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HATMAN
 Post subject: HS 7 Elevens
PostPosted: Tue Feb 02, 2010 2:01 pm 
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HS 7 X Elevens

I've been trying to put together a killer with just one cage total and chose 11 as sort of easiest. I've not found one satisfactory enough for an assassin, however this human solvable came out of the mix.

JSudoku uses about 20 fishes and SudokuSolver gives it 5.4. Once the primary HS move is identified it is still quite hard.

Image

Code (add 11(3) @r4c4r5c5r6c6):
3x3:d:k:2817:0000:0000:0000:4354:0000:0000:0000:2819:0000:2817:1540:0000:4354:0000:1029:2819:0000:0000:1540:2822:2822:2823:2823:2824:1029:0000:0000:0000:2825:0000:0000:2826:2824:0000:0000:0000:0000:2825:0000:2826:0000:2827:0000:0000:0000:0000:2828:2826:0000:0000:2827:0000:0000:0000:2061:2828:2830:2830:2831:2831:4112:0000:0000:2833:2061:0000:0000:0000:4112:2834:0000:2833:0000:0000:0000:0000:0000:0000:0000:2834:

Equivalent Code(following obvious initial deduction):
3x3:d:k:2817:0000:0000:0000:4354:0000:0000:0000:2819:0000:2817:1540:0000:4354:0000:1029:2819:0000:0000:1540:2822:2822:2823:2823:2824:1029:0000:0000:0000:2825:2570:0000:2571:2824:0000:0000:0000:0000:2825:0000:268:0000:2829:0000:0000:0000:0000:2830:2571:0000:2570:2829:0000:0000:0000:2063:2830:2832:2832:2833:2833:4114:0000:0000:2835:2063:0000:0000:0000:4114:2836:0000:2835:0000:0000:0000:0000:0000:0000:0000:2836:

Both solvers have problems with overlapping cages.
Solution:

732185469
845396127
619247538
293874615
568913274
174652983
427568391
986431752
351729846


Codes corrected follwing Borge's post


Last edited by HATMAN on Wed Feb 03, 2010 11:14 am, edited 1 time in total.

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Børge
 Post subject: Re: HS 7 Elevens
PostPosted: Tue Feb 02, 2010 10:01 pm 
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Is the PS code correct?
It yields the following puzzle, which is different from my interpretation of your image.

  • Cage with sum 6 in (r2c3 + r3c2) is missing.
  • The two cages with sum 11 in n5 are different.

I have triple checked by pasting your PS code into JSudoku + SudokuSolver + my program.
All three produces identical puzzles and images.

Image

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Børge
 Post subject: Re: HS 7 Elevens
PostPosted: Wed Feb 03, 2010 4:52 pm 
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Maurice,

From your image I did not interpret that the two 11(3) cages in n5 overlap in r5c5:
11(3)@r4c4+r5c5+r6c6
11(3)@r4c6+r5c5+r6c4

PS code does not support overlapping cages, nor does SumoCue or tarek.

Human Solvable 7 X Elevens images with udosuk Style Killer Cages: 
Image     Image

This is a clickable link to the "Human Solvable" series by HATMAN thread where I also have added the "udosuk Style Killer Cages" images for Human Solvable 7 X Elevens.

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Last edited by Børge on Thu Feb 04, 2010 2:36 pm, edited 1 time in total.

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HATMAN
 Post subject: Re: HS 7 Elevens
PostPosted: Thu Feb 04, 2010 1:30 pm 
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Borge - that looks good, now let us see if someone can solve it.
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Børge
 Post subject: Re: HS 7 Elevens
PostPosted: Thu Feb 04, 2010 3:57 pm 
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Settling for two less cages with a cage total of 11, I think that the following is a better presentation of HS 7 X Elevens.

Your second PS code gets an SS score of 6.17 versus 6.18 for mine.
JSudoku's solving path is virtually identical for the two representations; same solving techniques but some small differences in the number of times each technique is deployed.
I think that the minor differences are due to JSudoku's non-deterministic solving.

