Sudoku Puzzles #83, #84 & #85
In addition to our “Clueless” puzzle series and the feature puzzle for June, there is a special puzzle I would like to share with you. If you are up for it, you will be sufficiently challenged.
Clueless?
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 #83 have any more clues?
(The answer follows below after the conclusion of Puzzle #85, the feature puzzle for June)
Challenge Puzzle
The next puzzle represents a formidable challenge to all who have mastered Steps 6 & 7. It is one of the most difficult 17-given puzzles I’ve experienced in the last few years (unless, of course, I made it more difficult than it really is). Solve this puzzle on your own, and if you are successful, you will earn an A+ . . .
Feature Puzzle
The “Impossible” Series continues with Puzzle #85, the feature puzzle for June …
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.
PUZZLE PREPARATION
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 C1R1 & C2R2 have options 68.
Next, C4R4 & C5R4 have options 29.
C8R8 & C9R7 have options 89. Then, C7R9, C8R9 & C9R9 have options 267. However, there is already a 2 & 6 in column 8; therefore, C8R9=7.
C1R9, C2R9, C4R9 & C5R9 are limited to options 1345.
In box 3 the option 3 can only exist in C7R2 or C8R2; therefore, a 3 cannot exist as an option in C3R2.
Now your grid should look like Example #85.1 below:
This concludes Puzzle Preparation steps 1-4. We will now fill in the options for the unsolved cells, giving us Example #85.2 below:
TECHNIQUES 1-5
There are no other 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.
In Example #85.3 below we find two unsolved cells in column 3 that are not in the same box having a 1 as an option, C3R5 & C3R7 which become our “driver” cells. One of these two cells must be a 1.
We start with C3R5 and assume it is the 1 and assign a “Y”. We then mark the cells which can and cannot be a 1 with the Y’s and N’s. We then assume C3R7 is the 1 and assign a “y”. We then mark the cells which can and cannot be a 1 with the y’s and n’s. Where we see a N,n indicates a cell that cannot be an 1 regardless of whether C3R5 or C3R7 is the 1 in column three.
We can see from the exercise above that two cells have N,n designations, thus, they cannot have a 1 as an option. We also see that the only cell in box 4 that can now be a 1 is C3R5. Thus, C3R5=1. You can now see that the only unsolved cells in box four that can be a 4 are C2R4 & C2R5. Thus, a 4 cannot exist as an option in C2R8 or C2R9 (Interaction), leaving C3R8 the only cell in box 7 or column 3 that can be a 4. C3R8=4. From this point the 4’s cash out, and the puzzle has a relatively simple conclusion per Example #85.4 below:
In the event you are too busy to dedicate a few hours to these puzzles, you could print out the article and save it for a rainy day.
Best of summer to you!
May the gentle winds of Sudoku be at your back.
By Dan LeKander
Clue for Puzzle #83 … focus your attention on row 4. What do you observe?
Cells C6R4, C7R4, C8R4 & C9R4 cannot have options 4, 6 or 8. That leaves 3 unsolved cells in row 4 that now must have options 468. There is already a 4 & 6 in column 1; therefore, C1R4=8.
Editor's Note
Editor's Note: Summer 2021!
Dan and his proofreader (and, as they say, better half) Peggy, give us a new challenge each month.
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: