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Assassin 24 - Tetris
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Ruud
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PostPosted: Thu Nov 09, 2006 9:09 pm    Post subject: Assassin 24 - Tetris Reply with quote

I am currently testing a few new solving techniques in SumoCue, which will soon be released. So I decided to try and make a Killer that would be a match for this new solving power. After more than 10 attempts, this Tetris puzzle came out just right. Combined, SumoCue and SudoCue needed more than 160 solving steps (including singles). This Killer is an Assassin and a Nightmare.

Ed: remember the ALS!

Chinese proverb wrote:
May you solve interesting puzzles

Looking forward to your walkthroughs,

Ruud
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sudokuEd
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PostPosted: Sat Nov 11, 2006 4:57 am    Post subject: Reply with quote

John F. Kennedy wrote:
There is a Chinese curse which says "May he live in interesting times."
JFK is closer to the mark with this one Ruud!

OK team - this is as far as I could get. Can't see any ALS. emm?

Have also included below, the same marks spot which can be pasted into SudoCue.

SumoCue
Code:
.-----------------------.-----------------------.-----------.-----------------------.-----------------------.
|(17)                   |(15)                   |(13)       |(15)                   |(27)                   |
| 234589      23458     | 6           35        | 7         | 248         1         | 89          389       |
:-----------.           '-----------.           |           |           .-----------'           .-----------:
|(27)       |                       |           |           |           |                       |(18)       |
| 389       | 12348       4589      | 135       | 6         | 248       | 3789        789       | 45        |
|           '-----------.-----------:           :-----------:           :-----------.-----------'           |
|                       |(16)       |           |(21)       |           |(20)       |                       |
| 3578        3578      | 14        | 135       | 9         | 48        | 2         | 456         456       |
:-----------.           |           :-----------'           '-----------:           |           .-----------:
|(20)       |           |           |                                   |           |           |(23)       |
| 25689     | 69        | 25        | 4           1           7         | 569       | 3         | 25689     |
|           '-----------:           '-----------.-----------.-----------'           :-----------'           |
|                       |                       |(10)       |                       |                       |
| 123456789   123456789 | 12457       68        | 23        | 59          47        | 12456789    12456789  |
:-----------.           :-----------------------:           :-----------------------:           .-----------:
|(22)       |           |(17)                   |           |(23)                   |           |(17)       |
| 5679      | 1234678   | 347         68        | 23        | 59          459       | 124678    | 12        |
|           :-----------'           .-----------:           :-----------.           '-----------:           |
|           |                       |(9)        |           |(9)        |                       |           |
| 12346789  | 1234        2347      | 27        | 5         | 36        | 346789      124678    | 12346789  |
|           '-----------.-----------:           :-----------:           :-----------.-----------'           |
|                       |(24)       |           |(22)       |           |(20)       |                       |
| 12345679    12345679  | 4789      | 27        | 48        | 36        | 4689      | 1245679     12345679  |
:-----------------------'           :-----------'           '-----------:           '-----------------------:
|                                   |                                   |                                   |
| 2345678     2345678     4578      | 9           48          1         | 345678      245678      2345678   |
'-----------------------------------'-----------------------------------'-----------------------------------'

SudoCue
Code:
.------------------------------.------------------------------.------------------------------.
| 234589    23458     6        | 35        7         248      | 1         89        389      |
| 389       12348     4589     | 135       6         248      | 3789      789       45       |
| 3578      3578      14       | 135       9         48       | 2         456       456      |
:------------------------------+------------------------------+------------------------------:
| 25689     69        25       | 4         1         7        | 569       3         25689    |
| 123456789 123456789 12457    | 68        23        59       | 47        12456789  12456789 |
| 5679      1234678   347      | 68        23        59       | 459       124678    12       |
:------------------------------+------------------------------+------------------------------:
| 12346789  1234      2347     | 27        5         36       | 346789    124678    12346789 |
| 12345679  12345679  4789     | 27        48        36       | 4689      1245679   12345679 |
| 2345678   2345678   4578     | 9         48        1        | 345678    245678    2345678  |
'------------------------------'------------------------------'------------------------------'
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Andrew
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PostPosted: Sat Nov 11, 2006 4:55 pm    Post subject: Reply with quote

This is as far as I've got so far. No time for any more at the moment, we have to go out for the day. Here is the start of my walkthrough (in tiny text). At a quick glance I haven't got as far as Ed but these moves may be useful; sometimes knowing why things have already happened can be helpful. They may also be useful when Ed writes the condensed walkthrough after this puzzle has been solved.

1. 45 rule on N8 1 innie R7C5 = 5, both 9(2) cages in N8 = {18/27/36}, 22(4) cage = 49{18/27/36}, R56C5 = {14/23}

2. 49 rule on C6789 2 innies R49C6 = 8 = {17/26/35} -> R9C6 = {12367}, R4C6 = {12567}

3. 49 rule on C1234 2 innies R49C4 = 13 = {49/58/67} -> R9C4 = {46789}, R4C4 = {45679}

4. R89C5 must contain 4 and/or 9 -> R12C5 = {67}

5. 45 rule on N2 1 innie – 2 = 2 outies, min.R1C37 = 3 -> min.R3C5 = 5 -> R3C5 = {89}(5, 6 and 7 blocked in C5) -> R1C37 = 6 or 7

6. One of the 15(4) cages in N12 and N23 must contain 8 or 9 in N2
-> that cage = 12{39/48}
-> the other cage must contain 5 = {1356} with the 6 in R1C37 (cannot be {1257} from step 5)
-> the first cage must be {1248} with the 1 in R1C37
-> R1C37 = {16}, R12C5 = [76], R3C5 = 9, R4C456 = 12 -> no 8 in R4C5
-> R123C4 and R123C6 = {135}/{248}
-> R9C4 = 9, R89C5 = {48} (only cells for 4 in N8 and for 8 in C5), R9C6 = 1, R56C5 = {23}, R4C5 = 1
-> R123C4 = {135}, R123C6 = {248}
-> R1C3 = 6, R1C7 = 1

7. R78C4 = {27}, R78C6 = {36}

8. R4C46 = [47] from steps 2 and 3

9. R56C4 = {68}, R56C6 = {59}

10. The 27(4) cages in N14 and N3 must each contain 9 (corrected, the remainder of this step has been deleted)
[Steps 4, 5, 6 and 8 edited for clarity]

It has been pointed out to me by Ed, off-forum, that my assumption in the second part of the final step above (now deleted) was incorrect. Thanks Ed; I try to learn from my mistakes. Sorry if I've confused anyone or led them in the wrong direction; at the time of editing this message I now know that it would have been the wrong direction.

Back home now and I've made a bit more progress although only nibbling moves after the real progress made earlier. Again amended, removing steps that depended on the incorrect assumption.

11. 6 in N3 locked in R3 [Edited for typo, previously had C3]

12. 45 rule on N1 1 outie R4C2 – 5 = 1 innie R3C3 -> R4C2 = {689}, R3C3 = {134}

13. 45 rule on N3 1 outie R4C8 – 1 = 1 innie R3C7, R3C7 cannot be 6 because 7 is blocked in R4 -> 18(4) cage in N36 contains 6 in R3C89, also R3C7 cannot be 3 because 4 is blocked in R4

14. Valid combinations for the 18(4) cage in N36 are {2367} and {3456} = 36{27/45}, at this stage the 3 could go in any cell of this cage so 3 is also still a possible candidate for the 27(4) cage in N3, R4C8 = {35} (cannot be 2 because of step 13, 1 blocked from R3C7) -> R3C7 = {24} [Edited for typo in 36{27/45}]

15. 45 rule on R9 3 outies = 21 = {489}/{678} -> R8C3 = {4789}, R8C7 = {4689}

16. R4C8 cannot be 5 because that would require R3C7 = 4 and also another 4 in the 18(4) cage to make the {3456} combination -> R4C8 = 3, R3C7 = 2, 18(4) cage = {3456}, R2C9 = {45}, R3C89 = {456}, 27(4) cage in N3 = {3789} with 7 in R2C78

17. 7 in R3 locked in R3C12

18. 27(4) cage in N14 = 79{38/56} -> R2C1 = {389} (cannot be 5 because the {5679} combination can only put the 9 in R2C1), R3C12 = {3578}

19. 2 in N1 locked in 17(4) cage
[Steps 16 to 19 added; I did those later on Saturday. They were added when I edited the earlier steps on Sunday, before attempting to make further progress.]

