## Solution to Ocean's #1/M21/D21 ER 10.0

Advanced methods and approaches for solving Sudoku puzzles

### Solution to Ocean's #1/M21/D21 ER 10.0

Code: Select all
`   1 2 3   4 5 6   7 8 9 +-------+-------+-------+a| . . . | . . 1 | . . 2 |b| . 1 . | . 2 . | . 3 . |c| 4 . . | 5 . . | . . . | +-------+-------+-------+d| . . 4 | . . . | . . 6 |e| . 7 . | . 3 . | . 1 . |f| 8 . . | . . . | 9 . . | +-------+-------+-------+g| 5 . . | . . 8 | . . . |h| . . . | . 1 . | . 7 . |k| . . 6 | 4 . . | 5 . . | +-------+-------+-------+`

1. h6=5, d7f9=37 (hidden pair), k1g3=17 (hidden pair), x-wing be39=5, af3!=5

2. h7=3, (d7=7, f9=3, gk2=3, d1=3, f3=1, d4=1, g3=7, k1=1, h4=6, g5=9, k5=7, h123=2

2a. g2=4, g9=1 or g2=3, g4=2, a4=3, c3=3, c2=2, e13=2, df8=2, g7=2, g9=1 > g9=1

2b. g2=4, g4=3, c6=3, c9=7 or g2=3, g4=2, k8=2, hk9=89, c9=7 > c9=7

2c. g2=4, g4=3, c6=3 or g2=3, g4=2, k8=2, e79=2, df2=2, c3=2, c6=3 > c6=3, a3=3, g4=3, k2=3, g2=4, k6=2, h9=4, d6=9

2d. f4=2, e4=8, d8=8, d5=5, d2=2, e9=5, f2=5, e1=6, e6=4 or f4=7, b6=7, a5=4, b7=4, e6=4 > e6=4, a5=4, b7=4, f8=4, e1=6, h1=2, e3=9, h3=8, h2=9, c3=2, b3=5, a8=5, e9=5, b6=6, f6=7, c5=8, (non-uniqueness ab14), c2=6, a7=6, e7=8, column4!=8 contradiction >) h7!=3

3. h9=3, (f9=7, d7=3, a1=3, c6=3, g4=3, k2=3, f3=3, f4=1, d1=1, g3=1, k9=1, c7=1, k1=7, k5=9, k6=2, h4=6, g5=7, k8=8, c3=7, c2=2, h123=9, g2=4, h7=4, g9=9, c9=8, c5=6, c8=9, e7=8, g7=2, g8=6, f8=2, d8=5, e9=4, e3=5, h3=2, e1=2, d4=2, a2=5, a8=4, a5=8, box5!=8 contradiction >) h9!=3

4. k9=3, (d7=3, c6=3, f9=7, k1=1, f3=1, d4=1, g3=7, ab4=7, c79=7, c7=7, c9=1, g7=1, f2=3, e1=6, g4=3

4a. e7=2 or h7=2, gk2=2, c3=2 > e3!=2, d12=2

4b. f4=2 or f4=6, g5=6, h7=6, e7=2 > f8!=2, e7=2

4c. f4=6, g5=6 or f4=2, k6=2, g8=2, g5=6 > g5=6, h7=6, ab7=48, f58=45

4d. c5=8, e4=8 or c5=9, c8=6, a2=6, d2=5, d8=8, e4=8 > e4=8, d8=8, h9=8, k2=8, h2=4, b46=6

4e. h4=2, f4=6, b6=6, a5=4 or h4=9, g2=9, g9=4, f8=4, a5=4 > a5=4, a7=8, f5=5, e9=5, a8=5, d2=5, c5=8, b3=8, box1!=5 contradiction >) k9!=3, g79=3

5. k2=3 or k6=3, a4=3 > a2!=3

6. h3=3, (k6=3, a4=3, c2=3, d1=3, f9=3, g7=3, d7=7, f3=1, d4=1, k1=1, g9=1, c7=1, g3=7, k5=7, c3=2, hk2=8, gh4=2, a1=7

6a. k8=2, e7=2, h1=2 or k2=2, e1=2, h7=2 > gh2!=2, g8!=2, g4=2, x-wing eh17=2, e6!=2

6b. e1=6, (b1=9, a3=8, a2=6, b3=5, e3=9, e6=4, a5=4, a7=nil contradiction >) f2=6, f4=7, b1=6

6c. e3=9, d2=5, f5=5, a5=4 or e3=5, b34=89, b7=4, a5=4 > a5=4, f5=5, c56=6

6e. e3=9, e1=2, h7=2, g8=6, h9=4, b7=4 or e3=5, b9=5, b7=4 > b7=4

6f. e3=9, a3=8 or e3=5, d8=5, d5=8, b4=8, a3=8 > a3=8, a7=6, g8=6, h4=6, e6=6, f6=4, h9=4, box6!=4 contradiction >) h3!=3

7. c2=3, (h1=3, f3=3, k6=3, a4=3, d7=3, g9=3, d1=1, f4=1, g3=1, k9=1, c7=1, k1=7, f9=7, k5=9, e1=2, f2=6, c3=2, ab1=69, c56=7, gh7=2, k8=8, k2=2, df6=2, d45=8, h47=26

7a. h7=6 or h7=2, h4=6, e4=9, h3=9, h9=4, g7=6 > g8!=6, gh7=26, (g5=7 non-unique gh47=26 >) g5=6, g7=2, g4=7, h4=2, h7=6, a357=478, a2=5, d2=9, d4=8, b9=5, e3=5, g2=4, g8=9, c8=6, a8=nil contradiction >) c2!=3

