## Solution to Ocean's BB

Advanced methods and approaches for solving Sudoku puzzles

### Solution to Ocean's BB

Here is a solution to Ocean's BB or M20 #10111

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

No trivial starting numbers to be found.

1. e3=6 or e7=6, b6=6, h3=6 > d3!=6

2. k5=6 or a5=6, b7=6, e3=6, k2=6 > k6!=6

3. a5=6 or k5=6, h3=6, e7=6, a8=6 > a6!=6

4. e6=7 or e3=6, h6=6, b7=6 > d7!=6

5. b6=1 or b9=1, f8=1, g2=1, h6=1 > cg6!=1, bh6=16

6. f8=1 or c8=1, g5=1, f2=1 > f19!=1

7. e3=2, (e456=579, df5=28, e7=6, a8=6, b6=6, k5=6, h3=6, d2=6, c2=2, b4=2, k6=2, h9=2, h6=1, c5=1, b9=1, e9=4, e1=1, g2=1, f8=1, a1=4, d3=4, b1=7, f2=7, d8=2, d5=8, f5=2, d7=7, g8=7, h4=7, k1=8, (g3=5, a2=5 or g7=5, c7=4, c8=9, b3=9, a2=5 >)a2=5, k2=9, h1=3, h7=9, k8=4, c8=9, c7=4, g7=3, g3=5, k9=5, f7=5, d1=5, k4=3, g5=9, g6=8, g4=4, f1=9, f3=3, d9=9, f9=8, a9=3, b8=8, c3=8, b3=9, c6=5, ae56=79 non-unique (alternatively c4=nil) > contradiction >) e3!=2

8. d2=2, (e3=6, d8=6, b7=6, a5=6, h6=6, k2=6, b6=1, c8=1, e9=1, f2=1, h1=1, g5=1, a2=7, b4=7, g6=7, h7=7, f8=7, f9=2, k8=2, h4=2, b3=2, (k9=5, k4=4 or k1=5, g2=9, g8=4, k4=4 >) k4=4, (c7=3, c3=4 or g7=3, a9=3, d4=4, e1=4, c3=4 >) c3=4, g3=8, k6=8, (g7=3, g4=9 or c7=3, a4=3, g4=9 >) g4=9, g2=5, c2=9, b1=8, b9=9, box9!=9 contradiction >) d2!=2

9. c2=2, b4=2, b1=7 or f2=2, e1=1, h6=1, c5=1 > e1!=7, c5!=2

10. e7=4, (d8=6, b7=6, b6=1, g5=1, h1=1, e1=9, e3=6, e9=1, df5=89, c5=3, f2=1, c8=1, k2=6, h6=6, a5=6, c2=2, b4=2, b1=7, a9=3, a8=4, k9=4, g4=4, c3=4, d1=4, d2=7, a12=5, g7=5, h7=3, k4=3, g3=3, f1=3, h3=9, g2=nil contradiction >) e7!=4

11. e9=4, (f8=1, e1=1, b9=1, c5=1, h6=1, g2=1, b6=6, a8=6, e7=6, d2=6, h3=6, k5=6, e3=9, df5=89, e5=2, a1=4, d3=4
c8=9 or c8=4, g7=4, g3=5, k2=9 > c2!=9, k8!=9
c7=4 or c8=4, g7=4, g3=5, k2=9, b1=9, k8=2, h1=3, h9=9, c7=9 > c78=49, b7=8, a9=3, b3=2, a5=7, b4=9, a2=9, ck2=5 contradiction >) e9!=4, e13=4

12. e1=4 or e3=4, h3=6, h6=1, g2=1, e1=1 > e1!=9

13. d7!=7, e456=7, df5!=7 or e7=7, e3=6, d8=6, b7=6, a5=6, h6=6, k2=6, b6=1, c8=1, e9=1, f2=1, h1=1, g3=1, g8=7, h4=7, b1=7, d2=7, f5=7, a6=7, e1=4, c3=4, c2=2, b4=2, h9=2, f8=2, d3=2, d5=8 > d5!=7

14. k5!=2, def5=2, e46!=2 or k5=2, h6=6, g5=1, a5=6, b6=1, c5=3, e46=25, h9=2, c8=1, b7=6, e9=1, e1=4, f2=1, c2=2, b4=2 > e4!=2

15. c6=2, (b3=2, f2=2, e1=1, e3=4, d2=6, h3=6, h6=1, k5=6, g2=1, a2=7, b4=7, a1=4, b6=6, c5=1, a8=6, b9=1, f6=1, e7=6, e56=7, h7=7, d8=7, f1=7, f3=3, d13=59, a46=5, (k9=4, d7=4, c8=4 or k9=4, d7=8, b7=9, c8=4 >) c8=4, g8=9, k8=2, h4=2, h9=3, c7=3, h1=9, d1=5, d3=9, b1=8, b7=9, a9=8, k1=3, k2=5, k9=4, g4=4, d7=4, d9=2, e9=9, g3=8, d5=8, c2=9, c3=5, c4=8, f9=5, f7=8, g7=5, g6=7, e6=5, e4=nil contradiction>) c6!=2, bc4=2, k56=2, h9=2

16. c2=2, b4=2, b1=7 or f2=2, d8=2, e1=1, g2=1, h6=1, c5=1, b9=1, f8=1, b6=6, a8=6, e7=6, d2=6, h3=6, k5=6, a2=7, b4=7, b3=2, c4=2, e3=4, a1=4, a46=5, e9=9, e4=5, a6=5, a45=9, c6=8, b1=8, b7=9, c8=4, k8=9, k2=5, c2=9, c3=5 > c2=29, b4=27, b1=78, c3!=2, a1!=7

17. e9=9 or e9=1, b6=1, b7=6, d8=6, e3=6 > d8!=9, e3!=9

18. e9=9, df5=89 or e9=1, b6=1, a5=6, g5=1> ag5!=9

19. f2=2, (b3=2, b4=7, b1=8, a2=7, c2=9, g2=1, e1=1, e3=4, c3=5, a1=4, s2=6, k2=5, d3=9, f3=3, g3=8, h3=6, e9=9, f8=1, b9=1, b6=6, a8=6, e7=6, k5=6, h6=1, a5=3, c6=8, c5=1, c4=2, a9=8, b7=9, g5=7, gk8=49, c8=nil contradiction >) f2!=2, c2=2, b4=2, b1=7

20. d2=6, f2=7 or e3=6, e1=4, f2=1 > f2=17

21. d2=6 or e3=6, e1=4, f2=1, d2=7 > d2=67
(20+21 could of course also be reduced by noticing the naked quadruple, but this came later to me, somehow I see the forcing chains easier)

22. e3=4, (d2=6, f2=7, e1=1, e9=9, e7=6, f8=1, e9=9, d8=2, f3=2, a1=4, b9=1, b6=6, a8=6, c5=1, h6=1, k5=6, h3=6, g2=1, g8=7, d7=7, h4=7, d9=4, k1=8, g5=3, a5=7, e6=7, e4=5, k6=2, h1=3, h7=9, k8=4, k4=9, g6=8, g7=5, f7=8, b7=nil contradiction >) e1=4, e3=6, d8=6, b7=6, a5=6, h6=6, k2=6, b6=1, c8=1, e9=1, f2=1, h1=1, g5=1, d2=7, e56=2, ak8=49, g8=7, f8=2, d3=2, h4=7, a6=7, c3=4

23. colors with 9 at ag2, b39, h37, ak8 > a19!=9, c37!=9, g37!=9, k19!=9
(dunno if this is really coloring, but seems to me so, I don't care much about all the names. Anyway, it's a very nice pattern!)

24. g3=8, g6=9, k8=9 or b3=8, b9=9, k8=9 > k8=9 and the remaining numbers fall into place.

Greetings, Maria

edited: 3 of the solution step numberings were missing.
Last edited by maria45 on Fri Jul 28, 2006 4:16 pm, edited 1 time in total.
maria45

Posts: 54
Joined: 23 October 2005

Wow,

you are solving faster than i can read it. Are you sure that you are no program ?
ravel

Posts: 998
Joined: 21 February 2006

who could be sure of that?
but, may be, my typos give me away, that I'm not entirely preprogrammed.

On the other hand, you know, everything is made up of numbers and numerical relations, so numbers should come quite naturally to a mind in tune with everything...

But, I frankly hope, I won't become numb and number...
maria45

Posts: 54
Joined: 23 October 2005

Thanks for the lyrics, i will keep that in mind.

In the moment i'm too busy to look at this solution.
ravel

Posts: 998
Joined: 21 February 2006

Some comments to the solution now, which reads similar to my brute force programs output - with typos.
I cant follow step 19 (though i see another way to eliminate 2 from f2), the others are details.

Steps 1-6 can be done with 2 swordfishes.
Step 7: k6=2 after h6=1, e9=4 after e1=1
Step 8: typo d4=4->d9=4
Step 10: k4=3, g3=3, f1=3 can be left out
Step 11: dont see c4!=9 (not needed)
Step 13: typo g3=1->g5=1
Step 14: k5=2 leads to a contradiction in h9 (... b6=1=>h9=1 and c5=3, e46=25, h9=2) => k5!=2, e46!=2
Step 15: typo f6=1->f8=1, a46=5:missing a1=4, (.. k9=4, d7=8) should be (..d9=4, d5=2, d7=8)
Step 16: typo d8=2->h8=2
Step 18: g5=1: missing h5=6
Step 19: b3=2??? why not c3?
Step 22: e9=9 repeated, g6=8? (not necessary)
Step 23: Yes, can be done with (advanced) coloring (or strong links)
ravel

Posts: 998
Joined: 21 February 2006

Step 19:
I concluded in step 16, that c3!=2, because either c2=2 or f2=2,..., c3=5 (its the last step in the forcing chain before the ">"-sign, perhaps you overlooked it.)
maria45

Posts: 54
Joined: 23 October 2005

Ah thanks, i missed that.
ravel

Posts: 998
Joined: 21 February 2006

### Re: Solution to Ocean's BB

maria45 wrote:Here is a solution to Ocean's BB or M20 #10111

Thank you for taking the time to solve this puzzle! Hope you had fun! Will be interesting to analyze and compare the various solutions (yours, Ravel's and Explainer's).
Ocean

Posts: 442
Joined: 29 August 2005

Hi Ocean,

oh, really, your puzzles have already provided many hours of real enjoyment. Thank you very much!!!

At the moment I'm at your #7/18, but have not enough time, so it goes slowly.

Best regards, Maria
maria45

Posts: 54
Joined: 23 October 2005