Viggo wrote:ravel wrote:And we have a new leader !

No 7 is a very extreme puzzle. Though one guess (r1c2=4) could solve the puzzle with singles, it needed 12 steps.

The puzzle have 4 candidates in r1c2 and it can be solved by one guess (r1c2=4). Then this puzzle can be solved in 3 steps. The 3 steps are to eliminate the other three candidates in this cell.

Have I missed some point here?

Hm, why can nothing ever be easy..., but here is a solution:

- Code: Select all
`143: tso #7/31 (9.4)`

1 2 3 4 5 6 7 8 9

+-------+-------+-------+

a| . . . | 5 . . | 7 . . |

b| . 2 . | . 6 . | . 4 . |

c| . . 6 | . . 1 | . . 3 |

+-------+-------+-------+

d| 9 . . | 2 . . | 4 . . |

e| . 3 . | . . . | . 1 . |

f| . . 7 | . . 3 | . . 8 |

+-------+-------+-------+

g| 1 . . | 7 . . | 6 . . |

h| . 5 . | . 4 . | . 7 . |

k| . . 9 | . . 8 | . . . |

+-------+-------+-------+

1. d8=3 (that's still easy)

2. k2=4, (g2=8, df2=16, a2=9, c2=7, gh3=23, k1=7, h1=6, k4=6, g9=4, h7=8, k7=3, b7=1, a3=1, b6=7, e3=4, f4=4, a6=4, c1=4, h4=1, k9=1, g5=3, b4=3, b13=58, b9=9, h9=2, k5=2, box2!=2 contradiction >) k2!=4

3. g9=4, (g2=8, k1=4, k2=7, h1=6, k4=6, gh3=23, h7=8, k4=6, k7=3, b7=1

3a. d6=6, f2=6 or e6=6, a6=4, c2=4 > f2!=4, f4=4, a6=4, c2=4, a2=9, e3=4, h4=1, k9=1, h3=3, g3=2, g5=3, b4=3, ac5=2, k5=5, k8=2, a3=1, g6=9, h9=9, row2!=9 contradiction >) g9!=4, k9=4

4. e6=7, (b6=9, c5=7, b1=7, k2=7, a6=4, a5=2, c4=8, b4=3, d9=7, cef7=259, hk1=6

4a. c2=4 or c2=9, c78=25, b9=1,b7=8, g8=8, g2=4 > f2!=4

4b. g2=8 or g2=4, c2=9, c1=4, b3=5, e3=4, f4=4, c78=25, b7=8, g8=8, ck8=25, f8=69, d56=5, f258=169, cf7=25, e7=9, f5=9, h4=9, e4=6, k4=1, h6=6, d2=6 > d2!=8, df2=16

4c. g6=5, k8=5, k1=2 or g6=2, h6=6, k1=6 > k1!=3

4d. k4=6 or k4=1, k7=3, k5=5, g6=2, h6=6 > h4!=6

4e. k4=1, k7=3 or k4=6, k1=2, e3=2, g3=4, g2=8, h3=3, k7=3 > k7=3, g5=3, h4=9

4f. h1=6 or k1=6, k8=2, h9=1, h7=8, b3=8, a3=3 > h1=26, h3=3, a1=3, e1=8, d3=5, e3=2, e4=4, e9=6, h7=8, a8=6, box3!=8 >) e6!=7

5. c2=4, (a6=4, g2=8, a2=9, k2=7, g3=4, h7=8, k7=3, b7=1, a3=1, h9=1, h46=9, g5=3, b4=3, a1=3, h3=3, hk1=26, e3=2, ac5=2, b13=8

5a. f1=5, d3=8 or f1=4, e4=4, c4=8, a8=8, f8=6, d2=6, d69=57, d3=8 > d3=8, b3=5, b9=9, b6=7, g8=9

5b. a8=6, a5=8, e4=8 or f8=6, d2=6, d5=1, e5=7, e4=8 > e4=8, c4=9, h4=6, f4=4, h6=9, f1=5, k4=1, k5=5, k8=2, g9=5, e7=5, c7=2, box6!=2 >) c2!=4

6. f2=4, (g2=8, g3=4, h7=8, k7=3, b7=1, h9=1, g5=3, b4=3, d23=1, fhk4=169, b13=8

6a. d3=8 or d5=8, c4=8, a6=4, a1=3, a3=1 > d3!=1, d2=1, a2=9, c2=7, k2=6, a3=1, b6=7, k4=1, f5=1, a1=3, c1=4, a6=4, c4=8, a5=2, c5=9, k5=5, k8=2, e9=2, f1=2, h3=2, col3!=3 >) f2!=4

7. g3=8, (g2=4, h7=8, k7=3, h9=1, b7=1, g5=3, b4=3, b3=5, d3=1, f2=6, d2=8, k2=7, c2=9, b9=9, g8=9, b6=7, b1=8, c1=7, c4=4, e6=4, e4=8, e3=2, a8=6, a9=2, k8=2, a6=9, k1=6, k4=1, f4=9, box8!=9 >) g3!=8

8. g2=4, g8=8 or a2=4, c4=4, e6=4, f1=4, g3=4, g2=8, h7=8, k7=3, b7=1, h9=1, df2=16, k2=7, c2=9, a3=1, g5=3, b4=3, a1=3, h3=3, e3=2, e4=8, e1=5, d3=8, b3=5, b9=9, g8=9 > g8=89

