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nd's #9 (aka Night of the Living Sudoku)

 
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sudokuEd
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PostPosted: Sun Mar 23, 2008 6:55 am    Post subject: nd's #9 (aka Night of the Living Sudoku) Reply with quote

Hi everyone,
One of the many things I enjoy about Easter is the memory of this classic killer by Nate Dorward. I spent Easter '06 trying to solve this beauty and have been hopelessly hooked on (difficult) killers ever since.

It hasn't been posted here before and so really wanted to share it with you now. If you enjoy/hate this horror ( Wink ) and tell us about it, maybe we can encourage him to come out of puzzle retirement and make another new one for us.

Note - Nate has a walk-through with some alternative endings on his blog here. If someone finds a better way through, please publish!!

I tried to make a background image based on the classic 1968 movie - but...you'll just have to imagine the tombstone...

nd's #9 (aka Night of the Living Sudoku) SS(v3)score 2.45 (NOTE: no t&e)



PS code:
3x3::k:2816:2816:5378:2307:6660:6660:6660:6151:6151:2816:5378:5378:2307:6413:6660:7183:7183:6151:2834:3859:2836:2307:6413:7183:7183:6151:6151:2834:3859:2836:4126:6413:6413:7183:7202:7202:2834:5413:2836:4126:6413:6413:5930:5930:7202:5413:5413:4126:4126:6705:5938:5938:5930:7202:8502:5413:7736:6705:6705:6705:5938:5930:5930:8502:8502:7736:7736:7736:7736:5938:5938:6215:8502:8502:8502:8502:6215:6215:6215:6215:6215:

Thanks to nd for letting us have it published here.
Ed
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Afmob
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PostPosted: Sun Mar 23, 2008 7:17 pm    Post subject: Reply with quote

This was an interesting Killer since you could totally ignore some nonets to crack it which is the reason why my wt is quite short since I only used those "useless" nonets in the endgame.
At first I wanted to rate it 1.75 but I discovered that the complex combo analysis I had used wasn't necessary to solve it so I deleted it from my wt.

The overlap technique (step 2 from the blog) is quite useful in this Killer though you can come to the same results with more but easier moves.

I don't know why the SS rating so high (nearly off by 1.0!), maybe the X-Chain and techniques in the "useless" areas which SudokuSolver used, raised it so high.

ND's #9 Walkthrough:

1. C1234
a) Innies = 32(2+2) <> 1,2,3,4,5; R7C4 <> 6,7
b) Innies+Outies C4 : -20 = R6C3 - R789C4 -> R6C3 = (1234); R9C4 <> 1,2,3
c) Innies+Outies N14: R6C3 = R7C2 = (1234)
d) 30(5) = 89{157/247/256/346} because of step 1a
-> 8,9 locked between R8+N7 -> R8C12 <> 8,9
-> R8C56 = (12345)
e) Innies N1 = 13(3): R3C13 <> 6,7,8 because R3C2 >= 6
f) 5 locked in 33(7) @ N7 = 12567{39/48} -> 1,2 locked for N7
g) Innies+Outies N14: R6C3 = R7C2 = (34)
h) Innies+Outies C4 : -20 = R6C3 - R789C4 -> R789C4 = 23/24(3) = 89{6/7}
-> 8,9 locked for C4+N8
i) Innies+Outies C12: 1 = R9C34 - R2C2
-> R2C2 <> 4,5 because R9C34 >= 7
-> R9C3 = (1234) because R9C4 >= 6
j) 9(3) = 3{15/24} because {126} blocked by Killer pair (12) of 16(4) -> 3 locked for C4+N2

2. R789
a) Outies R9 = 12(3+1) -> R7C1+R8C9 <> 7,8,9
b) Hidden Killer pair (89) in 24(6) for R9 since 33(7) can't have both
-> 24(6) = 1234{59/68}
c) 7 locked in 33(7) @ R9 -> R8C12 <> 7
d) Killer quad (1234) locked in 24(6) + R9C3 for R9
e) 24(6) must have one of (1234) @ R8C9 (step 3d) -> R8C9 <> 5,6
f) Outies R9 = 12(3+1): R7C1 <> 5,6 since 12{3/4} are Killer triples of 30(5)
g) R8C9 <> 1 since it sees all 1 of N8
h) 24(6) = 1234{59/68} -> 1 locked for R9

3. C123 !
a) ! Hidden Killer quad (1234) in R18C2 for C2 since 21(4) can only have two of (1234)
-> R18C2 <> 5,6,7,8
b) 21(4) must have two of (1234) @ C2 -> R6C1 <> 1,2,3,4
c) Naked quad (1234) locked in R7C12+R8C2+R9C3 for N7
d) 1 locked in 11(3) @ C3 = 1{28/37/46} <> 5
e) 5 locked in 21(3) @ C3 = {579} locked for N1
f) 15(2): R4C2 <> 6,8
g) Naked pair (79) locked in R24C2 for C2

