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Ed
 Post subject: Assassin 299
PostPosted: Fri Aug 08, 2014 8:34 am 
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Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1043
Location: Sydney, Australia
My last puzzle for a good few months. Going on a nice long overseas holiday! Might see some of you!! Unusual cage pattern for me. No cages more than 4 cells. Quite hard. JS found it easy which is why I tried it. SudokuSolver has a hard time so gives it 1.85. Would have like to have posted it for the milestone 300 but will leave that honour....

Assassin 299

Image
code: paste into solver:
3x3::k:2304:2304:4353:4353:4610:2051:2051:6404:1029:4358:4358:4353:4610:4610:4359:6404:6404:1029:4358:2824:4105:4105:4610:4359:4359:6404:5130:2824:2824:5387:4105:2572:2572:4877:4877:5130:3086:3086:5387:5135:5135:5135:5135:4877:5130:784:5387:5387:4881:4370:4370:4371:4877:5130:784:4372:4372:4881:4370:4370:4371:2325:2325:6422:6422:4372:4881:5143:3864:4889:4889:4889:6422:6422:5143:5143:5143:3864:3864:3864:4889:
solution: 
+-------+-------+-------+
| 4 5 3 | 8 9 6 | 2 7 1 |
| 8 2 6 | 1 5 7 | 4 9 3 |
| 7 1 9 | 2 3 4 | 6 5 8 |
+-------+-------+-------+
| 6 4 8 | 5 1 9 | 7 3 2 |
| 9 3 1 | 6 7 2 | 5 8 4 |
| 2 7 5 | 3 4 8 | 9 1 6 |
+-------+-------+-------+
| 1 6 7 | 9 2 3 | 8 4 5 |
| 3 8 4 | 7 6 5 | 1 2 9 |
| 5 9 2 | 4 8 1 | 3 6 7 |
+-------+-------+-------+
Cheers
Ed
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Afmob
 Post subject:
PostPosted: Fri Aug 08, 2014 9:32 pm 
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Grand Master
Grand Master

Joined: Mon Apr 21, 2008 9:44 am
Posts: 310
Location: MV, Germany
Thanks for this Assassin, Ed! I'm quite surprised about SudokuSolver's score as this Killer isn't that hard but still no pushover. It took me some time to solve though that was more my fault since I had to start over because of a false move.
A299 Walkthrough:
1. C1234+R1
a) Outies N4 = 2(1+1) = {11} -> R3C2 = 1, R7C1 = 1
b) Innies+Outies N7: R6C1 = R9C3 = 2
c) 4(2) = {13} locked for C9+N3
d) 9(2) = {45}/[72] since {36} blocked by Killer triple (136) in 8(2) + R1C9 for R1
e) Innies C1234 = 11(3) <> 9

2. C789 !
a) 17(2) = {89} locked for C7
b) Outies C9 = 7(3) = {124} locked for N9; 1 also locked for R8
c) Innies C9 = 21(3) = 7{59/68} -> 7 locked for C9+N9
d) Innies N9 = 17(3) = 3{59/68} -> 3 locked for R9+15(4); R9C8 <> 8,9 since R7C7 = (89)
e) 15(4) = 36{15/24} since R9C78 = (356); R8C6 <> 4 since R9C678 <> 2; R9C6 = (14)
f) Innies N3 = 16(3): R3C9 <> 2,6 since R13C7 <> 8,9
g) 20(4) = 24{59/68} -> 2 locked for N6
h) ! Innies+Outies N6: 11 = R3C9+R7C7 - R5C7: R5C7 <> 6 since R3C9+R7C7 = {89} is a Killer pair of Innies N9

3. R123+C4 !
a) 9(2) + 8(2) = 17(4) = 5{147/237/246} -> 5 locked for R1
b) Innies+Outies N1: -1 = R1C4 - R3C3 -> R1C4 <> 1,9; R3C3 <> 6
c) Innies+Outies R123: -3 = R4C4 - R3C9: R4C4 = (1256)
d) Innies R123 = 19(3): R3C4 <> 5,9 since R3C39 <> 2,6 and R3C9 <> 3,7
e) 9 locked in 19(3) @ C4 = 9{28/37/46} <> 5
f) ! Hidden Killer pair (15) in R4C4 for C4 since Innies C1234 can only have one of them -> R4C4 = (15)

4. N569 !
a) ! Innies+Outies N1236: -9 = R4C4 - R56C7 = 1+[19] / 5+[59] -> R6C7 = 9; R5C7 = (15)
b) R7C7 = 8
c) Innies C9 = 21(3) = {579} locked for C9+N9