9. g2=4, g8=8 or a2=4, c4=4, e6=4, f1=4, g3=4, g2=8, h7=8, k7=3, b7=1, h9=1, df2=16, k2=7, c2=9, a3=1, g5=3, b4=3, a1=3, h3=3, e3=2, e4=8, e1=5, d3=8, b3=5, b9=9, g8=9, b6=7, b1=8, c1=7, e7=9, e5=7, e9=6, a9=2, g9=5, d9=7, a6=9, a5=8 > a8!=8

10. a2=1, (g2=4, f2=6, d2=8, k2=7, c2=9, d3=1, g8=8, ck8=25, f8=9, a8=6, ef7=25, c7=8, c4=4, e6=4, f4=1, f5=5, row4!=5 contradiction >) a2!=1, ab3=1

11. a3=4, (c4=4, e6=4, f1=4, g2=4, g8=8, b3=1, a9=1, hk7=13, de9=67, ab1=3, de3=5, f78=2, gh9=9, b9=5, k8=5, a8=6, c1=5, a56=2

11a. b1=7, b6=9, a2=9 or k1=7, ab1=38, a2=9 > a2=9, a6=2

11b. b6=7, c2=7, k1=7 or b6=9, h6=6, k1=6 > k1!=2, k5=2, k12=67

11c. b6=7, c2=7, k2=6, e1=6 or b6=9, d6=7, d9=6, b7=8, b4=3, k4=1, fh4=69, e4=8, e9=7, e1=6 > e1=6, d9=6, f4=6, e3=2, g3=3, g9=2, h9=9, hk47=13 nonunique contradiction or k1=7, b6=7, d6=5, box4!=5 contradiction >) a3!=4

12. c1=4 or c4=4, e6=4, f1=4, a2=4, g3=4, g2=8, h7=8, k7=3, b7=1, h9=1, df2=16, k2=7, c2=9, a3=1, g5=3, b4=3, a1=3, h3=3, e3=2, e4=8, e1=5, d3=8, b3=5, b9=9, g8=9, b6=7, b1=8, c1=7 > c1=47, b13=5

13. a6=4 or c4=4, e6=4, f1=4, a2=4, g3=4, c1=7, b6=7, g2=8, g8=9, g5=3, b4=3, k2=7, c2=9, h7=8, k7=3, b7=1, b9=9, e4=8, d3=8, b1=8, a5=8, a6=9 > a6!=2, ac5=2

14. e3=4 or g3=4, g2=8, h7=8, k7=3, b7=1, a3=1, g5=3, b4=3, a1=3, h3=3, e3=2 > e3=24

15. f4=4 or f1=4, a2=4, c4=4 > e4!=4

16. f1=4 or f4=4, a6=4, c1=4 > e1!=4

17. f4=4 or f1=4, a2=4, g2=8, h7=8, g8=9, c2=9, c1=7, k2=7, g3=4, e3=2, h3=3, g5=3, b4=3, a6=9, h4=9, c4=4, e4=8, d3=8, e1=5, e7=9, f5=9, e5=7, d9=7, b9=9, g9=5, k5=5, k4=1, f4=6 > f4=46, hk4=1

18. c1=4 or c4=4, f1=4 > a1!=4

19. b4=3 or a5=3, c5=2, b6=7, a1=8, a3=1, k5=5, g5=9, f5=1, f2=6, k2=7, c2=9, b4=9 > b4!=8

20. a5=3, (b4=9, a6=4, c5=2, b6=7, c4=8, a1=8, b3=3, d3=5, d6=6, e4=nil contradiction >) a5!=3, b4=3

21. b6=7 or b6=9, a6=4, c4=8, f4=4, e3=4, gh3=2, k78=2, a5=2, e9=2, d9=7 > d6!=7, b6=7, b79=9

22. b9=1 or b9=9, g9k8=25, h9=1 > a9!=1, a3=1, b13=58, a1=3, a5=8, c5=2, e4=8, bd3=58

23. g4=8, h7=8, k7=3, h9=1, k4=1 or g4=4, g8=8, c8=5, k8=2, k12=67, k4=1 > k4=1, k12=67

24. g8=9, h7=8, k7=3 or g8=8, f8=9, ef7=25, k7=3 > k7=3, k5=5, k8=2, a8=6, a9=2, g9=5, de9=67, g5=3, h3=3, ef5=9

25. c8=8, g2=8, d3=8 or c8=5, f8=9, f5=1, d2=1, d3=8 > d3=8, and then it becomes easy again.

Strategically, I tried to do something like that, eliminate the other values around a2=4, but the thing wouldn't bend. And when I was at last ready to have the alternative of a2=4 or g2=4, and I could prove that g2=4 leads to contradiction, I was too proud and looked for a way to circumvent further contradictions, since I still believe that the "hardness" of a sudoku consists of how many contradictions I am forced to use.

Perhaps the last contradiction step 20 wasn't really necessary, but then I wanted to get it done and it was such a beautiful short contradiction, with so many numbers still missing. So 8 contradictions, may be 9, needed, ranks this puzzle quite hard, compared with Ocean's BB with 7 contradictions.

Another idea of the "hardness" of the contradictions used is to count the number of substeps. Step 4 is clearly standing out with 6 substeps needed. Perhaps there are some easier ways to solution, but as I said, I tried this strategy.

Greetings, Maria