That's my lot for today. Hopefully make some more progress tomorrow.


Last edited by Andrew on Tue Nov 28, 2006 4:37 am; edited 5 times in total
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sudokuEd
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PostPosted: Sun Nov 12, 2006 6:31 am    Post subject: Reply with quote

Managed to solve Tetris [edit - this walkthrough is not the way to do it though - valid walkthrough in a following post]. Took some really neat tricks - but darned if I could find any ALS. Could you show us where you found ALS eliminations Ruud?

My walk-through starts from the beginning - used a boring way to get started compared to the beautiful logic of Andrew's. Please let me know of anything not accurate or clear. Thanks.

1. "45" n8: 1 innie r7c5 = 5, both 9(2) cages in n8 = {18/27/36} (no 4), 22(4) cage = 49{18/27/36}. r56c5 = 5 = {14/23} (no 6,7)

2. "45" c6789: 2 innies r49C6 = 8 = {17/26/35} -> r9c6 = {12367}, r4C6 = {12567}

3. "45" c1234: 2 innies r49c4 = 13 = {49/58/67} -> r9c4 = {46789}, r4c4 = {45679}

4. "45" n369: 2 outies - 13 = 1 innie -> min. r56c6 = 14 -> no 1,2,3,4. Max r56c6 = 17 -> max. r1c7 = 4

5. 4 in c6 now only in n2 -> 4 locked for n2 and no 4 in r1c7 -> 13(2) n2 = {67} -> {67} locked for n2, c5 -> 15(4) in n23 = 4{128} (no 3,5,9) -> 8 locked for n2, c6. Also, 5 in n2 locked in 15(4) in n12 -> no 5 in r1c3 and 15(4) n12 = 5{127/136} = 15{27/36} (no 4,8,9) -> r3c5 = 9 (single n2)

6."45" n2: 2 outies = 7 -> r1c37 = [61]. r12c5 = [76]

7. r123c4 = {135}: locked for c4-> r78c4 = {27}: locked for c4,n8. r123c6 = {248}: locked for c6 -> r78c6 = {36}: locked for c6, n8. r9c6 = 1, r9c4 = 9 (single n8), r89c5 = {48}: locked for c5 -> r56c5 = {23} -> r4c5 = 1. r4c46 = [47] (step 2,3). r56c6 = {59}, r56c4 = {68}

8. 27(4) in n3 now {3789}:locked for n3 with 7 locked for r2 -> 18(4) n36 {3456} only ({2349/2358} have 3,8/9 only in r4c8) -> r4c8 = 3 -> now 15(3) = {456}:locked for n3 -> r3c7 = 2

9. "45"n1: 1 outie - 5 = 1 innie -> r4c2 = {689}, r3c2 = {134}. 7 in n1 locked in 27(4) = 79{38/56} (no 4) and no 9 in r12c2

10. "45" n1: 4 outies = 21. Min. r4c2 + r5c4 = {66} = 12 -> max. r45c3 = 9 -> no 9 in r4c4, no 8,9 in r5c3.

11. "45" c12 -> 3 outies - 20 = 1 innie -> min. r289c3 = 21 -> no 123. Max. 3 outies = 24 -> max. r7c2 = 4. r289c3 = {489/579/589/789} (all combinations with 6 blocked) = 9{48/57/58/78} = [5/8,7/8] = 21, 22 or 24 -> no 3 in r7c2 and 9 locked for c3

12. 16(4) in n145 must have 6/8 (r5c4) = {1258/1267/1348/1456/2356} = [6/8], not both -> no 8 in r4c3 = {25} -> {1348} combo blocked (no 2,5). Only combo left with 3 is {2356} with 3 only in r3c3 -> no 3 in r5c3

13. Another way of looking at step 12 is at the combinations available in r345c3 (remembering [6/8] only in r5c4) = {125/127/145/235} = [5/7]. Now, remembering from step 11 that r289c3 = [5/8,7/8] -> 5, 7 and 8 in c3 are locked in r234589c3 (neat!)-> not in r67c3.

