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Maverick 3

 
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Nasenbaer
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Joined: 20 Jul 2006
Posts: 167
Location: Fellbach (Deutschland)

PostPosted: Fri Feb 29, 2008 1:20 pm    Post subject: Maverick 3 Reply with quote

Ruud seems to have some problems, no new assassin, no explosion. Oh well.

With the spare time on my hands I started to experiment with a cage design I had in mind for some time now. It consists only of 3-cell cages. I had a major problem with this design: the difficulty. Ratings between 0.7 and 1.0 are much too low for us! Wink But this one is a little higher: 1.5 on the RS(v2.2.3)-Scale (Richard's-SudokuSolver(v2.2.3)-Scale).

I wanted to name it Spiral of Death (because of the way it winds around) or Exercise in innies/outies (because of the the most used technique) but then I went with mhparker's suggestion to use his Maverick series, so now this is

Maverick 3 (RS-rating: 1.5)



3x3:d:k:3072:3072:3072:4867:4867:4867:3590:3590:3590:3849:3849:4875:4875:4875:2574:2574:2574:2065:3849:4115:4115:3093:3093:3093:5912:4633:2065:4123:4115:3869:2334:2334:2334:5912:4633:2065:4123:4389:3869:3367:3367:5929:5912:4633:4908:4123:4389:3869:3367:5929:5929:4403:4148:4908:3894:4389:1592:1592:1592:4403:4403:4148:4908:3894:4160:4160:4160:1859:1859:1859:4148:4167:3894:4681:4681:4681:4172:4172:4172:4167:4167:

Have fun! Twisted Evil

Cheers,
Nasenbaer
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Afmob
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Joined: 22 Sep 2007
Posts: 103
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PostPosted: Fri Feb 29, 2008 10:04 pm    Post subject: Reply with quote

Nice cage pattern! My unpolished walkthrough was quite long with lots of small steps but I realized that the breakthrough move (step 6b,6c) could be applied quite early. Therefore I can understand if one rates this Killer 1.5 since those steps are not easy to see.

M3 Walkthrough:

1. N56
a) 7 locked in 13(3) = 7{15/24}
b) Both 23(3) = {689} locked for C7/N5
c) 9(3) = 3{15/24} -> 3 locked for R4
d) 17(3) must have 6,8 or 9 and it's only possible @ R7C6 -> R7C6 = (689)
e) Naked triple (689) locked in R567C6 for C6

2. R789
a) 6(3) = {123} locked for R7
b) 7(3) = {124} locked for R8
c) 16(3) @ N7 = 3{58/67} -> 3 locked for R8
d) Innies+outies R9 : 5 = R8C9 - R9C1 -> R8C9 <> 5, R9C1 = (1234)
e) Innies+Outies R89: -2 = R7C1 - R8C8 -> R7C1 <> 8,9; R8C8 <> 5
f) 3 locked in R9C789 for R9
g) Innies+Outies R9: 5 = R8C9 - R9C1 -> R8C9 <> 8
h) Naked quad (1234) locked in R7C45+R8C56 for N8
i) 3 locked in R7C45 for R7

3. R789
a) 4 locked in R8C56 for R8
b) 18(3) <> {567} because it's blocked by R9C6 = (57)
c) Killer triple (124) locked in R7C3 + R9C1 + 18(3) for N7
d) 4 locked in R9C123 for R9
e) 16(3) = {178/259/358/367} because R9C6 = (57); R9C57 <> 5,7

4. C89
a) 8(3) = 1{25/34} -> 1 locked for C9
b) Innies+Outies C9 : -2 = R9C8 - R1C9 -> R1C9 <> 2,6; R9C8 <> 8,9
c) Innies+Outies C89: 1 = R1C7 - R2C8 -> R1C7 <> 1, R2C8 <> 5,7