Alternative easier images after obvious initial deduction: 
Image     Image
3x3:d:k:2817:20:21:22:4369:23:24:25:2818:26:2817:1549:27:4369:28:1038:2818:29:30:1549:2819:2819:2820:2820:2821:1038:31:32:33:2826:2578:34:2579:2821:35:36:37:38:2826:39:40:41:2822:42:43:44:45:2825:2579:46:2578:2822:47:48:49:2064:2825:2824:2824:2823:2823:4111:50:51:2827:2064:52:53:54:4111:2828:55:2827:56:57:58:59:60:61:62:2828:


While lingering at airports around the world waiting for delayed aircrafts, you might want to try this veQrsion: :twisted:
Image     Image
3x3:d:k:2817:20:21:22:4369:23:24:25:2818:26:2817:1549:27:4369:28:1038:2818:29:30:1549:2819:2819:2820:2820:2821:1038:31:32:33:2826:2834:34:2835:2821:35:36:37:38:2826:39:40:41:2822:42:43:44:45:2825:2835:46:2834:2822:47:48:49:2064:2825:2824:2824:2823:2823:4111:50:51:2827:2064:52:53:54:4111:2828:55:2827:56:57:58:59:60:61:62:2828:

Solution:

783291654
945683172
216574938
137968245
824715369
569342817
472836591
351429786
698157423

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Last edited by Børge on Thu Aug 26, 2010 6:14 pm, edited 1 time in total.

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HATMAN
 Post subject: Re: HS 7 Elevens
PostPosted: Thu Feb 04, 2010 7:45 pm 
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That is a brutal one - unique but both solvers fail on it and my HS technique does not work

So the challenge is what to add to make it solvable.
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Afmob
 Post subject:
PostPosted: Thu Feb 04, 2010 11:39 pm 
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Thanks for the new HS!

My walkthrough contains a lot of fun moves though some of them are quite difficult. I think step 7 and possible step 4 are not necessary to solve this Killer but I decided to keep them in anyways since they don't raise the rating.

HS 7 X Walkthrough:

1. D\/ + N9 !
a) 1 locked in 11(3) @ D\ for N5 -> 11(3) <> 5
b) Hidden Single: R5C5 = 1 @ D/
c) 16(2) = {79} locked for N9
d) 11(2) @ R8C8 <> 2,4
e) 9 locked in R1C1+R2C2+R3C3 @ D\ for N1
f) Innies D\ = 12(2) <> 2,6; R3C3 <> 3,5
g) ! Killer quad (3568) locked in Innies D\ + 11(3) + R8C8 + R9C9 for D\

2. R123
a) 17(2) = {89} locked for C5+N2
b) 4(2) = {13} locked for N3
c) 6(2) = {15} locked for N1 since (24) is a Killer pair of 11(2) @ R1C1
d) 11(2) @ R3C5 <> 2,3

3. D\/
a) Innies D/ = 12(2) <> 2,6; R7C3 <> 9
b) 5 locked in R7C7+R8C8+R9C9 @ D\ for N9
c) 5 locked in both 11(2) @ N9 -> One must be {56} -> CPE: R7C9+R6C6 <> 6
d) 9 locked in both 11(2) @ N1 -> One must be {29} -> CPE: R3C1+R4C4 <> 2

4. R34567 !
a) 9 locked in R5C46 @ N5 for R5
b) ! Jellyfish: 1 locked in R3467 for C1289

5. R37 + D\/ !
a) ! Innies R3 = 23(5): R3C9 <> 9 since 2 only possible there and {13469} blocked by Killer pair (46) of 11(2) @ R3C5
b) ! 9 locked in R3C37 @ R3 -> One of Innies D\ + Innies D/ must be {39} -> 3 locked in R7C37 for R7
c) 11(2) @ R7C4: R7C4 <> 2,8
d) 11(2) @ R7C6 = [65/74/83]
e) Innies D\ = 12(2): R3C3 <> 4
f) 11(2) @ R3C3: R3C4 = (234)
g) 3 locked in R7C37 @ R7 -> One of 11(2) must be {38} -> R7C3 <> 8

6. D\/ !
a) ! Consider placement of R2C3 -> R7C3 <> 5:
- i) R2C3 = 1 -> R2C7 = 3 -> R7C3 = 3 (HS @ R7)
- ii) R2C3 = 5
b) 11(2) @ R6C3: R6C3 = (478)
c) Innies D/ = 12(2): R3C7 <> 4,7
d) ! Consider placement of 3 in R7 -> R3C3 <> 8
- i) R7C3 = 3 -> R6C3 = 8
- ii) R7C7 = 3 -> Innie D\ = R3C3 = 9
e) Killer pair (79) locked in 11(2) @ R1C1 + R3C3 for N1+D\
f) 11(2) @ R3C3 <> 3
g) 11(3) @ R4C4 <> 3
h) 3 locked in R7C7+R8C8+R9C9 @ D\ for N9
i) 3,5 locked in both 11(2) @ N9 <> 4,7 -> CPE: R7C9 <> 8

7. C789 !
a) ! Killer quad (3579) locked in 11(2) @ R3C7 + 11(2) @ R5C7 + R78C7 for C7
b) R2C7 = 1, R3C8 = 3, R2C3 = 5, R3C2 = 1
c) Hidden Single: R7C9 = 1 @ N9

8. R123 !
a) 7 locked in both 11(2) @ N1 -> One must be {47} -> CPE: R3C1 <> 4
b) 8 locked in Innies R3 = 19(3) = 8{29/56} since 4,7 only possible @ R3C9
c) ! Consider placement of 9 in R3 -> R7C1 <> 8:
- i) R3C3 = 9 -> Innie D\ = R7C7 = 3 -> R7C6 = 8
- ii) R3C7 = 9 -> Innies R3 = 10(2) = [82] -> R3C1 = 8
d) Hidden Single: R7C6 = 8 @ R7 -> R7C7 = 3
e) Innie D\ = R3C3 = 9
f) Cage sum: R3C4 = 2
g) 11(2) @ R1C1 = {47} locked for N1+D\
h) R6C6 = 2 -> R4C4 = 8

9. D\/ + N49
a) 11(2) @ R3C7 = {56} -> R3C7 = 5, R4C7 = 6
b) 11(2) @ R6C3 = {47} locked for C3
c) 11(2) @ R4C3 = {38} -> R4C3 = 3, R5C3 = 8
d) Naked pair (47) locked in R4C6+R7C3 for D/
e) 11(2) @ R1C9 = {29} locked for N3+D/
f) 11(2) @ R8C2 = {38} locked for N7+D/
g) R6C4 = 6 -> R4C6 = 4
h) 8(2) <> 5

10. Rest is singles.

Rating:
(Easy 1.75?). I used short forcing chains and locked cages.

To add one more PS Code to this thread :D, here is one which even works for SumoCue which apparently isn't the case for PS codes given so far:
(Note that it contains a minor spoiler)

3x3:d:k:2816:1:2:3:4356:5:6:7:2824:9:2816:1547:12:4356:14:1039:2824:17:18:1547:2836:2836:2838:2838:2840:1039:26:27:28:2845:2846:31:2592:2840:34:35:36:37:2845:39:2846:41:2858:43:44:45:46:2863:2592:49:2846:2858:52:53:54:2103:2863:2873:2873:2875:2875:4157:62:63:2880:2103:66:67:68:4157:2886:71:2880:73:74:75:76:77:78:79:2886:


Last edited by Afmob on Wed Feb 10, 2010 7:15 am, edited 1 time in total.

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HATMAN
 Post subject: Re: HS 7 Elevens
PostPosted: Fri Feb 05, 2010 12:55 pm 
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Nice solution Afmob better than I would have thought without using my human solvable deduction.

I've pmed my HS bit to Afmob and will post it in a week.
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Andrew
 Post subject: Re: HS 7 Elevens
PostPosted: Fri Feb 12, 2010 12:39 am 
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Thanks HATMAN for another challenging HS! I must have another look at some of the earlier ones; I got stuck on two of them and haven't yet started two others.

I used many of the steps that Afmob used but also did some permutation analysis before I started looking at locking cages; I must admit that I was surprised to find how important some eliminations from non-cage cells were. Afmob expressed some steps more clearly than I did, an example being step 5g. Then Afmob's step 8c, an elimination from a non-cage cell, cracked this puzzle quickly. My breakthrough in steps 34 and 35 was different.

I also liked Afmob's step 4b. That's something that harder to spot for someone working on an Excel worksheet, as I do, or with paper and pencil; I understand that software solvers have a function which can be used to highlight where each number is.

Rating Comment:
I wasn't really sure how to rate HS7 so I'll go along with Afmob's rating of (Easy?) 1.75; my hardest steps were similar to Afmob's ones although I did use more of them.

Here is my walkthrough for Human Solvable 7:
Prelims

a) 11(2) cage at R1C1 = {29/38/47/56}, no 1
b) R12C5 = {89}
c) 11(2) cage at R1C9 = {29/38/47/56}, no 1
d) 6(2) cage in N1 = {15/24}
e) 4(2) cage in N3 = {13}
f) R3C34 = {29/38/47/56}, no 1
g) R3C56 = {29/38/47/56}, no 1
h) R34C7 = {29/38/47/56}, no 1
i) R45C3 = = {29/38/47/56}, no 1
j) R56C7 = {29/38/47/56}, no 1
k) R67C3 = {29/38/47/56}, no 1
l) R7C45 = {29/38/47/56}, no 1
m) R7C67 = {29/38/47/56}, no 1
n) 8(2) cage in N7 = {17/26/35}, no 4,8,9
o) 16(2) cage in N9 = {79}
p) 11(2) cage at R8C2 = {29/38/47/56}, no 1
q) 11(2) cage at R8C8 = {29/38/47/56}, no 1
r) 11(3) cage at R4C4 = {128/137/146/236/245}, no 9
s) 11(3) cage at R4C6 = {128/137/146/236/245}, no 9

Steps resulting from Prelims
1a. Naked pair {89} in R12C5, locked for C5 and N2, clean-up: no 2,3 in R3C3, no 2,3 in R3C56, no 2,3 in R7C4
1b. Naked pair {13} in 4(2) cage, locked for N3, clean-up: no 8 in 11(2) cage at R1C9, no 8 in R4C7
1c. Naked pair {79} in 16(2) cage, locked for N9, clean-up: no 2,4 in R7C6, no 2,4 in 11(2) cage at R8C8
1d. 9 in D\ only in 11(2) cage at R1C1 and R3C3, locked for N1
1e. 9 in N5 only in R5C46, locked for R5, clean-up: no 2 in R4C3, no 2 in R6C7

2. 1 in D\ only in 11(3) cage at R4C4, locked for N5
2a. R5C5 = 1 (hidden single in D/)
2b. 11(3) cage at R4C4 = {128/137/146}, no 5
2c. 11(3) cage at R4C6 = {128/137/146}, no 5

3. 45 rule on D\ 2 innies R3C3 + R7C7 = 12 = [48/75/84/93], no 2,6, no 5 in R3C3, clean-up: no 5,6 in R3C4, no 5,9 in R7C6

4. 45 rule on D/ 2 innies R3C7 + R7C3 = 12 = {48/57}/[93], no 2,6, no 9 in R7C3, clean-up: no 5,9 in R4C7, no 2,5,9 in R6C3

5. 45 rule on D\ 4 innies R3C3 + R4C4 + R6C6 + R7C7 = 22 = {2938/2947/2956/3847/3856/4756} (other combinations clash with one or both of the 11(2) cages on D\)
5a. R3C3 + R4C4 + R6C6 + R7C7 = {2938/3847/4756} (cannot be {2947/2956/3856} which clash with combinations for R3C3 + R7C7)
5b. 2 of {2938} must be in R6C6 (R3C3 + R4C4 cannot be [92] because of CCC with R3C34), no 2 in R4C4, clean-up: no 8 in R6C6 (step 2b)
5c. 4 of {3847} must be in R3C3 + R7C7, 4 of {4756} must be in R6C6 (R3C3 + R4C4 cannot be [74] because of CCC with R3C34), no 4 in R4C4, clean-up: no 6 in R6C6 (step 2b)

6. Killer quad 3,5,6,8 in R3C3 + R4C4 + R6C6 + R7C7 and 11(2) cage at R8C8, locked for D\

7. 6(2) cage in N1 = {15} (cannot be {24} which clashes with 11(2) cage at R1C1), locked for N1
7a. 1 in R1 only in R1C46, locked for N2
7b. 5 in D\ only in R7C7 + R8C8 + R9C9, locked for N9

8. 45 rule on D/ 4 innies R3C7 + R4C6 + R6C4 + R7C3 = 22 = {2938/2947/2956/3847/3856/4756} (other combinations clash with one or both of the 11(2) cages on D/)
8a. R3C7 + R4C6 + R6C4 + R7C3 = {2938/3847/4756} (cannot be {2947/2956/3856} which clash with combinations for R3C7 + R7C3)
8b. 2 of {2938} must be in R6C4 (R3C7 + R4C6 cannot be [92] because of CCC with R34C7), no 2 in R4C6, clean-up: no 8 in R6C4 (step 2c)

9. 9 in N1 only in 11(2) cage at R1C1 and R3C3 -> 11(2) cage at R1C1 = {29} or R3C34 = [92] (locking cages), CPE no 2 in R3C1
9a. 2 in R3 only in R3C4 and R3C9 -> R3C34 = [92] or R3C79 = [92] (locking cages), no 9 in R3C9

10. 9 in R3 only in R3C37 -> R3C3 + R4C4 + R6C6 + R7C7 = [9823] or R3C7 + R4C6 + R6C4 + R7C3 = [9823] (locking cages, permutations of {2938} follow from steps 3 and 4 which place the 3s and therefore the 2,8s) -> 8 locked in R4C46, locked for R4 and N5, 2 locked in R6C46, locked for R6 and N5, 3 locked in R7C37, locked for R7, clean-up: no 3 in R5C3, no 8 in R7C4, no 8 in R7C7, no 5 in R8C3, no 4 in R3C3 (step 3), no 7 in R3C4
10a. 2 in C5 only in R789C5, locked for N8

11. R3C3 + R4C4 + R6C6 + R7C7 (step 5a) = {2938/3847/4756} = [7645/8734/9823] (cannot be [8347] which clashes with R3C34], no 3 in R4C4, no 7 in R6C6

12. R3C3 = 9 or R7C3 = 3 (from locking cages in step 10) => R6C3 = 8 -> no 8 in R3C3, clean-up: no 7 in R4C4, no 3 in R6C6, no 4 in R7C7 (all step 11), no 3 in R3C4, no 7 in R7C6
12a. Killer pair 7,9 in 11(2) cage at R1C1 and R3C3, locked for N1
12b. Killer pair 3,5 in R7C7 and 11(2) cage at R8C8, locked for N9

13. R3C7 = 9 or R7C7 = 3 (from locking cages in step 10) => no 3 in R4C7 -> no 8 in R3C7, clean-up: no 3 in R4C7, no 4 in R7C3 (step 4), no 7 in R6C3

14. R3C7 + R4C6 + R6C4 + R7C3 (step 8a) = {2938/3847/4756} = [4378/5467/7645/9823] (cannot be [4783/5647/7465] which clash with R67C3]), no 7 in R4C6, no 3 in R6C4

15. 3 in R7 only in R7C37, R7C3 = 3 or R7C7 = 3 => R7C6 = 8 -> no 8 in R7C3, clean-up: no 4 in R3C7, no 3 in R4C6, no 7 in R6C4 (all step 14), no 7 in R4C7, no 3 in R6C3

16. Killer quad 3,5,7,9 in R7C3, R7C45, R7C7 and R7C8, locked for R7, clean-up: no 1,3 in R8C3

17. Killer quad 3,5,7,9 in R3C7, R56C7, R7C7 and R8C7, locked for C7 -> R2C7 = 1, R3C8 = 3, R2C3 = 5, R3C2 = 1, clean-up: no 7 in R3C7, no 6 in R4C6, no 4 in R6C4 (all step 14), no 6 in R1C9, no 6 in R45C3, no 4 in R4C7, no 6 in R6C3, no 7 in R8C3, no 8 in R9C9
17a. Naked quad {2468} in R46C46, 4,6 locked for N5
17b. 4 in N5 only in R46C6, locked for C6, clean-up: no 7 in R3C5
17c. 6 in N5 only in R46C4, locked for C4, clean-up: no 5 in R7C5
17d. 8 on D\ only in R4C4 + R8C8, CPE no 8 in R8C4

18. Naked pair {26} in 8(2) cage, locked for N7, clean-up: no 5,9 in 11(2) cage at R8C2
18a. Killer pair {37} in R7C3 and 11(2) cage at R8C2, locked for N7 and D/, clean-up: no 4 in 11(2) cage at R1C9
18b. Killer pair 5,9 in 11(2) cage at R1C9 and R3C7, locked for N3

19. R9C3 = 1 (hidden single in C3)
19a. R7C9 = 1 (hidden single in R7)
19b. Killer pair 4,8 in R7C1 and 11(2) cage at R8C2, locked for N7

20. 45 rule on R3 3 remaining innies R3C179 = 19 = {289/568} (cannot be {469} which clashes with R3C56, cannot be {478} because R3C7 only contains 5,9), no 4,7
20a. 4 in R3 only in R3C456, locked for N2

21. 6 in C3 only in R18C3
21a. 45 rule on C3 3 remaining innies R138C3 = 17 = {269/467} (cannot be {368} because R3C3 only contains 7,9), no 3,8
21b. 8 in C3 only in R56C3, locked for N4

22. R3C3 + R4C4 + R6C6 + R7C7 (step 11) = [7645/9823]
22a. R3C3 = 7 or R3C3 = 9 => R7C7 = 3 => R7C3 = 7 -> 7 locked in R37C3, locked for C3, clean-up: no 4 in R45C3

23. R3C7 + R4C6 + R6C4 + R7C3 (step 14) = [5467/9823]
23a. R3C7 = 5 or R3C7 = 9 => R7C3 = 3 => R7C7 = 5 -> 5 locked in R37C7, locked for C7, clean-up: no 6 in R56C7

24. 5 in R7 only in R7C47, R7C45 = [56] or R7C67 = [65] (locking cages), 6 locked in R7C56, locked for R7 and N8 -> R7C2 = 2, R8C3 = 6, clean-up: no 9 in R1C1, no 9 in R7C4, no 5 in R9C9
24a. Killer pair 2,4 in 11(2) cage at R1C1 and R1C3, locked for N1
24b. 2 in N1 only in R1C13, locked for R1, clean-up: no 9 in R2C2
24c. 6 on D\ only in R4C4 + R9C9, CPE no 6 in R4C9
24d. Naked pair {26} in R2C8 + R6C4, CPE no 2 in R2C4, no 6 in R6C8

25. 9 in D/ only in R1C9 + R3C7 -> R1C9 + R2C8 = [92] or R3C79 (step 9a) = [92] (locking cages), CPE no 2 in R2C9
[While checking my walkthrough I noticed that I’d missed another CPE using these 9s; however step 27 gives the same elimination and more.]

26. R7C8 = 9 (hidden single in R7), R8C7 = 7, clean-up: no 4 in R56C7, no 4 in R9C1
26a. 4 in D/ only in R4C6 + R8C2, CPE no 4 in R4C2

27. 9 in C7 only in R36C7 -> R34C7 = [92] or R56C7 = [29] (locking cages), 2 locked in R45C7, locked for C7 and N6

28. R3C3 + R4C4 + R6C6 + R7C7 (step 22) = [7645/9823], R3C34 = [74/92] -> R34C4 = [46/28]
28a. R3C3 + R4C4 + R6C6 + R7C7 = [7645/9823], R7C67 = [83/65] -> R67C6 = [46/28]
28b. Killer pair 4,8 in R4C6 + R67C6, locked for C6

29. R3C7 + R4C6 + R6C4 + R7C3 (step 23) = [5467/9823], R34C7 = [56/92] -> R4C67 = [46/82]
29a. Killer pair 6,8 in R4C4 and R4C67, locked for R4
29b. R3C7 + R4C6 + R6C4 + R7C3 = [5467/9823], R67C3 = [47/83] -> R6C34 = [46/82]
29c. Killer pair 2,4 in R6C34 and R6C6, locked for R6

30. 6 in C5 only in R37C5 -> R3C56 = [65] or R7C45 = [56] (locking cages), CPE no 5 in R1C4 + R89C6

31. 5 in R1 only in R1C69 -> R12C6 = [56] (no 6 in R3C56 when R1C6 = 5) or R1C9 + R2C8 = [56] (locking cages) -> 6 locked in R2C68, locked for R2
31a. R2C68 = {26} (hidden pair in R2)
31b. Naked quad {2468} in R2467C6, locked for C6, clean-up: no 5 in R3C5
31c. 5 in N2 only in R13C6, locked for C6

32. 5 in D/ only in R1C9 + R3C7 -> R1C9 + R2C8 = [56] or R34C7 = [56] (locking cages), CPE no 6 in R1C7

[At this stage I could see a contradiction chain which reduces the innies on each diagonal to one combination. However having tried to avoid such steps I decided to continue without using such a step.]

33. 3 in R7 only in R7C37, R7C3 = 3 => R6C3 = 8 or R7C7 = 3 => no 3 in R5C7 => no 8 in R6C7
-> no 8 in R6C7, clean-up: no 3 in R5C7
33a. Naked pair {28} in R5C37, locked for R5

34. 7 in C3 only in R37C3, R3C3 = 7 => R3C4 = 4 or R7C3 = 7 => no 4 in R7C45
-> no 4 in R7C4, clean-up: no 7 in R7C5
34a. Naked pair {46} in R37C5, locked for C5

35. R37C5 = {46} = 10, R3C56 = 11, R7C45 = 11 -> R3C6 + R7C4 = 12
[This establishes that R3C6 and R7C4 cannot both contain the same number.]
35a. Naked pair {57} in R3C6 + R7C4, CPE no 7 in R12C4 + R9C6
35b. R12C4 = [13]

and the rest is naked singles.


Last edited by Andrew on Mon Aug 02, 2010 12:07 am, edited 1 time in total.

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HATMAN
 Post subject: Re: HS 7 Elevens
PostPosted: Sun Feb 14, 2010 9:17 pm 
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 694
Location: Saudi Arabia
My principal move was the following contradiction chain:
Innies D\ r3c3r7c7 = 12(2), D/ r3c7r7c3 = 12(2)
r37c37 = 4857/4839/5739
if r3c3r7c7 = [48]-> r3c7r7c3 = [39/93/57/75] but r3c4=7 and r7c6=3
-> r3c7r7c3 = [93/57]
r7c7=8 -> r4c7 <>8 -> r3c7 <>3
r3c3=4 -> r6c3 <>4 -> r7c3 <>7
so all combos for r3c7r7c3 fail (this is symmetrical for the other three cases)
-> r37c37 = 39&57

Athough this would shorten Afmob or Andrew's solutions there is still quite a bit of work needed.

I know that for most people contradiction chains are only slightly above T&E, however I really liked this one.
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