[edit: neat maybe - but wrong - not true with {489} combo. The following steps depend on step 13 - so are not valid]

14. 17(4) in n547 now = {1268/2348} = 8{126/234} -> r6c4 = 8, r5c4 = 6, rest of 17(4) = {234} only (no 1) with 3 locked for c3.

15. r7c2 = {24} -> r289c3 = 22/24 (step 11) = {589/789} (no 4)

16. 16(4) in n145 now 10(3) = {127/145} = [127/154/451] -> r5c3 = {147}. r3c3 = {14} -> r4c2 = {69} (step 9)

17. "45" n7: 2 outies = 10 = [73/64] -> no 2 in r6c6 -> 2 locked in r7c23 for n7 and r7 -> r78c4 = [72]

18. "45" n7: 1 outie - 1 = 2 innies. r6c1 = 6/7 -> r7c23 = 5/6 and must have 2 = {23/24} = [3/4]. 24(4) in n7 = {3579/3678/4569/4578} ({3489} blocked by r7c23) = [3/4] -> Killer pair {34} with r7c23 in n7 -> 22(4) n47 = {1579/1678} = 17{59/68}

19. From step 17, r6c13 = [73/64] = [6/7]. Another way of looking at step 9 and 16 is that r4c2 + r45c3 = [627/654/951]. But now we can see that [627] is blocked by r6c13 -> r345c3 = [154/451] -> r4c3 = 5, r35c3 = {14}:locked for c3 -> r67c3 = [32], r7c2 = 4, r6c1 = 7, r56c5 = [32], r3c2 = 7 (single n1), 4 in n4 locked in r5

20. 20(4) n365 now 18(3) = {567} only -> r56c6 = [59], r45c7 = [67], r6c2 = 6 (single n4), r4c2 = 9 -> r3c3 = 4, r5c3 = 1, r5c1 = 4, r2c9 = 4, r3c89 = {56} locked for r3 ->....the rest are singles


Last edited by sudokuEd on Sun Nov 19, 2006 7:41 pm; edited 2 times in total
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Andrew
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PostPosted: Sat Nov 18, 2006 2:59 am    Post subject: Reply with quote

Thanks Ed for your kind comment about the logic for N2 in my earlier message.

Unfortunately I wasn't able to continue with such logic later in the puzzle. I must admit that I missed some of Ed's multiple innies/outies.

I ended up by solving the puzzle by considering the implications of the two possible combinations for the 17(4) cage in N1 and the 27(4) cage in N14. The initial intention was to work through from these two combinations and see how these two options limited the candidates in the cells further down the left-hand side of the puzzle. Rather to my surprise I was able to work right through from each of these combinations with one giving the solution and the other ending up as a massive contradiction move. Thus I effectively ended up by solving this puzzle by bifurcation although that certainly wasn't my intention when I started looking at those two possible combinations. I was just looking to limit candidates and then expected to have to look for more innies/outies to solve the rest of the puzzle. In view of the above comments, I won't be adding to the partial walkthrough in my earlier message.

Assassin 24 was certainly a challenge. Thanks Ruud! I was intrigued by the comment in the earlier message that it was set to use new solving techniques that are being included in SumoCue. What new techniques were used for this puzzle apart from it being harder than any previous Assassin?
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PostPosted: Sat Nov 18, 2006 12:26 pm    Post subject: Flaw in logic? Reply with quote

I've tried going through the walkthrough and can't follow the logic at step 13.

I can't see how at this point that we can say 5, 7 and 8 are locked in r234589c3. The logic is built on the assumption in 11 that r289c3 has (5/8, 7/8). Doesn't this ignore the possible 948 combination in these cells?

