tarek wrote:Today we have too many advanced deduction techniques that reduced the need for guessing (A year ago there were too many puzzles out there that required guessing, the same puzzles today don't need that), many logical deductions are made however at the machine level which humans can't grasp easily.
Exactly.
- Code: Select all
1 9 3 | 8 5 2 | 7 4 6
8 5 4 | 7 6 3 | 9 1 2
6 7 2 | 4 1 9 | 8 5 3
-------+-------+------
9 3 8 | 1 4 7 | 6 2 5
2 4 6 | . . . | 3 7 1
5 1 7 | 2 3 6 | 4 8 9
-------+-------+------
7 8 . | 6 . . | . 3 4
4 6 5 | 3 . . | . 9 7
3 2 . | . 7 4 | . 6 8
- Code: Select all
*--------------------------------------------------*
| 1 9 3 | 8 5 2 | 7 4 6 |
| 8 5 4 | 7 6 3 | 9 1 2 |
| 6 7 2 | 4 1 9 | 8 5 3 |
|----------------+----------------+----------------|
| 9 3 8 | 1 4 7 | 6 2 5 |
| 2 4 6 | 59 89 58 | 3 7 1 |
| 5 1 7 | 2 3 6 | 4 8 9 |
|----------------+----------------+----------------|
| 7 8 19 | 6 29 15 | 125 3 4 |
| 4 6 5 | 3 28 18 | 12 9 7 |
| 3 2 19 | 59 7 4 | 15 6 8 |
*--------------------------------------------------*
When this puzzle was first posed on
another Sudoku forum, under the title "Dead easy -- but beyond "logic" (it's the second puzzle in the thread) it was believed that it was "... obviously dead easy, yet ... can't be cracked without recourse to bifurcation." (Bifurcation is essentially placing each of the two remaining possible values in once cell into a copy of the puzzle and solving both puzzles from there. One will lead to a contradiction. The other is correct.)
We then learned to solve it by forcing chains or xy-wings:
r9c4=5 => r7c6=1 => r7c3=9 => r7c5=2
r9c4=9 => r7c5=2
therefore, r7c5=2
Then we learned BUG -- now the solution is trivial:
Row 7 column 7 is the only cell that has three candidates. On inspection, the candidate 1 appears three times in this cell's row, column and box. Therefore, r7c7=1.