5. R123+D/
a) Innies+Outies N2: 5 = R2C3 - R2C6 -> R2C3 = (6789), R2C6 <> 5,7
b) Innies+Outies N1: -2 = R4C2 - R2C3 -> R4C2 = (4567)
c) Innies+Outies R2: -1 = R3C1 - R2C9 -> R2C9 <> 1; R3C1 = (1234)
d) 9 locked in R1C9+R3C7 @ D/ for N3
e) Innies+Outies N3: -13 = R2C6+R4C9 - R3C78
-> R2C6+R4C9 >= 2 therefore R3C78 >= 15 -> R3C78 = (678)
-> R3C78 <= 17 so R2C6+R4C9 <= 4 -> R2C6+R4C9 <> 4,5
f) Innies+Outies R123: -10 = R4C29 - R3C78 -> R4C2 <> 7
g) Innies+Outies N1 : -2 = R4C2 - R2C3 -> R2C3 <> 9
h) 15(3): R2C12 <> 1 because R3C1 <= 4

6. N2 !
a) 1 locked in 10(3) = 1{27/36/45}
b) ! 10(3): R2C78 <> 3 since 1{36} leaves no combo for Outies = 15(3)
c) ! 10(3) <> 4,5 because 1{45} is blocked by Killer pair (45) of 8(3)

7. C789
a) Innies+Outies C89: 1 = R1C7 - R2C8 -> R1C7 <> 4,5
b) 4,5 locked in 17(3) @ C7 = {458} -> R7C6 = 8
c) Hidden Single: R6C5 = 8 @ N5
d) 7 locked in R12C7 for N3

8. R789+D/
a) 16(3) @ R9C5 = {259/367} <> 1
b) 18(3) <> 2,7 since {279} is blocked by Killer pair (27) of 16(3) @ R9C5
c) 9 locked in R9C45 for R9
d) 2 locked in R9C1+R7C3 for D/

9. R123
a) 10(3): R2C7 <> 2 because 7 only possible there
b) 10(3): Hidden Killer pair (23) @ R1C6 -> R1C6 <> 1
c) 1 locked in 12(3) @ N2 for R3
d) Hidden Single: R4C9 = 1 @ C9
e) 1 locked in 10(3) for N3
f) 14(3) = 7{25/34} since other combos blocked by Killer pairs (23,24,35) of 8(3)
-> R1C7 = 7, R1C8 <> 5
g) 10(3) = {136} -> R1C6 = 3, R1C7 = 1, R1C8 = 6
h) 18(3) = {378} -> R3C8 = 8, R4C8 = 7, R5C8 = 3

10. N56
a) 23(3) = {689} -> R3C7 = 9, {68} locked for N6
b) 19(3) = {469} -> R7C9 = 6, {49} locked for C9+N6
c) 9(3) = {234} -> R4C6 = 4, 2 locked for R4+N5

11. N12
a) 16(3) = 7{36/45} -> 7 locked for R3+N1
b) 12(3) @ N2 = {156} locked for R3+N2

12. N18
a) 7(3) = {124} -> R8C5 = 4, R8C6 = 1, R8C7 = 2
b) Hidden Single: R7C3 = 1 @ R7
c) R2C3 = 8
d) 15(3) = {249} locked for N1, 9 locked for R2
e) R9C1 = 2
f) Hidden Single: R2C2 = 2 @ N1

13. Rest is singles without considering diagonals.

Rating:1.25 since there is only one key move (combo analysis) and M3 can be solved in a short way.


Last edited by Afmob on Mon Mar 03, 2008 11:10 am; edited 1 time in total
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HATMAN
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Joined: 06 Jan 2008
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Location: Britain, Turkey

PostPosted: Sat Mar 01, 2008 3:22 pm    Post subject: Reply with quote

Nice one Nasenbaer

I did not find it too difficult, but I like outies minus innies and I immediately noticed the R2 10/3 interaction with the C9 8/3 which placed seven cells and it rolled from there.
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HATMAN
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Joined: 06 Jan 2008
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Location: Britain, Turkey

