Spring is just around the corner. Perhaps, until then, you can solve this tough Sudoku puzzle and put it on display in your Sudoku trophy room!
As a bonus each month we start with a Sudoku puzzle in progress, where it appears there are no more obvious or not-so-obvious clues. Can you find the hidden clue in Puzzle #102?
(The answer follows after the conclusion of Puzzle #103, the feature puzzle for March)
Last month our primarily focus was Step 7. We will stay with a puzzle requiring Step 7 as a way to reinforce your comfort level with this advanced technique.
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, 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 C7R3=8, C1R2=5 & C2R7=5. C8R1 & C8R3 have options 26. C7R2, C8R2 & C9R2 have options 379. C3R2=1, C5R2=4 & C4R7=7. In box 8 a 2 can only exist as an option in C4R9 and C5R9; therefore, a 2 cannot exist as an option in C1R9, C3R9, C7R9 & C9R9. In column 6 C6R1, C6R7, C6R8 & C6R9 are limited to options 3489; therefore, C6R3, C6R4 & C6R6 can only have options 156. In box 4 a 7 can exist as an option only in C1R4 & C1R6; therefore, a 7 cannot exist as an option in C1R1 & C1R3.
These clues give us Example #103.1 below:
This concludes Puzzle Preparation steps 1-4, but before we move on to step 5 by filling in the options for all the unsolved cells, we will look at the puzzle and ask if there are any good Step 6 potentials. As in previous articles, we determined a particular number was a potential for a successful Step 6 exercise if that number appears as a given answer in 3 separate boxes, such that the boxes are not side-by-side, nor over each other. Which numbers do you see that are good candidates? Yes, there are no examples, so we will fill in the options for the unsolved cells, giving us Example #103.2 below:
We will now proceed to Step 7, Dan’s Close Relationship Challenge. As we have previously stated, all you need to qualify for a Step 7 exercise is at least one unsolved cell with just two options. We will choose C6R4 as our “starter cell”, per example #103.3 below:
We will pick a sequence for the starter cell C6R4 as 6,5, which we annotate on the 2nd level of this cell per Example #103.3 above. We begin by asking ourselves that if this cell is actually a 6, what adjacent cells could not be a 6 and annotate those cells as “N6”, again on the 2nd level of the cells.
Next, we assume the starter cell is a 5 and track the results through the puzzle. If any N6 cell is a number other than 6, it means that cell is not a 6 regardless if the starter cell is a 6 or 5, and the 6 could be eliminated as an option from that cell.
Before we perform this exercise, I will list the potential outcomes …
• The tracking of the second number of the starter cell doesn’t reach the N1 cells, and therefore, the exercise is unsuccessful.
• The tracking of the second number goes entirely through the puzzle without a conflict, indicating 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 5 through the puzzle above on the third level of the unsolved cells to preserve the integrity of the original puzzle.
You may want to track the puzzle also. Please note column 7. There is no unsolved cell that can be a 5. (If there is a conflict, there will be many conflicts in rows, columns or boxes. Please bear in mind that if you find a conflict, it may be in a different location than mine.)
What does this conflict tell us? It tells us that the 5 in C6R4 cannot be the correct number, and that C6R4=6 The puzzle is easily solved from this point and the solution is Example #103.4 below:
Let’s pause here for a moment to ask ourselves the best way to select a starter cell. You start by finding a 2-digit starting cell where one of the two numbers has a reasonable chance to track through the puzzle. The 5 in C2R3 certainly seems it will track far. Then you ask if the other number has at least two adjacent cells (in the same row, column or box) that have the same number as an option. With a puzzle like this with three 2-digit option cells in the same column (a triplet), picking one of those cells as a starter cell almost guarantees that the second number of the starting sequence will track very well!
May the gentle winds of Sudoku be at your back.
Author's Note: Clue for Puzzle #102 … did you find the clue? If not, read on.
We see that in box 2 an 8 can only exist as an option in C4R2 or C6R2; therefore, an 8 cannot exist as an option in C7R2, C8R2 & C9R2. The only cell in box 3 that can be an 8 is C7R1. Now check out column 9. The options 5 & 8 can only exist in two unsolved cells, C9R1 & C9R4. Since C7R1=8, we now know that C9R2=5 and C9R4=8. Then C9R6=6.
This is a fun puzzle to finish, as it does not require advanced techniques.
Editor's Note: March 2022 - into the 100s
When we published the final article in Dan's Series of steps to learn the logic of Sudoku, I never in a zillion years thought that Dan would so graciously offer to do one or two puzzles for us each month - and he has done so with this being numbers 102 & 103. What can I say . . . you Dan and your wonderful proofreader, Peggy are amazing. We appreciate it. (How about a really easy "Susie Smith One" for next month?)
And, if you have not already done so, I suggest you purchase Dan’s book: