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PostPosted: Sat Oct 20, 2012 3:33 pm 
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Grand Master
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 694
Location: Saudi Arabia
Almost Human Solvable 12

Sudoku solver fails on this one however on stepping though it I think it is a software fault. JSudoku solves it comfortably.

I would estimate it is about 1.0.


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JS code:
3x3:d:k:10497:10497:10497:10497:9993:10243:10243:10243:10243:10497:9993:1295:1295:9993:16:17:8714:10243:10497:18:9993:9993:9993:8714:8714:19:10243:10497:20:7691:9993:21:8714:22:23:10243:7691:7691:7691:24:25:26:8714:8714:8714:10244:27:28:7691:29:9996:9996:30:10498:10244:31:7691:32:9996:33:9996:34:10498:10244:7691:2829:2829:9996:1806:1806:9996:10498:10244:10244:10244:10244:9996:10498:10498:10498:10498:

Solution:

256937481
871452396
439681275
763148529
182569743
594723618
615294837
948376152
327815964


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PostPosted: Sat Oct 20, 2012 11:36 pm 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Thanks HATMAN for another enjoyable puzzle. :D
It was fun:
getting out all the 1s and 3s which form the way into this puzzle. I assume that "Almost Human Solvable 12" means that it's not quite as hard as some other Human Solvables.

So many hidden singles and hidden pairs. My solving path might have been shorter if I'd seen some of the hidden singles sooner.

Here is my walkthrough for Almost Human Solvable 12:
Prelims

a) R2C34 = {14/23}
b) R8C34 = {29/38/47/56}, no 1
c) R8C67 = {16/25/34}, no 7,8,9
d) 41(7) cage at R1C1 = {2456789}, no 1,3
e) 41(7) cage at R6C9 = {2456789}, no 1,3

1. Hidden killer pair 1,3 in R1C5 and 40(7) cage at R1C6 for R1, 40(7) cage contains one of 1,3 -> R1C5 = {13}, 1 or 3 in 40(7) cage must be in R1 -> no 1,3 in R234C9
1a. R15C9 = {13} (hidden pair in C9)
1b. Naked pair {13} in R1C59, locked for R1

2. Hidden killer pair 1,3 in 40(7) cage at R6C1 and R9C5 for R9, 40(7) cage contains one of 1,3 -> R9C5 = {13}, 1 or 3 in 40(7) cage must be in R9 -> no 1,3 in R678C1
2a. R15C1 = {13} (hidden pair in C1)
2b. Naked pair {13} in R5C19, locked for R5
2c. Naked pair {13} in R9C15, locked for R9
2d. Naked pair {13} in R19C5, locked for C5
2e. Naked pair {13} in R1C9 + R9C1, locked for D/

3. R4C4 + R6C6 = {13} (hidden pair in N5), locked for D\
3a. Naked pair {13} in R1C5 + R4C4, locked for 39(7) cage at R1C5
3b. 39(7) cage at R1C5 = {1356789} (only remaining combination), no 2,4
3c. Naked pair {13} in R6C6 + R9C5, locked for 39(7) cage at R6C6
3d. 39(7) cage at R6C6 = {1356789} (only remaining combination), no 2,4
3e. 2,4 in C5 only in R456C5, locked for N5

4. R2C3 + R3C2 = {13} (hidden pair in N1) -> R2C34 = [14/32]
4a. 2 in N1 only in R1C123 + R23C1, locked for 41(7) cage at R1C1, no 2 in R1C4 + R4C1

5. R7C8 + R8C7 = {13} (hidden pair in N9) -> R8C67 = [43/61]
5a. 2 in N9 only in R78C9 + R9C789, locked for 41(7) cage at R6C9, no 2 in R6C9 + R9C6

6. 40(7) cages at R1C6 and R6C1 each contain one of 2,4, 41(7) cages at R1C1 and R6C9 each contain both of 2,4
6a. 2,4 in R19 and C19 can only be in the 40(7) and 41(7) cages -> R1C1 + R9C9 = {24} (only way to place enough 2s and 4s in R19 and C19), locked for D\
6b. R46C5 = {24} (hidden pair in N5)

7. 30(7) cage at R4C3 = {1234569/1234578} -> R4C3 + R5C1 = {13}, locked for N4
7a. Naked pair {13} in R4C34, locked for R4
7b. Naked pair {13} in R24C3, locked for C3, clean-up: no 8 in R8C4

8. 30(7) cage at R4C3 = {1234569/1234578}, CPE no 5 in R5C5

9. R6C68 = {13} (hidden pair in R6)
9a. Naked pair {13} in R67C8, locked for C8

10. R1C9 + R2C7 = {13} (hidden pair in N3)
10a. Naked pair {13} in R2C37, locked for R2)

11. R1C5 + R3C6 = {13} (hidden pair in N2)
11a. Naked pair {13} in R36C6, locked for C6

12. R7C2 + R9C1 = {13} (hidden pair in N7)
12a. Naked pair {13} in R7C28, locked for R7

13. R9C5 = 1 (hidden single in N8), R1C59 = [31], R5C19 = [13], R9C1 = 3, R2C7 = 3, R2C3 = 1, R2C4 = 4, R3C26 = [31], R4C34 = [31], R6C68 = [31], R7C28 = [13], R8C7 = 1, R8C6 = 6
13a. R8C4 = 3 (hidden single in N8), R8C3 = 8