4. R123 !
a) ! Consider combos of 15(2) -> 11(3) @ R3C1 <> 7:
- i) 15(2) = [69] -> Innies N1 = {346} -> 1 locked in 11(3) @ C3 for N2 -> 11(3) @ R3C1 <> 1
- ii) 15(2) = [87] -> 11(3) <> {137}
b) Hidden pair (79) in R69C1 for C1 -> R69C1 <> 5,6,8
c) Naked pair (79) locked in R4C2+R6C1 for N4
d) 11(3) @ C3 = 1{28/46}
e) Innies+Outies C1: -23 = R1C2 - R6789C1 -> R7C1 <> 1 because R689C1 <= 22
f) ! Innies+Outies C1: -23 = R1C2 - R6789C1
-> R7C1 <> 2 since only combo R6789C1 = {2679} blocked by Killer pair (26) of 11(3) @ R3C1
g) 33(7) = 12567{39/48} -> R8C2 = 1, R9C3 = 2
h) 11(3) @ C3 = {146} locked for C3, 6 locked for N4
i) Innies+Outies N14: R6C3 = R7C2 = 3
j) 21(4) = 39{27/45} -> R6C1 = 9

5. R123
a) 15(2) = {78} -> R3C2 = 8, R4C2 = 7
b) Innies N1 = 13(3) = {148} locked for R3+N1
c) Hidden Single: R9C2 = 6 @ C2, R8C1 = 5
d) R7C1 = 4, R9C1 = 7 -> R9C4 = 8
e) Outies = 23(3) = {689} -> R8C4 = 6, R7C4 = 9

6. N568
a) 26(4) = {2789} because R7C56 = (257) -> R6C5 = 8, {27} locked for R7+N8
b) 3 locked in 25(6) @ N5 -> 25(6) = {123469}
c) 28(4) = 89{47/56} -> 8,9 locked for N6
d) R7C3 = 8, R8C3 = 9
e) Naked pair (34) locked in R8C56 for R8+N8
f) R8C9 = 2
g) 23(5) @ R5C7 = 567{14/23} -> 7 locked for N6
h) 28(4) = {5689} locked for N6
i) 23(5) @ R5C7 must have 5 and 6 and it's only possible @ R7C89 -> {56} locked for N9

7. N56
a) 23(5) @ R6C6 = {12578} -> R7C7 = 1, R6C6 = 5, R7C6 = 2
b) 16(4) = {2347} -> {247} locked for C4+N5
c) 25(6) = {123469} -> R2C5 = 4, R3C5 = 2
d) 23(5) @ R5C7 = {14567} -> 4 locked for N6, 1 locked for C8
e) R4C7 = 3 -> 28(5) = {23689} -> R2C8 = 2, R2C7 = 8, {69} locked for R3

8. Rest is singles.

Rating: 1.5. I used one forcing chain and a Hidden Killer quad.


Last edited by Afmob on Mon Apr 07, 2008 4:24 pm; edited 1 time in total
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mhparker
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PostPosted: Tue Mar 25, 2008 1:06 pm    Post subject: Reply with quote

Afmob wrote:
Rating: 1.5. I used one forcing chain and a Hidden Killer quad.

Congratulations, Afmob, for making yet another difficult puzzle look easy again! Applause It's great to have another WT from a sudocue.net regular to compare with nd's blog and udosuk's analysis.

I won't be joining in, though, because it's probably more fun (and less time-consuming!) to analyze individual steps rather than to provide a complete WT and undoubtedly "re-invent the wheel" in the process. It's also extremely unlikely that I can improve on Afmob's 1.5 rating! Shocked (<-- very surprised, because I would have expected a 1.75 - or even a 2.0 Exclamation - here, due to need for a chain to break the deadlock).

sudokuEd wrote:
One of the many things I enjoy about Easter is the memory of this classic killer by Nate Dorward... If you enjoy/hate this horror ( ) and tell us about it, maybe we can encourage him to come out of puzzle retirement and make another new one for us.

I have a dream... (but would be great if it would come true! Smile)
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sudokuEd
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PostPosted: Mon Apr 07, 2008 12:17 pm    Post subject: Reply with quote

Afmob wrote:
At first I wanted to rate it 1.75 ...Rating: 1.5. I used one forcing chain and a Hidden Killer quad
Oh Afmob, some really great moves in steps 1-3! But your first instinct works much better for me - no way could I seriously put this classic onto the rating sticky as a 1.5 (more like a 2.0 with that type of chain)! Did the 1.75 way you used still need a looking-3-ways-chain? I'd much, much rather combo-crunching.

