The New Sudoku Players' Forum

[Wecoc]

Classical sudoku. This puzzle has something a little weird going on, but I'm not sure if that can be deduced from some point on the solving process to get easy givens from there (a situation similar to Gurth's Symmetrical Placement), or it has to be solved by default meanings all the way through.

Code: Select all

+-----------+
|1.6|9..|...|
|.2.|.45|...|
|4..|.7.|...|
+-----------+
|...|3..|6..|
|..9|.2.|.4.|
|.8.|..1|..5|
+-----------+
|8..|.5.|1.6|
|...|7.3|.2.|
|..7|...|4..|
+-----------+

Code: Select all

1.69......2..45...4...7.......3..6....9.2..4..8...1..58...5.1.6...7.3.2...7...4..

Let's see what you find

[SpAce]

Let's see what you find

Well, since you mentioned the symmetry, I placed 6 in r9c1 after basics (pairs up with 4 in r1c9) and it got solved. I don't know if it could have been seen without your hint, though, or determined with certainty anyway. I've never used the symmetry property in a live puzzle before, and am not sure what's enough to determine that a puzzle has it. In other words, I don't know if my solution could have been a valid deduction based on the available information, or just a somewhat informed guess.

Either way it was based on the fact that all the solved 4s and 6s seemed to have rotational pairwise symmetry, as well as 5s and 7s, and 2s with themselves. There was nothing contradictory to a symmetry assumption either. Was it enough to determine that the whole puzzle had to be symmetrical? I have no idea.

I hope some experts on the subject will comment.

Added. Expert judgment has been received (thanks again, eleven!). The verdict is kind of what I suspected: the information on the grid is not enough to draw a symmetry conclusion (without solving more cells). In other words, my solution was just a good guess based on the given hint. I think I'm quite happy with a guessed solution for this puzzle anyway. Seems like a real time drag to solve normally.

[Wecoc]

Thank you for trying this.

the information on the grid is not enough to draw a symmetry conclusion (without solving more cells)

That's good to know. If the given placement were also symmetrical it would be possible to know from the very start, but I was wondering if it has to be that way.
I will try to find one with symmetrical pairs but not symmetrical placement on the givens that has a non-symmetrical solution (proof by contradiction).

Either way it was based on the fact that all the solved 4s and 6s seemed to have rotational pairwise symmetry, as well as 5s and 7s, and 2s with themselves.

That's just part of the symmetry:
- Rotational symmetry with pairs 22, 13, 46, 57, 89.

But that is just the result of the two main symmetries on the grid combined:
- Diagonal symmetry [ / ] with pairs 22, 44, 66 (inside the diagonal) and pairs 13, 59, 78 (outside the diagonal)
- Diagonal symmetry [ \ ] with pairs 11, 22, 33 (inside the diagonal) and pairs 46, 58, 79 (outside the diagonal)