8. f3=3, (a1=3, c6=3, h4=3, k2=3, d7=3, g9=3, f4=1, d1=1, g3=1, k9=1, c7=1, k1=7, f9=7, k5=9, k6=2, k8=8, h6=6, g78=2, e79=8

8a. b1=6, f2=6, f8=2 or b1=9, a4=9, e1=6, e4=2 > e7!=2, g7=2

8b. d4=2, d5=8, d6=7 or e4=2, df2=2, c3=2, c5=7, d6=7 > d6=7

8c. b1=6 or b1=9, a4=9, e1=6, e4=2, h1=2, c3=2, c5=7, g5=6, f6=6, b4=6 > b6!=6, ef6=6

8d. f2=2 or f8=2, d8=5, f5=5 > f2!=5

8e. f2=2, c3=2, c5=7, e1=6, b4=6, b1=9, a4=9, d4=8, d5=5 or f8=2, d8=5 > d2!=5, e3=5, a2=5, b9=5, e79=48

8f. c2=8 or h2=8, g2=4, g8=9, c8=6 > c2!=6, b1=6, f2=6, f6=4, f5=5, f8=2, d8=5, d5=8, a5=4, b7=4, e9=4, g8=4, h2=4, g2=9, d4=9, d2=2, c2=8, a7=8, box3!=7 contradiction >) f3!=3

9. c3=3 or c6=3, h4=3, k2=3, d1=3 > a1!=3

10. g7=1, (k1=1, f3=1, d4=1, c9=1, g9=3, d7=3, f2=3, h1=3, k6=3, a4=3, c3=3, g3=7, k5=7, f9=7, d6=7, b4=7, a1=7, c7=7, c2=2, h3=2, g4=2, k8=2, e7=2, f6=2, d2=2, e1=6, f4=6, g5=6, h7=6, a2=6, c8=6, b6=6, a5=4, e6=4, f8=4, h9=4, g2=4, b7=4, b1=9, a3=8, b9=8, box9!=8 contradiction >) g7!=1, c7=1

11. g9=3, (d7=3, f2=3, h1=3, k6=3, a4=3, c3=3, k9=1, g3=1, d1=1, f4=1, f3=2, c2=2, box7!=2 contradiction >) g9!=3, g7=3, f9=3, d7=7

12. d1=1, (h1=3, f3=2, c2=2, box7!=2 contradiction >) d1!=1, f3=1, d4=1, k1=1, g9=1, g3=7

13. h7=2, (gk2=2, c3=2, c6=3, h4=3, row8!=6 contradiction >) h7!=2, e7=2, dh1=23

14. h3=2, h1=3 or c3=2, c6=3, h4=3, h1=2, k2=3 > ghk2!=2, h4!=2, h2!=3

15. b9=5, c9=7, a2=5 or a8=5, d8=8, e4=8, f8=4, a5=4, b146=679, c9=7, b79=48, a7=6 > c9=7, a2!=6, b9!=9, hk9=9

16. a2=5 or b3=5, e3=9, e1=6, ab1=9, a2=8 > a2!=9

17. b9=5 or e9=5, df2=5, a2=8, h3=8, h29=49, h7=6, ab7=48, b9=5 > b9=5, a2=5, e3=5, d58=58

18. c3=2 or h3=2, h1=3, a4=3, c3=3 > c3=23

19. e1=9, d6=9 or e1=6, c2=6, c3=2, c6=3 > c6!=9

20. c6=3, h4=3 or c6=6, f2=6, e4=6 > h4!=6, h7=6, ab7=48

21. c6=3, a3=3 or c6=6, f2=6, e4=6, d5=8, c2=8, b3=9, a3=3 > a3=3, c6=3, h4=3, k2=3, d1=3, h1=2, c3=2

22. h3=9, k9=9, k5=7 or b3=9, c2=8, cg5=69, k5=7 > k5=7

23. h3=9, k9=9, k6=2, d6=9 or b3=9, c2=8, f2=6, e1=9, d6=9 > d6=9 etc. singles

in summary the "important" or strategic steps:
2. h7!=3
3. h9!=3
4. k9!=3
5. a2!=3
6. h3!=3
7. c2!=3
8. f3!=3
9. a1!=3
10. g7!=1
11. g9!=3
12. d1!=1

The remaining steps are "bread and butter". Enjoy!
maria45

Posts: 54
Joined: 23 October 2005

### Re: Solution to Ocean's #1/M21/D21 ER 10.0

Nice and elegant solution, Maria!
(I study your solutions in slow motion - therefore my comments come slowly...).
Impressive how you find the eliminations, and steer towards the solution.
Ocean

Posts: 442
Joined: 29 August 2005

To give a feeling, how hard this puzzle is:
I looked at two of the 17 steps solutions my program found. In both it needed 10 eliminations, before the first time another candidate could be kicked off with basic methods! (I dont know, how much of the eliminations are really necessary.) There are so much possibilities to combine eliminations (in average there are about 10 possible eliminations for each of the 10 first steps, but there are big differences), that it is impossible for me, to optimise the order in reasonable time (without big effort).

To compare: in the (first) 9.9 puzzle (8 steps) of Ocean's recent list already after the second elimination other candidates fell out.

BTW: in the 2 17-steppers only 2 of the eliminations are common (r2c9<>7,r6c3<>2)
ravel

Posts: 998
Joined: 21 February 2006