If it did still need that chain, here's a way that looks simpler for step 4.

Marks at the end of Amob's step 3

Code:
.-------------------------------.-------------------------------.-------------------------------.
| 123468    1234      579       | 12345     2456789   2456789   | 23456789  123456789 123456789 |
| 123468    79        579       | 12345     12456789  2456789   | 123456789 123456789 123456789 |
| 1234      68        1234      | 12345     12456789  12456789  | 123456789 123456789 123456789 |
:-------------------------------+-------------------------------+-------------------------------:
| 12345678  79        1234678   | 124567    123456789 123456789 | 123456789 456789    456789    |
| 12345678  1234568   1234678   | 124567    123456789 123456789 | 123456789 123456789 456789    |
| 56789     1234568   34        | 124567    23456789  123456789 | 123456789 123456789 456789    |
:-------------------------------+-------------------------------+-------------------------------:
| 1234      34        6789      | 89        234567    234567    | 123456789 123456789 123456789 |
| 56        1234      6789      | 6789      12345     12345     | 123456789 123456789 234       |
| 56789     568       234       | 6789      123456    123456    | 12345689  12345689  12345689  |
'-------------------------------.-------------------------------.-------------------------------'

Code:
.-----------------------------------------------------------------------.
|(11)   :       |(21)   |( 9)   |(26)   :       :       |(24)   :       |
|  123  :  123  |       |  123  |   2   :   2   :   23  |  123  :  123  |
|  4 6  :  4    |   5   |  45   |  456  :  456  :  456  |  456  :  456  |
|   8   :       |  7 9  |       |  789  :  789  :  789  |  789  :  789  |
|.......--------|.......|.......|-------:.......--------|-------:.......|
|       |       :       |       |(25)   |       |(28)   :       |       |
|  123  |       :       |  123  |  12   |   2   |  123  :  123  |  123  |
|  4 6  |       :   5   |  45   |  456  |  456  |  456  :  456  |  456  |
|   8   |  7 9  :  7 9  |       |  789  |  789  |  789  :  789  |  789  |
|-------|---------------|.......|.......|-------|.......--------|.......|
|(11)   |(15)   |(11)   |       |       |       :       |       :       |
|  123  |       |  123  |  123  |  12   |  12   :  123  |  123  :  123  |
|  4    |    6  |  4    |  45   |  456  |  456  :  456  |  456  :  456  |
|       |   8   |       |       |  789  |  789  :  789  |  789  :  789  |
|.......|.......|.......|-------|.......|-------:.......|---------------|
|       |       |       |(16)   |       :       |       |(28)   :       |
|  123  |       |  123  |  12   |  123  :  123  |  123  |       :       |
|  456  |       |  4 6  |  456  |  456  :  456  |  456  |  456  :  456  |
|  78   |  7 9  |  78   |  7    |  789  :  789  |  789  |  789  :  789  |
|.......|-------|.......|.......|.......:.......|-------|-------:.......|
|       |(21)   |       |       |       :       |(23)   :       |       |
|  123  |  123  |  123  |  12   |  123  :  123  |  123  :  123  |       |
|  456  |  456  |  4 6  |  456  |  456  :  456  |  456  :  456  |  456  |
|  78   |   8   |  78   |  7    |  789  :  789  |  789  :  789  |  789  |
|-------|.......|-------|.......|---------------|-------:.......|.......|
|       :       |       :       |(26)   |(23)   :       |       |       |
|       :  123  |    3  :  12   |   23  |  123  :  123  |  123  |       |
|   56  :  456  |  4    :  456  |  456  |  456  :  456  |  456  |  456  |
|  789  :   8   |       :  7    |  789  |  789  :  789  |  789  |  789  |
|-------:.......|---------------|.......|-------:.......|.......|-------|
|(33)   |       |(30)   |       :       :       |       |       :       |
|  123  |    3  |       |       :   23  :   23  |  123  |  123  :  123  |
|  4    |  4    |    6  |       :  456  :  456  |  456  |  456  :  456  |
|       |       |  789  |   89  :  7    :  7    |  789  |  789  :  789  |
|.......|-------|.......|-----------------------|.......|---------------|
|       :       |       :       :       :       |       :       |(24)   |
|       :  123  |       :       :  123  :  123  |  123  :  123  |   23  |
|   56  :  4    |    6  :    6  :  45   :  45   |  456  :  456  |  4    |
|       :       |  789  :  789  :       :       |  789  :  789  |       |
|.......:.......|-------------------------------|---------------|.......|
|       :       :       :       |       :       :       :       :       |
|       :       :   23  :       |  123  :  123  :  123  :  123  :  123  |
|   56  :   56  :  4    :    6  |  456  :  456  :  456  :  456  :  456  |
|  789  :   8   :       :  789  |       :       :   89  :   89  :   89  |
.-----------------------------------------------------------------------.

