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i recently was playing sudoku on my iPad. As i was stuck on the puzzle i tipped on "Tip" to receive a hint on how i can solve this sudoku (I am still learning the game) - so please don't judge me for this.

It added all kinds of pencil marks - and i was unable to follow why some of them were not populated. Unfortunately I do not have a before & after picture. I have marked the 2's in different colors - of my current understanding of the game. Can somebody explain, why the red ones were not marked?

Sudoku help Thanks for any help.

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This tool looks pretty sophisticated! I think each red circle might have slightly different reasons for not containing a 2 hint, but as an example, let's look at the red circle on Row 1, Column 2.

Suppose we did write a 2 there. Then:

  • To complete Column 2, we must write a 4 in Row 3 (it can't go in Row 8 because of the box) and a 3 in Row 8.
  • From there, we know Row 8, Column 5 must be 6 (all other numbers are already aligned with the cell in at least one direction).
  • Which solves Row 7: Column 4 contains a 3 and Column 7 contains a 6.
  • This in turn solves Row 5: Column 7 contains a 3 and Column 9 contains a 6.
  • And it finishes off Column 9 because we know to write a 3 on Row 3.
  • But now we are in trouble: where, on Row 1, can we write a 3?

It can't go in Column 2 because we started by writing a 2 there. It can't go in Column 4 because we added a 3 to Column 4 on Row 7. It can't go in Column 6 or Column 7 either, and that's all the open columns. Since we arrived at this point by following the only possible logical path beginning with a 2 at Row 1, Column 2, we've "proven" that writing a 2 there would be a mistake.

I haven't tried the other cells you circled in red in the image, but I imagine following a similar algorithm leads each choice into a contradiction or error of some kind.

Edit: Importantly, each of the other choices along this path are valid on their own (which is why the numbers indicated in these steps also tend to show up in those hints); for example, we might be able to put a 3 on Row 8, Column 2, without making it impossible to solve Row 1, as long as the cell on Row 1, Column 2 remains open. It's the combination of all these steps, beginning with writing a 2 on Row 1, Column 2, which leads to the unsolvable scenario at the end.

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  • $\begingroup$ Welcome to Puzzling, and great answer! I was trying to figure out what logical path it had followed, and couldn't get it. This is a perfect explanation. $\endgroup$ – Deusovi Apr 13 at 0:42
  • $\begingroup$ Thanks for the detailed response! I guess I will have to take some more time to redo this sudoku, with all the pencil marks, in order to fully understand what the algorithm has done here. $\endgroup$ – Muffinzlol Apr 15 at 7:25

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