After 10 years of intense study of Sudoku, we return to my roots, when I published my book in 2015. With each copy sold I sent 2 green plastic and 33 black tokens to assist in Step 6 exercises. The concept was to identify the two starter cells by placing green tokens on them, and then placing black tokens on all the unsolved cells with the number being used for the exercise. It was, and still is, a great way to visualize which cells cannot being the number being used.
The key was to fill in the options for all the unsolved cells, then place the tokens, and complete the exercise. Then I replaced the green tokens with the Y for yes for one of the starter cells, and a y for the other starter cell. This, of course, works like a charm, but it is labor intensive filling in all the options for the unsolved cells first.
On the morning of Sept 23 an idea came to me, which was to identify the number being used, and to mentally place the black tokens on the cells that could be the number without filling in all the options for the unsolved cells. Usually, the technique identifies clues, which leads to solving the puzzle. If successful, it would eliminate the need to fill in the options for all of the unsolved cells.
First puzzle (the feature puzzle of this article) was successful. Bingo! For this discovery, given being over 5 years late, I awarded myself the “dah” award for the decade.
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. Can you find the missing clue in Puzzle #94?
(The answer follows below after the conclusion of Puzzle #95, the feature puzzle for November)
This “impossible” puzzle #95 below will illustrate the discovery described in the intro for the Step 6 Exercise …
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.
Solving Puzzle #95
The first thing we observe is that C8R6 and C9R4 must have options 19. This means that C7R4, C7R5 & C7R6 can only have options 567. There is already a 6 & 7 in row 4; therefore, C7R4=5. This leaves C7R5 & C7R6 with options 67. C4R3 & C5R2 must have options 79. C3R8 & C3R9 must have options 16. In box five, only C4R4 & C4R5 can have a 2 as an option; therefore, C4R1 cannot have a 2 as an option. These clues lead to Example #95.1 below:
So now, before we complete 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 potentially successful Step 6 exercise if that number appears as a given answer in 3 boxes, such that the boxes are not side-by-side, nor over each other. Which numbers are good candidates? Yes, 4 and 8.
We will first pick the number 4 and perform the exercise. At this point at your home, you would put green tokens on two starter cells that are 4’s and black tokens on all unsolved cells that could have the option 4. For purposed of illustration, in Example #95.2 below we will highlight two starter cells in green, and the unsolved cells that could be a 4 in yellow (vs black).
Now we will perform the exercise. We will start with C2R1 and assume it is the 4. Then we can see that C3R2 & C8R1 cannot be a 4.
Next, we assume that C2R6 is the 4. It follows that C4R6 & C6R6 could not be a 4, then C4R4 would be a 4, then C4R7 & C4R8 could not be a 4, then C6R8 would be a 4, then C7R8 & C8R8 would not be a 4, then C8R7 would be a 4, then C8R1 & C8R2 would not be a 4, and C7R2 must be a 4, then C3R2 would not be a 4.
So regardless of which starter cell is a 4, cells C3R2 and C8R1 could not be a 4, thus eliminating them as options for those cells. This leaves C2R1 as the only cell in box 1 that can be a 4. C2R1=4.
We then see that in box 1 the option 8 can only exist in C2R3 or C3R3, eliminating C7R3, C8R3 & C9R3 from being an 8; therefore C9R1=8.
The 8’s are quickly dispatched, and then the 4’s, leading to an easy conclusion per Example #95.3 below …
We just shaved many minutes off the solving of this puzzle. Look for this technique to be used in some future article.
And Puzzle #94?
Clue for Puzzle #94 … what do you see in column 9?
Options 5, 8 & 9 cannot exist in C9R1. They cannot exist as options in C9R4, C9R5 or C9R6. That leaves C9R2, C9R7 & C9R9 with the only candidates for options 5, 8 & 9. We already know that C9R2 =89.
We see that options 5 & 9 cannot exist in C9R9; therefore, C9R9=8. It follows that C9R2=9, C9R7=5 and C7R3=8.
From this point on it is a fun puzzle to complete.
May the gentle winds of Sudoku be at your back.
Dan LeKander, Wellesley Island