I keep seeing the following permutations for r289c3 at this point
(984, 894,975,985,895,987,597,897,948,978,498,598) and the following permutations for r345c3 (451,152,352,154,125,325,127) - I just can't convince myself that this implies 5,7,8 are locked (e.g 984152 is a valid combo for r234589c3).

I'd really love to eliminate 57 from r6c3 because the puzzle just falls out from there.

Am I missing some trick?
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PostPosted: Sat Nov 18, 2006 1:36 pm    Post subject: Re: Flaw in logic? Reply with quote

rcbroughton wrote:
I've tried going through the walkthrough and can't follow the logic at step 13. Doesn't this ignore the possible 948 combination in these cells?

Am I missing some trick?
No - I've been tricked. You're spot on - the {489} does not allow this deduction. OOps.

I originally solved it a different - and much longer way. Will have to dig through the notes tomorrow. In the mean time - any help greately appreciated!
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PostPosted: Sat Nov 18, 2006 4:59 pm    Post subject: Reply with quote

Tall buildings often do not have a 13th floor. I wonder why...

Andrew wrote:
What new techniques were used for this puzzle apart from it being harder than any previous Assassin?


My current - under development - version of SumoCue does all fish-type moves, and also Law of Leftovers for Jigsaws and Jigsaw Killers, which is similar to fish.

Even with these additions, it cannot solve Tetris completely. When it got stuck, I transferred this candidate grid to SudoCue:

Code:
.---------------------.---------------------.----------.---------------------.---------------------.
|(17)                 |(15)                 |(13)      |(15)                 |(27)                 |
| 234589     23458    | 6          35       | 7        | 24         1        | 89         389      |
:----------.          '----------.          |          |          .----------'          .----------:
|(27)      |                     |          |          |          |                     |(18)      |
| 89       | 1234       589      | 135      | 6        | 24       | 379        789      | 45       |
|          '----------.----------:          :----------:          :----------.----------'          |
|                     |(16)      |          |(21)      |          |(20)      |                     |
| 357        357      | 14       | 13       | 9        | 8        | 2        | 456        456      |
:----------.          |          :----------'          '----------:          |          .----------:
|(20)      |          |          |                                |          |          |(23)      |
| 2568     | 69       | 25       | 4          1          7        | 569      | 3        | 25689    |
|          '----------:          '----------.----------.----------'          :----------'          |
|                     |                     |(10)      |                     |                     |
| 1234578    12345789 | 147        6        | 23       | 59         47       | 245789     245789   |
:----------.          :---------------------:          :---------------------:          .----------:
|(22)      |          |(17)                 |          |(23)                 |          |(17)      |
| 67       | 23467    | 34         8        | 23       | 59         59       | 2467     | 1        |
|          :----------'          .----------:          :----------.          '----------:          |
|          |                     |(9)       |          |(9)       |                     |          |
| 469      | 24         234      | 7        | 5        | 36       | 8          1        | 3469     |
|          '----------.----------:          :----------:          :----------.----------'          |
|                     |(24)      |          |(22)      |          |(20)      |                     |
| 145678     145678   | 789      | 2        | 48       | 36       | 469      | 45679      345679   |
:---------------------'          :----------'          '----------:          '---------------------:
|                                |                                |                                |
| 345678     345678     578      | 9          48         1        | 34567      24567      234567   |
'--------------------------------'--------------------------------'--------------------------------'


The first move it found was an XYZ-Wing:

Code:
.---------------------------.---------------------------.---------------------------.
| 234589   23458    6       | 35       7        24      | 1        89       389     |
| 89       1234     589     | 135      6        24      | 379      789      45      |
| 357      357      14      | 13       9        8       | 2        456      456     |
:---------------------------+---------------------------+---------------------------:
| 2568    #69       25      | 4        1        7       |*569      3        2568-9  |
| 1234578  12345789 147     | 6        23       59      | 47       245789   245789  |
| 67       23467    34      | 8        23       59      |#59       2467     1       |
:---------------------------+---------------------------+---------------------------:
| 469      24       234     | 7        5        36      | 8        1        3469    |
| 145678   145678   789     | 2        48       36      | 469      45679    345679  |
| 345678   345678   578     | 9        48       1       | 34567    24567    234567  |
'---------------------------'---------------------------'---------------------------'