PostPosted: Sat Mar 01, 2008 4:42 pm    Post subject: Reply with quote

My walkthrough


"45" on N124 -> r7c2 = r2c6 + 6 r7c2 = 7/8/9, r2c6 = 1/2/3
"45" on N2 -> r2c3 = r2c6 + 5 r2c3 = 6/7/8
"45" on N1 -> r2c3 = r4c2 + 2 r4c2 = 4/5/6
"45" on R2 -> r3c19r4c9 = 7, r2c9 <>1
"45" on R23 -> r3c78 = r4c29 + 10 max r4c29 = 7 min r3c78 = 15 r3c8 = 6/7/8/9
r4c9 = 123-> r23c9 = {4/5}
-> 10(3) <> 145 = 1{27}/1{36}/2{35}/2{17}/3{15}/3{24}
"45" on N3 -> r3c78 = r2c6 + r4c9 + 13 r2c6&r4c9 = {11}/{12}/{13/22}
R3c78 = {69/78}/{79}/{89}
if r2c6=2 -> r2c3= 7 r4c2 = 5 r2c78 = {35} r4c9 = 12 no solution for 8(3)
if r2c6=1 -> r2c3= 6 r47c2 = [47] r2c78 = {27} <> 45 KP r23c9
-> r3c78 {9(6/8)} -> r4c9<>2, r3c23 = [57] -> r3c456 = {246},
-> r3c78 = {89} r3c19 = [31]-> 8/3 = [413] but N1 15(3) [483] conflict
-> r2c36 = [83], r47c2 = [69] -> r4c9 = 1 -> r23c9 = {25} r3c1 = 1/4, r3c78 = {89}
r5c7 = 6, r2c78 = [16]
straightforward from here


Edit: lingo changed from Djapes to your's (I hope) and the elimination tightened up a bit.
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Last edited by HATMAN on Thu Mar 06, 2008 3:41 pm; edited 1 time in total
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mhparker
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Joined: 20 Jan 2007
Posts: 345
Location: Germany

PostPosted: Sun Mar 02, 2008 12:10 pm    Post subject: Reply with quote

Hi folks,

Nice to be able to try a Maverick for the first time! Very Happy

Unfortunately, after two medium-sized sessions, I seem to have ground to a halt Brick wall , and am in danger of having to give up due to a "time out" (a self-imposed limit of 30 minutes without any eliminations). It certainly feels like a 1.5 so far, and definitely a notch more difficult than the A91, which I managed in under two hours yesterday evening.

Obviously, Afmob and HATMAN saw something I'm still missing. Well done guys! Applause

If anyone's interested in comparing progress, here's how far I've managed to get so far:

Code:
.-----------------------------------.-----------------------------------.-----------------------------------.
| 1234678     123456789   123456789 | 23456789    23456789    23457     | 23457       12345678    34579     |
:-----------------------.-----------'-----------------------.-----------'-----------------------.-----------:
| 23456789    2345789   | 678         23456789    23456789  | 123         123457      12346     | 2345      |
|           .-----------'-----------.-----------------------'-----------.-----------.-----------:           |
| 1234      | 12345679    123456789 | 123456789   123456789   123457    | 89        | 678       | 12345     |
:-----------:           .-----------+-----------------------------------:           |           |           |
| 456789    | 456       | 456789    | 12345       12345       2345      | 689       | 45789     | 12        |
|           :-----------:           :-----------------------.-----------:           |           :-----------:
| 123456789 | 123456789 | 123456789 | 12457       2457      | 689       | 689       | 12345789  | 2345789   |
|           |           |           |           .-----------'           :-----------+-----------:           |
| 123456789 | 123456789 | 123456789 | 12457     | 689         689       | 123457    | 12345     | 2345789   |
:-----------:           :-----------'-----------'-----------.-----------'           |           |           |
| 567       | 789       | 12          123         123       | 689         457       | 45789     | 456789    |
|           :-----------'-----------------------.-----------'-----------------------:           :-----------:
| 56789     | 35678       35678       5678      | 124         124         12        | 789       | 679       |
|           :-----------------------------------+-----------------------------------+-----------'           |
| 124       | 12456789    12456789    56789     | 689         57          123       | 12357       235678    |
'-----------'-----------------------------------'-----------------------------------'-----------------------'


Edit: Well, finally did it, after having missed the key moves completely, using a contradiction move from the above position instead! Total time around 4 hours!! Shocked .

Many thanks for a great little puzzle, Nasenbaer! Very Happy

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Mike
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Andrew
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Joined: 11 Aug 2006
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Location: Lethbridge, Alberta

PostPosted: Mon Mar 03, 2008 12:56 am    Post subject: Reply with quote

A nice puzzle. The spiral was very obvious when I was colouring the cages in my worksheet. A nice touch although it doesn't, and probably can't, contribute to the solution of the puzzle.

