Here are a couple of great rainy day Sudoku puzzles!
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 and July 2016.
PUZZLE #13 can be solved with Steps 1-5. Please remember to process obvious pairs in the puzzle preparation phase.
If you need assistance, Puzzle Preparation should result in the puzzle looking like below:
Puzzle #13: Through Puzzle Preparation
Hint for solving Puzzle 13 … after a Triplet, a Turbo, and another Turbo, consider solving the puzzle with two Step 4’s, by thinking outside of the box!
Steps to complete Puzzle #13 …
Step 1 … Cells C1R6 (column 1, row 6), C8R6 & C9R6 form a Triplet 3,5,9. Since they own a monopoly on 3,5,9 you can remove the 3 from C2R6 and C3R6.
Step 2 … C7R2 & C9R3 form a Turbo with C3R2 & C9R4 eliminating an 8 from C3R4.
Step 2 … C8R8 & C9R7 form a Turbo with C2R8 & C9R4 eliminating a 4 from C2R4.
Step 4 … C6R2, C7R2 & C9R3 form an XY-Wing, eliminating a 9 from C6R3 & C8R2. C6R2=9. C6R3=1.
Step 4 … C1R3, C1R6 & C9R3 form an XY-Wing, eliminating the 9 from C9R6. This is a rare case of an XY-Wing formed by three cells in three different boxes, affecting a cell in the fourth box. For traditional XY-Wings you look within a box for two cells that start an XY-Wing, along with a cell from another box. This will account for a vast majority of XY-Wings. However, an XY-Wing involving four different boxes is just plain fun when you detect it.
The puzzle can easily be solved from here.
Puzzle #13: Complete
This month the second puzzle features a Step 6 …
Dan’s YES-NO CHALLENGE and a Step 7 … Dan’s CLOSE RELATIONSHIP CHALLENGE.
Puzzle Preparation should result in the puzzle looking like below:
Puzzle #14: Through Puzzle Preparation
Hint … what is the only cell in row 5 that can contain a 5? If you miss this clue, you are in for a long ride; it jump starts the puzzle. Once you have filled in some answers to cells, be sure to pay particular attention to column 7!
Again, if your puzzle does not look like the one above, you probably missed something in Puzzle Preparation. If so, and you do not find the clue, then I suggest you continue with the above, to see if you can reach a conclusion to Puzzle #14.
Steps to completing Puzzle #14…
Step 1 … C4R1, C4R3 & C4R8 form a Triplet 2,3,9, eliminating the 2 and 3 from C4R4 and eliminating the 9 from C4R7.
Step 2 … C4R1 & C4R3 form an Interaction, eliminating the 3 from C5R1.
Step 4 … C1R1, C2R3 & C4R3 form an XYZWing eliminating the 3 from C1R3.
Step 4 … C8R3, C9R2 & C8R7 form an XYWing eliminating the 7 from cells C9R7, C9R8 & C9R9.
Step 6 … C5R5 & C8R5 join, to create a fun Dan’s Yes-No Challenge; there must be a 2, in one of these two cells, in row 5. First, we will assume the 2 is in C5R5. If this is the case, then C5R9 is not a 2. Next, we will assume C8R5 is a 2; if this is the case, then C8R8 is not a 2. The only other unsolved cell in box 9, which has a 2 as an option,is C7R9; so then it must be a 2. If that is the case, then C5R9 is not a 2. So regardless of which cell in row 5 is a 2, C5R9 is not a 2. You can eliminate the 2 from cell C5R9.
Step 7 … we will choose a two-option, unsolved cell, to execute this Dan’s Close Relationship Challenge; C9R1, which has options 6 & 8. It is highlighted in yellow below for ease of identification. If C9R1=8, then C9R7, C9R8 & C9R9 cannot be an 8. If C9R1= 6, then only one of the cells C9R7, C9R8 & C9R9 can be an 8 (these cells are highlighted in blue). Therefore there are at least two of these three cells that cannot be an 8. How can we find which cells are not an 8?
Puzzle #14: at the beginning of Step 7
We first assume the yellow cell is an 8, and then a 6; so we annotate the yellow cell with the sequence “8,6” per below; if the yellow cell is an 8, then the blue cells are not an 8, and we annotate them as “N8”. Next, we assume the yellow cell is a 6, and “track” the 6 through the puzzle, to see which of the blue cells is not an 8.
Puzzle #14: with Tracking
Here is the sequence of tracking, per above, with C9R1=6:
· Now C1R3 has options 4,9; therefore C1R6 is not a 9, nor an 8; C1R6=7
· Now C8R5 & C9R5 both have options 1,4 (pair) therefore C5R5 is not a 4. C5R5=2
We will stop here and examine what has happened with the tracking; if the yellow cell is a 6, then we have two cells in column 5, which both have 2 as an answer. Since we must not repeat a number in a row, column or box, we have witnessed that the yellow cell is not a 6; therefore C9R1=8.
You can see in the tracking process that we did not arrive at the point of determining the answers for the blue cells, if C9R1=6; however, now that the yellow cell is an 8, we have determined that none of the blue cells is an 8; C1R1=3, and you can easily solve the puzzle from here.
Puzzle #14: Complete
Picking a Step 7: Starting Cell
All 2-digit, unsolved cells, are candidates. All 2-digit cells can have two sequences (in Puzzle #14, for example, cell C9R1 could have a sequence 6,8 or 8,6); so you are looking for a 2-digit, unsolved cell, where a sequence has the greatest chance of producing a successful Step 7.
In the example above, we chose sequence 8,6, in cell C9R1; the first number, 8, can expose at least 2 cells in column 9 that are not an 8. Note that you need at least 2 cells in the same row, column, or box, in addition to the starting cell, in order for this to work. The second number, 6, tracks well; as you have witnessed, this was a successful Step 7.
Ok, let’s ask ourselves if we could have done a 6,8 sequence, in C9R1. Well, the 8 looks like it could track, but there is only 1 other unsolved cell in row 1, column 9 & box 3 that has a 6 as an option; so this 6,8 sequence will not work for C9R1.
With experience you will improve your selection of a starting cell and sequence.
If you have any questions, comments, or suggestions to improve my monthly articles, I would really like to hear from you. You can post on this TI Life issue, or contact me directly at my e-mail address … firstname.lastname@example.org.
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 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 coming year. Remember when your teacher said – no such thing as a silly question – as we can all learn together.
Dan’s book is available at two locations online, djlsuniverse.com,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.…
And THANKS… We had a Free Book Offer last month and Dan reported three US winners and two from Canada!
Thank you for your interest. May the gentle winds of Sudoku be at your back!
By Dan LeKander, Wellesley Island, email@example.com