Maverick 3

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Nasenbaer
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Maverick 3

Post by Nasenbaer »

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)

Image

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:

Cheers,
Nasenbaer
Afmob
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Post by Afmob »

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.
HATMAN
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Post by HATMAN »

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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Post by HATMAN »

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.
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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Post by mhparker »

Hi folks,

Nice to be able to try a Maverick for the first time! :D

Unfortunately, after two medium-sized sessions, I seem to have ground to a halt ](*,) , 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! =D>

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

Code: Select all

.-----------------------------------.-----------------------------------.-----------------------------------.
| 1234678     123456789   123456789 | 23456789    23456789    23457     | 23457       12345678    34579     |
&#58;-----------------------.-----------'-----------------------.-----------'-----------------------.-----------&#58;
| 23456789    2345789   | 678         23456789    23456789  | 123         123457      12346     | 2345      |
|           .-----------'-----------.-----------------------'-----------.-----------.-----------&#58;           |
| 1234      | 12345679    123456789 | 123456789   123456789   123457    | 89        | 678       | 12345     |
&#58;-----------&#58;           .-----------+-----------------------------------&#58;           |           |           |
| 456789    | 456       | 456789    | 12345       12345       2345      | 689       | 45789     | 12        |
|           &#58;-----------&#58;           &#58;-----------------------.-----------&#58;           |           &#58;-----------&#58;
| 123456789 | 123456789 | 123456789 | 12457       2457      | 689       | 689       | 12345789  | 2345789   |
|           |           |           |           .-----------'           &#58;-----------+-----------&#58;           |
| 123456789 | 123456789 | 123456789 | 12457     | 689         689       | 123457    | 12345     | 2345789   |
&#58;-----------&#58;           &#58;-----------'-----------'-----------.-----------'           |           |           |
| 567       | 789       | 12          123         123       | 689         457       | 45789     | 456789    |
|           &#58;-----------'-----------------------.-----------'-----------------------&#58;           &#58;-----------&#58;
| 56789     | 35678       35678       5678      | 124         124         12        | 789       | 679       |
|           &#58;-----------------------------------+-----------------------------------+-----------'           |
| 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!! :shock: .

Many thanks for a great little puzzle, Nasenbaer! :D
Cheers,
Mike
Andrew
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Post by Andrew »

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 I’d 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 hadn’t 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.
Nasenbaer
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Post by Nasenbaer »

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:

Cheers,
Nasenbaer
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