Maybe I found myself too influenced by the introductory comment about innies-outies, which are certainly a key part of this puzzle, so I took a long time to spot a key clash. I also missed a few of the relationships used by Afmob and HATMAN and therefore missed one of Afmob's two key moves.

Unlike Mike, although my walkthrough is a long one, I found this puzzle definitely easier than A91 and didn't get stuck like I did for that one. I'll therefore rate M3 as a Hard 1.25.

Here is my walkthrough, edited thanks to feedback from Afmob.

I've removed {357} from the combinations in step 20. I originally included it because Iíd been careless with my eliminations in step 5, deleting 3 from R8 but not from the rest of N7.

An interesting point is that {357} would clash with R8C234 = {358/367} even if 3 hadnít been eliminated from R8C4 in step 2 and from R789C1 in step 5.



This is a Killer-X

Prelims

a) R1C456 = {289/379/469/478/568}, no 1
b) R2C345 = {289/379/469/478/568}, no 1
c) R2C678 = {127/136/145/235}, no 8,9
d) R234C9 = 1{25/34}, 1 locked for C9
e) R345C7 = {689}, locked for C7
f) R4C456 = {126/135/234}, no 7,8,9
g) 23(3) cage in N5 = {689}, locked for N5
h) R7C345 = {123}, locked for R7
i) R8C567 = {124}, locked for R8

1. R4C456 = {135/234}, 3 locked for R4 and N5

2. Naked quad {1234} in R7C45 and R8C56, locked for N8
2a. 3 in N8 locked in R7C45, locked for R7
2b. 4 in N8 locked in R8C56, locked for R8

3. 17(3) cage at R6C7 = {179/278/359/458/467} (cannot be {269/368} because R7C7 only contains 4,5,7)
3a. 6,8,9 of {179/278/467} must be in R7C6 -> no 7 in R7C6
3b. 8,9 of {359/458} must be in R7C6 -> no 5 in R7C6

4. Naked triple {689} in R567C6, locked for C6

5. R8C234 = {358/367}, no 9, 3 locked for R8 and N7

6. R9C567 = {178/259/358/367/457} (cannot be {169/268/349} because R9C6 only contains 5,7)
6a. 1,2,3,4 must be in R9C7 -> R9C7 = {1234}

7. 45 rule on R2 1 innie R2C9 = 1 outie R3C1 + 1, R2C9 = {2345}, R3C1 = {1234}

8. 45 rule on R9 1 outie R8C9 = 1 innie R9C1 + 5, R8C9 = {679}, R9C1 = {124}

9. 9 on D/ locked in R1C9 + R3C7, locked for N3

10. 45 rule on C1 1 outie R2C2 = 1 innie R1C1 + 1, no 9 in R1C1, no 1 in R2C2

11. 45 rule on C9 1 innie R1C9 = 1 outie R9C8 + 2, no 2 in R1C9, no 8,9 in R9C8

12. 45 rule on N1 1 innie R2C3 = 1 outie R4C2 + 2, no 2,5 in R2C3, no 8,9 in R4C2

13. 15(3) cage at R2C1 = {159/168/249/258/267/348/357/456}
13a. 1 of {159/168} must be in R3C1 -> no 1 in R2C1

14. 45 rule on N2 1 outie R2C3 = 1 innie R2C6 + 5, no 3,4 in R2C3, no 5,7 in R2C6, no 1,2 in R4C2 (step 12)

15. 45 rule on N3 2 innies R3C78 = 2 outies R2C6 + R4C9 +13
15a. Max R3C78 = 17 -> max R2C6 + R4C9 = 4, R2C6 = {123}, R4C9 = {12}, clean-up: no 9 in R2C3 (step 14), no 7 in R4C2 (step 12)
15b. Min R2C6 + R4C9 = 2 -> min R3C78 = 15, min R3C8 = 6

16. Killer pair 1,2 in R4C456 and R4C9, locked for R4

17. 45 rule on N4 1 outie R7C2 = 1 innie R4C2 + 3, no 4,5,6 in R7C2

18. 45 rule on R89 1 innie R8C8 = 1 outie R7C1 + 2, no 8,9 in R7C1, no 5 in R8C8

19. 45 rule on R8 3 innies R8C189 = 22 = {589/679}
19a. 5 of {589} must be in R8C1 -> no 8 in R8C1