Then an ALS-XZ move:
Code:
A=r2c13789
B=r3c1289
X=4
Z=3
r2c2<>3


This enabled a second XYZ-Wing:

Code:
.---------------------------.---------------------------.---------------------------.
| 234589   23-458   6       | 35       7        24      | 1        89       389     |
| 89      *124      589     | 135      6        24      | 379      789      45      |
| 357      357     #14      | 13       9        8       | 2        456      456     |
:---------------------------+---------------------------+---------------------------:
| 2568     69       25      | 4        1        7       | 569      3        2568    |
| 1234578  12345789 147     | 6        23       59      | 47       245789   245789  |
| 67       23467    34      | 8        23       59      | 59       2467     1       |
:---------------------------+---------------------------+---------------------------:
| 469     #24       234     | 7        5        36      | 8        1        3469    |
| 145678   145678   789     | 2        48       36      | 469      45679    345679  |
| 345678   345678   578     | 9        48       1       | 34567    24567    234567  |
'---------------------------'---------------------------'---------------------------'

Followed by a second ALS-XZ move:
Code:
A=r2c269
B=r3467c3
X=1
Z=5
r2c3<>5, r4c9<>5


After this move, a pair {89} in N1/R2 breaks the puzzle.

We may not need the second XYZ-Wing, but the 3 other steps must be executed in sequence to isolate the pair.

Ruud
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rcbroughton
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PostPosted: Sat Nov 18, 2006 6:54 pm    Post subject: As far as I get Reply with quote

I can only get som far with my solver. But it did pick up one ALS. The candidate list it gets to before giving up is

Code:

. . . removed - solver now completes


The steps it goes through are (excuse the rather raw format of my program output and some of my own terminology that I made up way before I knew any better)

Code:

. . . edited and replaced in later post


After that I'm stuck - can't see any other obvious reductions to move past this.


Last edited by rcbroughton on Mon Nov 20, 2006 8:51 pm; edited 1 time in total
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PsyMar
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PostPosted: Sat Nov 18, 2006 11:27 pm    Post subject: Reply with quote

sudokuEd wrote:
John F. Kennedy wrote:
There is a Chinese curse which says "May he live in interesting times."

This was also an Agatean curse, in the Discworld series.

In the meantime, I think I'll go look at the older Assassins -- no way am I ready for this one, even with the confidence boost from 25.
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PostPosted: Sun Nov 19, 2006 10:44 am    Post subject: Reply with quote

PsyMar wrote:
This was also an Agatean curse, in the Discworld series.
Terry Pratchet wrote:
This is the strongest curse that the people of the ‘Counterweight Continent’ can muster.
Very perceptive!

Well, here is the original solving for this puzzle - before those thought fairies took over! Hopefully, its valid this time. Good luck - not easy reading [edit: but a bit easier after very helpful suggestions from Andrew. Thanks].

1. "45" n8: 1 innie r7c5 = 5, both 9(2) cages in n8 = {18/27/36} (no 4), 22(4) cage = 49{18/27/36}. r56c5 = 5 = {14/23}

2. "45" c6789: 2 innies r49c6 = 8 = {17/26/35} -> r9c6 = {12367}, r4c6 = {12567}

3. "45" c1234: 2 innies r49c4 = 13 = {49/58/67} -> r9c4 = {46789}, r4c4 = {45679}

4. "45" n369: 2 outies - 13 = 1 innie -> min. r56c6 = 14 -> no 1,2,3,4. Max r56c6 = 17 -> max. r1c7 = 4

5. 4 in c6 now only in n2 -> 4 locked for n2 and no 4 in r1c7 -> 13(2) n2 = {67} locked for n2, c5 -> 15(4) in n23 = 4{128} (no 3,5,9) -> 8 locked for n2,c6. Also, 5 in n2 locked in 15(4) in n12: 5 locked for c4 -> no 5 in r1c3 and 15(4) n12 = 5{127/136} = 15{27/36} (no 4,8,9) -> r3c5 = 9 (single n2)

