Can the River water level be much lower? This has been a challenging year for St. Lawrence boaters! Let’s switch focus to Sudoku.
As a bonus each month this year we will start with a Sudoku puzzle in progress, where it appears there are no more obvious or not-so-obvious clues. Does this puzzle #90 have any more clues? (Of course, it does!) Can you find the clue?
(The answer follows below after the conclusion of Puzzle #91, the feature puzzle for September)
Can you solve “Impossible” Puzzle #91 on your own?
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.
Step 1: Sudoku Pairs, Triplets and Quads – See September 2015
Step 2: Turbos & Interaction – See October 2015
Step 3: Sudoku Gordonian Rectangles and Polygons – See November 2015
Step 4: XY-Wings & XYZ Wings – See December 2015
Step 5: X-Wings – See January 2016
Step 6: DAN’S YES/NO CHALLENGE
Step 7: DAN’S CLOSE RELATIONSHIP CHALLENGE
Step 8: AN EXPANSION OF STEP 7Steps 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.
Prior to utilizing Steps 1-8, complete the 5 Steps of Puzzle Preparation . . .
- FILL IN DATA FROM OBSERVATIONS
- 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
We will complete all of the first 4 steps in the order we observe them, until we conclude all Puzzle Preparation Step 1-4 clues.
The first thing we observe is that C6R4=4, then C5R6=7. That is it for clues.
In box 1 a 2 can only exist as an option in C1R2 or C2R2; therefore, a 2 cannot exist as an option in C5R2 or C6R2. Indicate this by placing a small 2 in the bottom of those two cells.
In box 9 a 6 can only exist as an option in C8R9 or C9R9; therefore, a 9 cannot exist as an option in C5R9 or C6R9.
Cells C4R4, C5R4 & C6R4 must have options 236.
Now your grid should look like Example #91.1 below:
This completes puzzle preparation, so we will fill in the options for the unsolved cells, giving us Example #91.2 below:
Are there any pairs, triplets, quads or quints? Check out column 3. A 5 and 9 only exist as options in two cells, C3R4 & C3R7. Change those options to 59. There are no more Step 1-5 clues.
We will now proceed to Step 6: Dan’s Yes-No Challenge. We will start by searching the 1’s to see if there is a potential Step 6 clue, and then navigate through the 2-9’s.
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.
Before we begin a Step 6 exercise, we need to take a moment and discuss what conditions can lead to a successful Step 6. If you have followed previous articles, you realize that by naming a cell yes (Y or y), you need to track the yes’s & no’s through the puzzle such that an unsolved cell or cells are affected by both starter cells, hopefully leading to a N,n or Y,y, indicating that a cell cannot be that number or is that number. So far in my experience, you need a certain condition to exist. For a number to track successfully through the puzzle you need …
1. Three solved cells with that number
2. These three cells are not in the same box, row or column
This definitely brings up questions. Are there any instances where a Step 6 exercise can be successful with less or more than three solved cells with that number? Can the solved cells be in the same box, row or column? So far, the answer seems to be no. It will require a smarter person than me to definitively answer those question. In all of the successful Step 6 exercises I have performed, I have not recorded a successful Step 6 without these two requirements.
With this in mind, in Example # 91.3 below we shall look for numbers 1-9 that fit the criteria above. The first one that surfaces is the number 5, so let’s jump in and perform the exercise with the number 5. We will make C4R1 and C4R9 our starter cells. We will always begin with the starter cell with upper case Y.
If C4R1 is the 5, then C6R2 and C7R1 are not a 5 (N’s), then C8R2=Y, C8R4 and C8R6 =N, C7R4=Y, C2R4 and C3R4=N, C2R6=Y, C2R9=N, C3R7=Y, and C6R7=N.
Next, we will assume C4R9 is the 5. Then, C6R7=n, C2R9=n, C3R7=y, and C3R4=n. So what do we have? Three cells with the N,n cannot be a 5, and C3R7 is a 5 and then C3R4 is a 9.
The puzzle is easily solved with these clues, again illustrating the power of a successful Step 6 exercise. The final solution is shown below in Example #91.4
May the gentle winds of Sudoku be at your back.
Clue for Puzzle #90 … focus your attention on row 1. What do you observe?
The Answer: C6R1, C7R1, C8R1 & C9R1 cannot have options 4,8 or 9. Therefore, the remaining 3 unsolved cells in row 1 (C2R1, C3R1 and C5R1) must have options 489. There already exists an 8 and 9 in column 3; therefore, C3R1=4. Then C5R1=8 and C2R1=9.
Editor's Note: Septembr 2021!
Dan, when not out fishing, and his proofreader (and, as they say, better half) Peggy, give us a new challenge each month. Please not this month we have 90 & 91 = getting very close to 100. So stay tuned as we will certainly have a celebration.
It was back in January 2016, when we published a final article in Dan's Series of Steps to learn the logic of Sudoku – he asked if we would like a puzzle to solve every month … this editor said an enthusiastic… Yes, please!
If you have not already done so, I suggest you purchase Dan’s book: