We will be changing things up a bit this month. Hope you will be pleased.
We start with a Sudoku puzzle in progress, where it appears that there are no more obvious or not-so-obvious clues. Can you find the hidden clue in Puzzle #125?
(The answer follows the conclusion of Puzzle #128, the feature puzzle for November)
Simply Logic Puzzle - #126
Difficult rating … 9.5/10
(Rating based on puzzles not requiring advanced techniques)
Puzzle #126 should present a formidable challenge!
If you have trouble with this puzzle, read on. Keep an eye out for hidden pairs, triplets, and/or quads!
Impossible to solve? Puzzle #127
As you have noticed I only publish 17-given puzzles. (To possibly be a puzzle that has only 1 correct answer, it must have at least 17 given numbers). Theory goes that 17-given puzzles must be some of the most challenging imaginable. Each day I solve two or three 17-given puzzles on the average. The puzzles that best illustrate various points are included in these articles. I would classify about one puzzle in a thousand to be “profoundly difficult”. Thus, I am adding this “Impossible to solve?” puzzle as a fourth puzzle this month, #127, for those of you who need the ultimate challenge.
Feature Puzzle #128
Difficult rating … 4 /10
(Rating based on puzzles requiring advanced techniques)
Prior to utilizing techniques 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
The first thing we observe is that C2R3=5 & C7R9=2.
The only unsolved cells in box 1 that could be have options 3 & 9 are C1R1 & C2R1. Mark those cells with options 3 & 9. Then, C3R1, C3R2 & C3R3 are limited to options 2, 4 & 7.
Now, in column 3, C3R4, C3R5 & C3R7 can only have options 1, 6 & 8. There is already a 6 & 8 in row 4, so C3R4=1. Now, C3R5=6 & C3R7=8. Now, C7R6=6.
In box 5 only C3R5 & C4R5 can be a 2; therefore, C1R5 & C2R5 cannot be a 2.
In box 9 only C8R7 & C8R9 can be a 9; therefore, C8R2, C8R3, C8R4 & C8R5 cannot be a 9.
Now your grid should look like Example #128.1 below:
This completes Puzzle Preparation Steps 1-4. Next, we will fill in options for all unsolved cells, giving us Example #128.2 below:
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 7. Steps 1-5 are relatively common techniques and are explained in the TI LIFE articles. Steps 6-Posts 8 are covered in detail, in Dan’s book.
The first thing we observe is a quad in row 8. C1R8, C7R8, C8R8 & C9R8 are limited to options 4, 5 7 & 8. We can now remove those options from C2R8, C4R8 & C5R8, giving us Example #128.3 below:
That completes techniques 1-5. There are no Step 6 candidates, so we will move on to Step 7, Dan’s Close Relationship Challenge.
We will select C4R8 as our starter cell, with a sequence of 3,1. We will annotate this on the 2nd level of this cell, as per Example #128.4 below:
So, why did I pick C4R8 as a starter cell with a sequence 3,1?
By selecting C4R8 with the sequence 3,1, we would have immediate answers for C2R8 & C5R8. This almost guarantees that the 1 will track through the puzzle far enough to give us positive results.
We annotate C4R2, C4R5, & C4R6 with N3 indicating that those cells cannot be a 3 if the starting cell is a 3. As we track the 1 through the puzzle, if any of these N3 cells is a value other than 3, it would indicate that this cell is not a 3 regardless if the starter cell is a 3 or 1, and the 3 could be deleted as an option for that cell. We will track the 1 through the puzzle in Example #128.5 be-low:
Before we perform this exercise, we will list the potential outcomes …
• The tracking of the second number of the starter cell doesn’t reach the N9 cells, and there-fore, the exercise is unsuccessful.
• The tracking of the second number goes entirely through the puzzle without a conflict, in-dicating that the 2nd number is correct for the starter cell and you have solved the puzzle.
• The tracking of the second number creates a conflict, such as a number showing up twice in a row, column or box. Or it could show up by having no cell for a particular number in a row, column or box. Regardless of how the conflict arises, it would mean the second number is incorrect for that cell, and therefore, the answer to the starter cell is the first number.
We will now track the 1 through the puzzle above on the third level of the unsolved cells to pre-serve the integrity of the original puzzle.
As you can see from example above, in tracking the 1 through the puzzle, we have reached a conclusion. C4R8 is a 1 and the puzzle is solved on the 3rd level of the cells.
May the gentle winds of Sudoku be at your back.
By Dan LeKander
Clue for Puzzle #125 … did you find the clue? If not, read on:
Check column 4. What do you see?
We see that there is a hidden pair in column 4. Only C4R2 & C4R5 can have options 4 & 8.