6."45" n2: 2 outies = 7 -> r1c37 = [61]. r12c5 = [76]

7. r123c4 = {135}: locked for c4-> r78c4 = {27}: locked for c4,n8. r123c6 = {248}: locked for c6 -> r78c6 = {36}: locked for c6, n8. r9c6 = 1, r9c4 = 9 (single n8), r89c5 = {48}: locked for c5 -> r56c5 = {23} -> r4c5 = 1. r4c46 = [47] (step 2,3). r56c6 = {59}, r56c4 = {68}

8. 27(4) n3 now {3789}:locked for n3 with 7 locked for r2 -> 18(4) n36 {3456} only ({2349/2358} have 3,8/9 only in r4c8) -> r4c8 = 3 -> now 15(3) n3 = {456}:locked for n3 -> r3c7 = 2

9. "45" n1: 1 outie - 5 = 1 innie -> r4c2 = {689}, r3c3 = {134}. 7 in n1 locked in 27(4) = 79{38/56} (no 1,2,4) and no 9 in r12c2
9a. When 8 in r4c2, must have 3 in r3c3. But the only combo with 8 in 27(4) n12 is {3789} -> two 3's in n1 -> no 8 in r4c2, no 3 in r3c3

10. "45" n1: 4 outies = 21. Min. r4c2 + r5c4 = {66} = 12 -> max. r45c3 = 9 -> no 9 in r4c3, no 8,9 in r5c3
10a. When r45c3 max. = 9, [81] is blocked by 1 in r3c3 (since 6 in r4c2 - step 9) -> no 8 can be in r4c3 = {25}

11. "45" c12 -> 3 outies - 20 = 1 innie -> min. r289c3 = 21 -> no 123. Max. 3 outies = 24 -> max. r7c2 = 4
11a. r289c3 = {489/579/589/789} = 9{48/57/58/78} = [5/8,7/8] = 21, 22 or 24 -> no 3 in r7c2 and 9 locked for c3

12. 16(4) in n145 must have 6/8 (r5c4) and 1/4 (r3c3) and 2/5 (r4c3) = {1258/1267/1456} = 1{258/267/456} with 1 locked for c3, no 3 in r5c3

13. Another way of looking at step 12 is at the combinations available in r345c3 (remembering [6/8] only in r5c4) = {125/127/145} = [5/7]
13a. ->{579} combo. blocked from r289c3 = {489/589/789} = 89{4/5/7} -> 8 locked for c3
13b. r345c3 = [125/152/127/154/451]
13c. another way to see 13b.and step 9: r4c2 + r45c3 = [625/652/627/654/951] = [5/7]: rest of n4 has 5/7 but not both

14. 3 in c3 now locked in 17(4) n547 and must have 6/8 (r6c4) = {1358/1367/2348}

15. "45" n7: r6c1 - 1 = r7c23. Min r7c23 = {12} = 3 -> min r6c1 = 4

16. 17(4) n547: {1358} combo, must have r7c23 = {13} = 4 But this means 5 must be in both r6c1 (step 15) and r6c3 -> no {1358} combo
16a. 17(4) = {1367/2348} (no 5)
16b. r6c34 = [36/76/28/38/48]

17. "45" n7: 3 outies = 18. From 16b. r6c134 = [936/576/828/738/648] ([828] not valid) -> no 4,or 8 in r6c1, no 2 in r6c3
17a. r6c13 = [93/57/73/64]. But from 13c. [57] is blocked -> no 5 in r6c1, no 7 in r6c3

We come now to the key moves to unlock this puzzle. Hopefully its neat and valid this time!
18. "45" r6789 3 innies r6c258 = 12.
18a. r6c5 = {23} -> r6c28 = 9/10. When 5 in either r6c28 -> r6c28 can only = 9 (can't have {55} = 10} -> must have 3 in r6c5 and {45} in r6c28 = {345}. But this is blocked by r6c3 -> no 5 in r6c28

