April is bonus month. In addition to the “Clueless series” and feature puzzle, April will be the first month with a 3rd puzzle, a challenging Sudoku puzzle, but you will be able to solve it without advanced techniques. Let’s call it the “Logic series”, since Sudoku is a sport of pure logic.
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 #104?
(The answer follows after the conclusion of Puzzle #106, the feature puzzle for April)
Puzzle #105 can be solved by just using logic versus needing advanced techniques. Since there can be only one answer for a valid puzzle, the answer will not be printed in the article. You are on your own. Please enjoy.
Difficult rating … 5/10.
Feature Puzzle #106
Print this puzzle and give it a go.
Difficult rating … 7/10.
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 C1R8=6, C5R9=6 & C9R7=9. C1R7 & C2R7 have options 2 & 3. In box 1 a 4 can only exist as an option in C1R1 & C1R3; therefore, a 4 cannot exist as an option in C1R4, C1R5, & C1R6. In box 5 a 9 can exist as an option only in C5R4 & C5R6; therefore, a 9 cannot exist as an option in C5R1, C5R2 & C5R3.
These clues give us Example #106.1 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 #106.2 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 #106.3 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 there-fore, 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 pre-serve 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 can-not be the correct number, and that C6R4=6
The puzzle is easily solved from this point and the solution is Example #106.4 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.
By Dan LeKander
[Author's note: Clue for Puzzle #104 … did you find the clue? If not, read on. Take a look at column 6. What do you see?
Only two unsolved cells can have option 2 & 6.
So, mark C6R5 and C6R8 as options 2/6. Now, a 4 can only exist in one unsolved cell in column 6, which is C6R4. C6R4=4.]
Editor's Note: April 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 #104,105,& 106. What can I say . . . you Dan and your wonderful proofreader, Peggy are amazing. Just look at the list below to prove it!
And, if you have not already done so, I suggest you purchase Dan’s book: