1, then C5R9 = 5, then C5R6 = 4, then C6R6 = 2, then C4R6 = 5. Then C4R7 = 2. Your grid should look like Example 21.6 below.
Puzzle # 21.6
We pause now to see what we have accomplished thus far. We go back to our starting cell C4R5 with options 2,7. If C4R5 is a 2, then C4R6 is not a 2. If C4R5 is a 7, then C4R6 is a 5, and therefore C4R6 is not a 2. So regardless if C4R5 is a 2 or 7, C4R6 is not a 2, eliminating the 2 as an option for C4R6.
Can we learn more? Yes! The puzzle will continue to track, such that you arrive at Example 21.7 below.
Puzzle # 21.7
Now look at the cells with answers and the numbers in the 3rd level of the unsolved cells. No number has been repeated in a row, column, or box. So C4R5 = 7, and you have solved the puzzle!
(Had we found a conflict in a row, column, or box, such as two 9’s in row two, then C4R5 could not be a 7 and would therefore have been a 2.)
Thank you for your interest. 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? 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 easy 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.…
Now as we start a whole new year, I want to say THANKS Dan and THANKS to his better half, Peggy LeKander, who helps make sure the article is correct and reads well. What a team!
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 any suggestions for future articles? You can post on this TI Life issue, or contact me directly at my e-mail address … firstname.lastname@example.org.