5. R789
a) 19(3) = 9{28/37/46} -> 9 locked for N8
b) 20(4) = 2{378/468/567} <> 1
c) Hidden Single: R9C6 = 1 @ N8
d) 15(4) = {1356} -> R8C6 = 5; 6 locked for R9
e) 20(4) = 28{37/46} -> R8C5 = (36); 8 locked for R9+N8
f) Innies R89 = 11(2) = {47}/[83/92]
g) Hidden Single: R7C4 = 9 @ N8

6. R123+N69
a) 8(2) <> 7
b) Killer pair (25) locked in 9(2) + 8(2) for R1
c) 17(3) @ R1 <> 7 since {467} blocked by Killer pair (47) of 9(2)
d) 1,5 locked in 18(4) @ N2 = 15{39/48}
e) Innies C12 = 13(2) = {67}/[85]
f) Innies N1 = 18(3) = {369/378/459/468} since {567} blocked by Killer pair (57) of 9(2)
g) Killer pair (34) locked in Innies N1 + 17(3) @ N7 for C3
h) 21(4) = 15{69/78} -> 5 locked for C3+N4
i) 17(3) @ R1 = {368}

7. R123+N4
a) Killer triple (368) locked in 17(3) @ R1 + 8(2) for R1
b) R1C9 = 1, R2C9 = 3
c) 8 locked in 17(3) @ R1 for 17(3)
d) R2C3 = 6
e) 17(3) @ R1 = {368} -> 3 locked for R1
f) 8(2) = {26} locked for R1
g) 9(2) = {45} locked for R1+N1
h) 17(3) @ R2C1 = {278} -> R2C2 = 2; 7,8 locked for C1+N1
i) R1C3 = 3, R1C4 = 8, R1C5 = 9
j) 17(3) @ N3 = {467} -> CPE: R3C45 <> 4,6,7
k) 16(3) = {259} since R4C4 = (15) -> R3C3 = 9, R3C4 = 2, R4C4 = 5
l) 9 locked in 12(2) @ N4 = {39} locked for R5+N4

8. Rest is singles.

Rating:
1.25. I used some Killer triples.
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Andrew
 Post subject: Re: Assassin 299
PostPosted: Sat Aug 16, 2014 2:04 am 
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Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
I'm also surprised about the SS score, I'm not sure which steps SS can't manage. It was a hard puzzle but didn't require any technically difficult steps.

My later steps were re-worked after I realised that I'd missed the killer pair in step 26; before I found that the later stages had been harder and I'd used locking-out cages.

Here is my walkthrough for Assassin 299:
I've corrected some typos. Thanks Afmob for finding a couple of errors, and pointing out that I'd reached naked singles a couple of sub-steps earlier.
Prelims

a) R1C12 = {18/27/36/45}, no 9
b) R1C67 = {17/26/35}, no 4,8,9
c) R12C9 = {13}
d) R4C56 = {19/28/37/46}, no 5
e) R5C12 = {39/48/57}, no 1,2,6
f) R67C1 = {12}
g) R67C7 = {89}
h) R7C89 = {18/27/36/45}, no 9
i) 11(3) cage at R3C2 = {128/137/146/236/245}, no 9
j) 19(3) cage at R6C4 = {289/379/469/478/568}, no 1

Steps resulting from Prelims
1a. Naked pair {13} in R12C9, locked for C9 and N3, clean-up: no 5,7 in R1C6, no 6,8 in R7C8
1b. Naked pair {12} in R67C1, locked for C1, clean-up: no 7,8 in R1C2
1c. Naked pair {89} in R67C7, locked for C7

2. 45 rule on C9 3 outies R7C8 + R8C78 = 7 = {124}, locked for N9, clean-up: no 6 in R7C9

3. 45 rule on C9 3 innies R789C9 = 21 = {579/678}, 7 locked for C9 and N9
3a. Killer pair 8,9 in R7C7 and R789C9, locked for N9

4. 45 rule on N3 3 innies R1C7 + R3C79 = 16 = {259/268/457}
4a. 8,9 of {259/268} must be in R3C9 -> no 2,6 in R3C9
4b. 2 in C9 only in R456C9, locked for C9

5. 45 rule on C12 2 innies R67C2 = 13 = {49/58/67}, no 1,2,3

6. 45 rule on N7 two innies R7C1 + R9C3 = 3 = {12}, locked for N7

7. 3 in N9 only in R9C78, locked for R9 and 15(4) cage at R8C6, no 3 in R8C6
7a. 15(4) cage = {1356/2346} (only combinations containing at least two of 3,5,6 for R9C78}, no 7,8,9
7b. 15(4) cage = {1356/2346}, CPE no 6 in R9C45