ALT
4a) no 7 in r9c4 because of 7's in n1
i. 7 in r12c3 -> 7 in n7 in r9c1 -> no 7 in r9c4
ii. 7 in r2c2 -> r9c34 = 8 (i/o c12) -> no 7 in r9c4
b. r9c1 = 7 (hidden single r9)
c. r6c1 = 9 (hidden single c1)

On it goes from here.

Cheers
Ed
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Afmob
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PostPosted: Mon Apr 07, 2008 2:47 pm    Post subject: Reply with quote

Great chain Ed! It's certainly simpler than mine. I rated ND 9 only "1.5" because when I solved it, it flowed quite well meaning I didn't really came to halt despite those difficult moves. Also my wt is quite short and doesn't have this many ! moves where as my other 1.75 walkthroughs are usually quite large and have many ! moves and they also wouldn't be cracked with one chain only.

My first version had combo analysis in R89 to remove some candidates from R7C1 (can't remember which ones) which I found quite complicated, so with it I would have surely rated ND 9 1.75. On the other hand, I immediately saw the chain which cracked the Killer. So maybe it's more a hard 1.5.

Compared to UA97 V2 which I'm tackling at the moment (made 4 placements so far) ND9 is way easier.
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mhparker
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PostPosted: Thu Apr 10, 2008 7:33 pm    Post subject: Reply with quote

sudokuEd wrote:
If it did still need that chain, here's a way that looks simpler for step 4.

Love this chain, Ed! Indeed, I think it's an example of a Grouped Turbot Fish, which is a specific type of AIC. Before discussing it in more detail below, I'd like to first of all present an example of a grouped turbot fish taken from a regular Sudoku, found with the help of JSudoku (thanks J-C!):

Code:
.-----------------------.-----------------------.-----------------------.
| 8       7       6     | 5       4       1     | 23      9       23    |
| 125     125     12    | 9       3       6     | 4       78      78    |
| 9       3       4     | 78      78      2     | 56      56      1     |
:-----------------------+-----------------------+-----------------------:
| 16      4       178   | 2       15689   578   | 589     3       68    |
| 12367   128     5     | 13678   16789   4     | 289     128     268   |
| 1236    9       128   | 1368    1568    358   | 7       1258    4     |
:-----------------------+-----------------------+-----------------------:
| 17      18      3     | 1678    2       9     | 68      4       5     |
| 4       258     278   | 368     568     3578  | 1       2678    9     |
| 125     6       9     | 4       158     578   | 238     278     2378  |
'-----------------------'-----------------------'-----------------------'

From this position, the following grouped Turbot fish can be applied:
Code:
(1)R4C13=R4C5-R9C5=R9C1 => R56C1<>1

In other words, if R4C13 do not contain a 1, then R4C5 must be 1 (strong link R4), implying that R9C5 cannot be 1 (weak link C5), in turn implying that R9C1 must be 1 (strong link R9). Thus, (even) if R4C13 do not contain a 1, R9C1 must be 1. Expressed differently, at least one of the two chain ends must contain a 1, thus allowing the digit 1 to be removed from the common peers R56C1.

Note that a turbot fish is an AIC where all links are based on the same digit. In this case, it's a grouped turbot fish on (the digit) 1 with 3 links, where the term "grouped" refers to the use of a multi-cell node at R4C13. As is traditionally the case with AICs in general, the chain begins and ends with a strong link.

Now let's turn our attention to Ed's move, using the marks diagram he presented above. Here, Ed used bifurcation based on two possible locations for the digit 7 in N1, namely R2C2 and R12C3. This is, however, simply making use of the fact that there is a grouped strong link between R2C2 and R12C3, allowing us to reformulate his chain in standard AIC form as follows:
Code:
(7)R9C1=R78C3-R12C3=R2C2 => R9C4<>7

In other words, if R9C1 does not contain a 7, then R78C3 must contain a 7 (strong link N7), implying that R12C3 cannot contain a 1 (weak link C3), in turn implying that R2C2 must be 7 (strong link R9). Thus, (even) if R9C1 does not contain a 7, R2C2 must do. This allows us to eliminate the candidate 7 from R9C4, even though this is not a common peer of both chain end nodes. This is because the general rule for AICs is that we can eliminate any candidate that is weakly linked to both end nodes, which (as in this case) includes any such candidates in cells that are not directly seen by either (or even both) ends of the chain.

In this case, one of the weak links is complex, in that it depends on the possible combinations ({267/289/379/469}) for the innie/outie difference cage at R2C2+R9C34, none of which contain multiple occurrences of the digit 7. Therefore, a 7 in R2C2 precludes a 7 in R9C34.
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