20. R789C1 = {159/249/267/456}
20a. 4 of {456} must be in R9C1 -> no 4 in R7C1, clean-up: no 6 in R8C8 (step 19)
20b. 4 in N7 locked in R9C123, locked for R9, clean-up: no 6 in R1C9 (step 11)

21. R9C567 (step 6) = {178/259/358/367}
21a. R9C6 = {57} -> no 5,7 in R9C5

22. Hidden killer pair 5,7 in R89C4 and R9C6 for N8 -> R89C4 must contain 5 or 7
22a. R56C4 cannot be {57} -> no 1 in R5C5

23. 45 rule on C89 1 outie R1C7 = 1 innie R2C8 + 1, no 1 in R1C7, no 5,7 in R2C8

24. 1 in R2 locked in R2C678 = {127/136/145}
24a. 6 of {136} locked in R2C8 -> no 3 in R2C8, clean-up: no 4 in R1C7 (step 23)
24b. 5,7 of {127/145} must be in R2C7 -> no 2,4 in R2C7

25. R678C8 = {169/178/259/268/349/358/367/457}
25a. 1,2,3 of {169/178/259/268/349/358/367} must be in R6C8 -> no 6,8,9 in R6C8
25b. 9 of {169/259} must be in R8C8 -> no 9 in R7C8
25c. 1 of {178} must be in R6C8, 7 of {367/457} must be in R8C8 -> no 7 in R6C8

26. 16(3) cage at R3C2 = {169/259/268/349/358/367/457} (cannot be {178} because R4C2 only contains 4,5,6)
26a. 6 of {169/268/367} -> no 6 in R3C23

27. R345C8 = {189/279/369/378/468/567} (cannot be {459} because R3C8 only contains 6,7,8)
27a. 1,2,3 of {189/279/369} must be in R5C8 -> no 9 in R5C8

28. 4 in C7 locked in R67C7
28a. 17(3) cage at R6C7 (step 3) = {458/467}, no 1,2,3,9

29. 9 in C6 locked in R56C6, locked for N5
29a. 9 in N8 locked in R9C56, locked for R9

30. R9C234 = {189/279/459/468} (cannot be {567} which clashes with R9C6)
30a. 9 of {279/459} must be in R9C4 -> no 5,7 in R9C4

31. Naked triple {689} in R7C6 + R9C45, locked for N8

32. R8C234 (step 5) = {358/367}
32a. R8C4 = {57} -> no 5,7 in R8C23

33. R1C456 = {289/379/469/478/568}
33a. 2,5 of {289/568} must be in R1C6 -> no 2,5 in R1C45

34. R1C789 = {158/239/248/257/347} (cannot be {149} because no 1,4,9 in R1C7, cannot be {167} because 1,6 only in R1C8, cannot be {356} which clashes with R23C9), no 6

35. 45 rule on N4 3 innies R456C2 = 14 = {149/167/248/257/356} (cannot be {158/347} because R567C2 would be {18}8/{37}7, cannot be {239} because R4C2 only contains 4,5,6)
35a. 4 of {149/248} must be in R4C2 -> no 4 in R56C2

36. R789C1 (step 20) = {159/267/456}
36a. 45 rule on C1 3 innies R123C1 = 14 = {149/158/239/248/347} (cannot be {167/257/356} which clash with R789C1), no 6, clean-up: no 7 in R2C2 (step 10)

37. R2C678 (step 24) = {127/136} (cannot be {145} which clashes with R234C9), no 4,5

38. Hidden killer pair 4,5 in R1C789 and R23C9 for N3 -> R1C789 must contain 4 or 5
38a. R1C789 = {158/248/257/347}, no 9, clean-up: no 7 in R9C8 (step 11)

39. R3C7 = 9 (hidden single in N3)
39a. Naked pair {68} in R45C7, locked for N6
39b. 6 on D/ must be in R2C8 or R8C2, CPE no 6 in R2C2, clean-up: no 5 in R1C1 (step 10)
39c. 8 on D/ must be in R1C9 or R8C2, CPE no 8 in R1C2