[Just spotted …]
8. 45 rule on N4 2(1+1) outies R3C2 + R7C1 = 2 -> R3C2 = 1, R7C1 = 1, R6C1 = 2, R9C3 = 2, clean-up: no 8 in R1C1, no 8 in R7C9
8a. R3C2 = 1 -> R4C12 = 10 = {37/46}, no 5,8
8b. 1 in N9 only in R8C78, locked for R8

9. 1 in N4 only in 21(4) cage at R4C3 = {1389/1569/1578} (cannot be {1479} which clashes with R4C12), no 4, clean-up: no 9 in R7C2 (step 5)

10. 45 rule on N1 1 remaining innie R3C3 = 1 outie R1C4 + 1, no 1,9 in R1C4

11. 45 rule on R89 2 innies R8C34 = 11 = {38/47/56}/[92], no 9 in R8C4

12. 45 rule on N5689 1 remaining outie R3C9 = 1 innie R4C4 + 3, R3C9 = {4589} -> R4C4 = {1256}

13. 45 rule on N6 2 innies R56C7 = 1 outie R3C9 + 6
13a. R56C7 cannot total 12,13 (because no 6,7 in R3C9) -> no 4 in R5C7

14. R1C12 = {45}/[72] (cannot be {36} which clashes with R1C67 + R1C9, combo clash block), no 3,6 in R1C12
[Alternatively R1C679 can be written as a combined cage with variable total.]
14a. R1C12 = {45}/[72], R1C67 = [17]/{26}/[35] -> combined cage R1C1267 = {45}[17]/{45}{26}/[72][35], 5 locked for R1, clean-up: no 6 in R3C3 (step 10)

15. 45 rule on R1 2 innies R1C58 = 2 outies R2C39 + 7
15a. Min R2C39 = 4 -> min R1C58 = 11, no 1 in R1C5

16. 45 rule on R123 3 remaining innies R3C349 = 19 = {289/379/469/478/568}
16a. 2 of {289} must be in R3C4, 9 of {379} must be in R3C9, 9 of {469} must be in R3C3 (R3C34 cannot be [46] because 16(3) cage at R3C3 cannot be [46]6 and there’s no 6 in R3C3) -> no 9 in R3C4
16b. 5 of {568} must be in R3C9 (R3C34 cannot be [56] because 16(3) cage at R3C3 cannot be [56]5) -> no 5 in R3C34, clean-up: no 4 in R1C4 (step 10)

17. 45 rule on N1 using R3C2 = 1, 3 outies R134C4 = 15 = {168/258/357/456} (cannot be {267/348} which clash with 19(3) cage at R6C4
17a. 1,5 only in R4C4 -> R4C4 = {15}, clean-up: no 5,9 in R3C9 (step 12)
17b. 2 of {258} must be in R3C4 (cannot be [285] which clashes with R3C9 + R4C4 = [85], IOD clash, step 12) -> no 2 in R1C4, clean-up: no 3 in R3C3 (step 10)
17c. R3C349 (step 16) = {289/469/478} (cannot be {379} because R3C9 only contains 4,8), no 3 in R3C4
17d. 8 of {289} must be in R3C9, 8 of {478} must be in R3C49 (cannot be [874] which clashes with R1C4 + R3C3 = [78], IOD clash, step 10) -> no 8 in R3C3, clean-up: no 7 in R1C4 (step 10)
17e. 9 in N3 only in R123C8, locked for C8

18. 45 rule on N1 using R3C2 = 1, 3 innies R123C3 = 18 = {369/378/459/468} (cannot be {567} which clashes with R1C12)
18a. 7 of {378} must be in R3C3 -> no 7 in R12C3
18b. 5 of {459} must be in R2C3, 4,7,9 of the other combinations must be in R3C3 -> no 4,9 in R2C3

19. R1C7 + R3C79 (step 4) = {268/457}
19a. R3C9 = {48} -> no 4 in R3C7

20. 15(4) cage at R8C6 = {1356/2346}
20a. 1 of {1356} must be in R9C6, 2,4 of {2346} must be in R89C6 -> R9C6 = {14}, no 4 in R8C6
20b. 15(4) cage = {1356/2346}, CPE no 6 in R8C9

21. R1C7 + R3C79 (step 19) = {268/457}
21a. R56C7 = R3C9 + 6 (step 13)
21b. R3C9 = {48} -> R56C7 = 10,14, R3C9 + R56C7 = 4[19]/8[59] (cannot be 8[68] which clashes with R1C7 + R3C79 = {26}8) -> R5C7 = {15}, R6C7 = 9, R7C7 = 8, clean-up: no 5 in R6C2, no 4 in R7C2 (both step 5)