14. 40(7) cage R6C1 = {2356789} (only remaining combination), no 4
14a. 8 must be in R6C1 + R9C4, CPE no 8 in R6C4

15. 4 in N7 only in R7C3 + R8C2, locked for D/ and 30(7) cage at R4C3, no 4 in R5C23
15a. 4 in C1 only in R1234C1, locked for 41(7) cage at R1C1, no 4 in R1C23
15b. 4 in N1 only in R123C1, locked for C1
15c. 4 in R9 only in R9C6789, locked for 41(7) cage at R6C9, no 4 in R678C9
15d. 4 in N9 only in R9C789, locked for R9

16. 4 in R5 only in R5C78, locked for N6
16a. 34(7) cage at R2C8 contains 3,4 = {1234789/1345678}, CPE no 7,8 in R5C5

17. 30(7) cage at R4C3 = {1234578} (only remaining combination, cannot be {1234569} which clashes with R5C5), no 6,9 -> R5C2 = 8

18. 40(7) cage R6C1 (step 14) = {2356789} -> R9C4 = 8
18a. 41(7) cage at R6C9 = {2456789}, 8 locked for C9
18b. 8 in C5 only in R23C5, locked for N2

19. R4C6 = 8 (hidden single in C6)

20. R7C7 = 8 (hidden single on D\), R1C8 = 8 (hidden single in R1), R6C9 = 8 (hidden single in R6)

21. 39(7) cage at R6C6 (step 3d) = {1356789} -> R6C7 = 6
21a. 39(7) cage = {1356789}, CPE no 9 in R5C5 -> R5C5 = 6, placed for both diagonals

22. 39(7) cage at R1C5 (step 3b) = {1356789} -> R3C4 = 6

23. R2C9 = 6 (hidden single in N3), R9C8 = 6 (hidden single in N9), R7C1 = 6 (hidden single in N7)

24. R7C46 = [24] (hidden pair in N8)
24a. Naked pair {57} in R6C4 + R7C3, locked for D/ and 30(7) cage at R5C1 -> R5C2 = 2, R8C2 = 4
24b. Naked pair {29} in R2C8 + R3C7, locked for N3 and 34(7) cage at R2C8, no 9 in R5C78

25. R16C3 = [64] (hidden pair in C3), R46C5 = [42]
25a. 9 in R6 only in R6C12, locked for N4

26. 40(7) cage at R1C6 contains 1 = {1456789}, no 2, 4 locked for N3

27. 2 in R1 only in R1C12, locked for N1

28. R2C6 = 2 (hidden single in N2), R2C8 = 9, R3C7 = 2

29. R3C3 = 9 (hidden single on D\)
29a. 9 in C5 only in R89C5, locked for N8
29b. Naked pair {57} in R9C36, locked for R9

30. Naked pair {57} in R38C8, locked for C8 -> R45C8 = [24]

31. 34(7) cage at R2C8 (step 16a) = {1234789} (only remaining combination) -> R5C7 = 7

32. R6C4 = 7 (hidden single in N5), R7C3 = 5, R9C37 = [75]

33. Naked pair {29} in R8C1 + R9C2, locked for 40(7) cage at R6C1 -> R6C1 = 5, R6C2 = 9, R9C2 = 2, R9C9 = 4, placed for D\, R1C1 = 2

and the rest is naked singles, without using the diagonals.

SudokuSolver:
v3.3.1 (the version I've got on my computer until I complete Archive Part G) couldn't manage part of my step 1. It didn't eliminate 1,3 from R234C9 so didn't get some of my {13} naked pairs in steps 1 and 2.


Rating Comment:
I'll rate my walkthrough for Almost Human Solvable 12 at 1.25, mainly because of step 6 plus there were so many hidden singles and hidden pairs.

SudokuSolver v3.3.1 scores it at 7.82, using extensive T&E. I've mentioned above one thing it, surprisingly, couldn't do.


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PostPosted: Mon Oct 22, 2012 5:25 pm 
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Grand Master
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Joined: Wed Apr 30, 2008 9:45 pm
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Location: Saudi Arabia
Andrew similar to mine but after your step 2 I did "overlaps r19c19 to get r1c1&r9c9 = {24}"


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PostPosted: Mon Oct 22, 2012 6:35 pm 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
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Location: Lethbridge, Alberta, Canada
Thanks for posting that. I tend to forget about overlaps. I got the same result in step 6 using different logic.


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PostPosted: Tue Oct 23, 2012 4:22 pm 
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Grand Master
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Joined: Wed Apr 30, 2008 9:45 pm
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Location: Saudi Arabia
Would that change your rating?


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PostPosted: Tue Oct 23, 2012 6:08 pm 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
HATMAN wrote:
Would that change your rating?
No, I don't think so. I'd say that both ways are in the same rating range, although at a Human Solvable level your way may seem easier.

[Note that I've deliberately avoided including any rating numbers in this reply. If anyone wants to see my rating for this puzzle, it's in hidden text in my walkthrough post.]


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PostPosted: Thu Dec 06, 2012 7:45 pm 
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Addict
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Joined: Fri May 16, 2008 12:18 am
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This one was really nice. Great use of the diagonals.


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PostPosted: Fri Dec 07, 2012 12:51 pm 
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Grand Master
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Thanks Bram - I've got a bit obsessive about sevens recently


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