19. "45" n9: 1 outie + 8 = 2 innies
19a. 5 in r6c9 -> r7c78 = 13. -> other 2 cells in 23(4) in n569 must = 10. But this is not possible since 9 must be in r6c6 when r6c9 = 5, and no 1 is available in r6c7 -> no 5 in r6c9

20. 5 in r6 now locked in r6c67 in 23(4) = 5{189/279/369/378/468}

21. "45" n9: 3 outies r6c679 = 15 and must have 5 = [546/564/582/591/951]. r6c7 = {45689}, r6c9 = {1246}

22. When r6c134 = [936] (step 17), r6c5 = 2, however, [9362] is blocked by r6c679 (step 21) -> no 9 in r6c1 = {67}


23. now-from step 13c. r4c2 + r45c3 = [625/652/654/951] ([627] blocked by r6c1 -step 22) -> no 7 in r5c3

24. 16(4) in n145 now = {1258/1456} = 15{28/46} -> 5 locked for c3 and n4

25. from step 13a. r289c3 now {489/789} = 89{4/7} = 21/24 -> no 2 in r7c2 (step 11)

26. from step 16a. 17(4) n547 = {1367/2348} = 3{167/248} -> r7c3 = {27}(only cell in this cage with 2 or 7), {27} locked for r7 in r7c34 and r6c3 = 3 (only 3 left!)

27. n7 2 outies r6c14 = 15 = [78], r7c23 = [42], r78c4 = [72], r5c4 = 6, r4c3 = 5, r35c3 = {14}, 4 in n4 locked in r5

28. 20(4) n365 now 18(3) = {567} -> r56c6 = [59], r456c7 = [675], 23(4) n6 = {2489} -> r6c89 = [41], {36} blocked from r7c78 (r7c6) -> = [81], r4c2 = 9 -> r3c3= 4 (step 9), rest of 27 (4) in n14 = {378} -> r3c2 = 7, r23c1 = {38}.... the rest are singles


Last edited by sudokuEd on Mon Nov 27, 2006 2:57 am; edited 2 times in total
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nd
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PostPosted: Sun Nov 19, 2006 6:27 pm    Post subject: Reply with quote

sudokuEd wrote:
John F. Kennedy wrote:
There is a Chinese curse which says "May he live in interesting times."
JFK is closer to the mark with this one Ruud!

Actually the Chinese quotation is apocryphal (see discussion here: http://itre.cis.upenn.edu/%7Emyl/languagelog/archives/003347.html).

Haven't posted a walkthrough because I couldn't produce one that seemed very satisfactory (i.e. not using ugly T&E steps). Time for me to brush up my midrange-to-advanced techniques in "regular" sudoku, I think...

Incidentally, I don't suppose that anyone here's been fiddling around with Ruud's Sudopedia site? So far only about 3-4 people seem to be contributing. It could be a really useful resource, I think. -- Not much Killer terminology there yet, though I've added a little.
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emm
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PostPosted: Sun Nov 19, 2006 8:36 pm    Post subject: Reply with quote

In Sudoku 'Que no hayan novedades' would be a curse!

Can we have an emoticon for looking at them with narrowed eye? Smile
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PostPosted: Sun Nov 19, 2006 9:08 pm    Post subject: Reply with quote

emm wrote:
Can we have an emoticon for looking at them with narrowed eye?

Sure Narrow
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rcbroughton
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PostPosted: Sun Nov 19, 2006 10:31 pm    Post subject: Solver now works Reply with quote

Thanks to sudokuEd for the walkthrough - it highlighted a couple of Duh! checks that I hadn't coded into my solver when looking at innies/outies and candidates locked in cages.

Made the mods and now it runs through from start to finish - no ALS checks needed. Also doesn't require any trial and error (although on innies/outies it does do an exhaustive check for valid combinations in the included/excluded cells)

I also don't think the limited T&E step 9a is strictly necessary to eliminate 8 from r4c2 - I get to that elimination a slightly different way.

I'll translate the output of my solver into a more friendly stepped walkthrough and post later.

(edited - reposted the walkthrough separately)
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