22. R789C9 (step 3) = {579} (only remaining combination), 5 locked for C9 and N9
22a. Naked pair {36} in R9C78, locked for R9 and 15(4) cage at R8C6, no 6 in R8C6
22b. Naked quad {2468} in 20(4) cage at R3C9, 6 locked for N6

23. 45 rule on N36 3 remaining innies R135C7 = 13 = {157/256}, 5 locked for C7

24. 21(4) cage at R4C3 (step 9) = {1389/1569/1578}
24a. 6 of {1569} must be in R6C2 -> no 6 in R456C3

25. 17(3) cage at R7C2 = {359/368/458/467}
25a. 5 of {359/458} must be in R7C2 -> no 5 in R78C3, clean-up: no 6 in R8C4 (step 11)

26. Killer pair 3,4 in R123C3 and 17(3) cage at R7C2, locked for C3
26a. 21(4) cage at R4C3 (step 9) = {1569/1578}, 5 locked for C3 and N4, clean-up: no 7 in R5C12

27. R1C4 + R2C3 = {368} -> 17(3) cage at R1C3 = {368} (only remaining combination), no 4,9
27a. Caged X-Wing for 3 in 17(3) cage and R12C9, no other 3 in R12, clean-up: no 5 in R1C7
27b. R1C12 = {45} (cannot be [72] which clashes with R1C67), locked for R1 and N1, clean-up: no 3 in R1C4 (step 10)
27c. R123C3 (step 18) = {369/378}, 3 locked for C3 and N1, clean-up: no 8 in R8C4 (step 11)
27d. R2C2 = 2 (hidden single in N1)
[Cracked. The rest is straightforward.]

28. 4 in C3 only in 17(3) cage at R7C2, locked for N7
28a. 17(3) cage (step 25) = {458/467}, no 9, clean-up: no 2 in R8C4 (step 11)
28b. 25(4) cage at R8C1 = {3589/3679}, 3 locked for R8, clean-up: no 8 in R8C3 (step 11)

29. 19(3) cage at R6C4 = {379/469} (cannot be{289} because 2,9 only in R7C4, cannot be {478/568} which clash with R134C4) -> R7C4 = 9, R68C4 = [37/64], clean-up: no 6 in R8C3 (step 11)

30. Naked pair {47} in R8C34, locked for R8
30a. Naked pair {12} in R8C78, locked for R8 and N9
30b. R8C6 = 5, R9C78 = {36} -> R9C6 = 1 (cage sum), clean-up: no 7 in R1C7, no 9 in R4C5
30c. R9C3 = 2 -> 20(4) cage at R8C5 = {2468} (only remaining combination) -> R8C5 = 6, R9C45 = {48}, locked for R9 and N8, clean-up: no 4 in R4C6

31. Naked pair {26} in R1C67, locked for R1 -> R1C34 = [38], R2C3 = 6, R9C45 = [48], clean-up: no 2 in R4C6

32. R1C7 + R3C79 (step 19) = {268} (only remaining combination, cannot be {457} because 5,7 only in R3C7) -> R3C9 = 8, R13C7 = {26}, locked for C7 and N3 -> R9C78 = [36]
32a. R3C9 = 8 -> R4C4 = 5 (step 12)
32b. R4C5 = 5 -> R3C34 = 11 = [92] -> R23C1 = [87], R3C7 = 6, R1C67 = [62], clean-up: no 4 in R4C5
32c. 9 in N4 only in R5C12 = {39}, locked for R5
32d. 11(3) cage at R3C2 = {146} (only remaining combination), 4,6 locked for R4 and N4 -> R4C9 = 2, clean-up: no 8 in R4C6
32e. Killer pair 1,7 in R4C56 and R4C7, locked for R4 -> R4C3 = 8
[Thanks Afmob for pointing out that I'd reached naked singles after step 32c. I check for them manually, doing so when I think I might have reached naked singles.

and the rest is naked singles.

Rating Comment:
I used combination analysis and a caged X-Wing. None of my steps were more that 1.25 but I found this puzzle hard and it took me a long time to solve, so I'll rate my walkthrough at Hard 1.25.


I'm also going on an overseas holiday and I've got a lot to do before I leave, so this will probably be the last walkthrough I post until late September.

Maybe Afmob, HATMAN and wellbeback (possibly others) will keep this forum going while Ed and I are away?
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