40. R345C8 (step 27) = {189/279/369/378/567} (cannot be {468} because 6,8 only in R3C8), no 4

41. R567C9 = {289/379/469/478} (cannot be {568} because 6,8 only in R7C9), no 5
41a. 6 of {469} must be in R7C9 -> no 4 in R7C9

42. 16(3) cage at R3C2 (step 26) = {358/367/457} (cannot be {268} because that would make R2C3 + R3C23 8{28}), no 1,2
42a. 4 of {457} must be in R4C2 (cannot be {47}5 because that would make R2C3 + R3C23 7{47}) -> no 4 in R3C23

43. 6 in N3 locked in R23C8, locked for C8, clean-up: no 8 in R1C9 (step 11)

44. R1C789 (step 38a) = {248/257/347} (cannot be {158} because 1,8 only in R1C8), no 1

45. 1 in R1 locked in R1C123, locked for N1, clean-up: no 2 in R2C9 (step 7)
45a. R1C123 = {129/138/156} (cannot be {147} which clashes with R1C789), no 4,7

46. R1C456 = {289/379/469/568} (cannot be {478} which clashes with R1C789)
46a. 4 of {469} must be in R1C6 -> no 4 in R1C45

47. R234C9 = {125/134}
47a. 5 of {125} must be in R2C9 -> no 5 in R3C9

48. R2C345 = {289/469/478/568} (cannot be {379} which clashes with R2C678), no 3

49. R8C2 = 8 (hidden single on D/), R8C34 = 8 = [35], clean-up: no 5 in R4C2 (step 17), no 7 in R2C3 (step 12), no 2 in R2C6 (step 14), no 6 in R7C1 (step 18)

50. R2C8 = 6 (hidden single on D/), R2C67 = 4 = {13}, locked for R2, R2C3 = 8, R4C2 = 6 (step 12), R45C7 = [86], R7C2 = 9 (step 17), R2C6 = 3 (step 14), R2C7 = 1, R89C7 = [23], clean-up: no 3 in R1C12 (step 45a)

51. R4C9 = 1 (hidden single in C9), R9C8 = 1 (hidden single in C8), clean-up: no 5 in R4C56 (step 1)

52. R7C3 = 1 (hidden single in N7), locked for D/

53. R1C9 = 3 (hidden single on D/), R1C78 = 11 = [74], R23C9 = [52], R3C1 = 4 (step 7), R2C2 = 2, locked for D\, R1C1 = 1 (that seems to have been a hidden single on D\ since step 51), R1C23 = [56], R1C6 = 2, R4C6 = 4, R4C45 = [32], R7C45 = [23], R56C4 = [17], R5C5 = 5, locked for D\, R9C1 = 2, R8C56 = [41], R3C23 = [37], 7 locked for D\, R56C2 = [71], R9C23 = [45], R9C4 = 9 (step 30), R1C45 = [89], R3C4 = 6, R2C45 = [47], R3C56 = [15], R2C1 = 9, R4C1 = 5, R78C1 = [76], R3C8 = 8, R78C8 = [59], 9 locked for D\, R8C9 = 7, R67C7 = [54], R4C3 = 9, R4C8 = 7, R9C6 = 7

54. Naked pair {68} in R6C56, locked for R6 and N5

and the rest is naked singles and a cage sum

1 5 6 8 9 2 7 4 3
9 2 8 4 7 3 1 6 5
4 3 7 6 1 5 9 8 2
5 6 9 3 2 4 8 7 1
8 7 2 1 5 9 6 3 4
3 1 4 7 8 6 5 2 9
7 9 1 2 3 8 4 5 6
6 8 3 5 4 1 2 9 7
2 4 5 9 6 7 3 1 8


Last edited by Andrew on Tue Mar 11, 2008 2:36 am; edited 2 times in total
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Nasenbaer
Master
Master


Joined: 20 Jul 2006
Posts: 167
Location: Fellbach (Deutschland)

PostPosted: Mon Mar 03, 2008 7:02 pm    Post subject: Reply with quote

Wow! 3 different walkthroughs in 3 days. Great work, my fellow killer-solvers! (or should I call you Mavericks?) Wink

To prevent deprivation I'll give you a new one in a couple of minutes... Twisted Evil

Cheers,
Nasenbaer
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