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 Post subject: Assassin 267
PostPosted: Fri Aug 23, 2013 6:55 pm 
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Joined: Tue Jun 16, 2009 9:31 pm
Posts: 282
Location: California, out of London
Here's my second one. Little easier than the first.
Assassin 267
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Hidden Text:
3x3::k:6168:6168:3353:3353:3850:3850:6414:6414:6414:6168:3092:3353:3850:3850:3859:3859:6414:6414:4873:3092:7937:7937:7937:7937:3859:3858:6408:4873:3092:3349:3349:3349:7937:7937:3858:6408:4873:8963:8963:8963:8963:8963:8963:8963:6408:4873:3089:7426:7426:4119:4119:4119:2326:6408:4873:3089:5392:7426:7426:7426:7426:2326:6408:4879:4879:5392:5392:7691:7691:2074:2326:4891:4879:4879:4879:7691:7691:2074:2074:4891:4891:


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 Post subject: Re: Assassin 267
PostPosted: Sun Aug 25, 2013 5:27 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Nice puzzle - thanks wellbeback! I found it quite a bit easier than your first one but no gimme since it took a while to find the key (step 9 in this highly optimised WT). Just one tricky step and the middle comes out much easier than that other resistant monster.

Assassin 267 Walkthrough
26 steps:
Preliminaries courtesy of SudokSolver
Cage 15(2) n36 - cells only uses 6789
Cage 12(2) n47 - cells do not use 126
Cage 24(3) n1 - cells ={789}
Cage 8(3) n89 - cells do not use 6789
Cage 9(3) n69 - cells do not use 789
Cage 21(3) n78 - cells do not use 123
Cage 19(3) n9 - cells do not use 1
Cage 30(4) n8 - cells ={6789}

1. 30(4)n8 = {6789} only: all locked for n8

2. 19(5)n7 must have 1: 1 locked for n7

3. 8(3)r8c7 must have 1 and 19(5)r8c1 must have 1, both cages are only in r89 -> 1 locked for r89 (Caged X-wing)
3a. ie, no 1 in r8c8

4. "45" on r89: 1 innie r8c8 + 7 = 1 outie r7c3
4a. -> r8c8 = 2, r7c3 = 9 (only permutation)
4b. no 3 in r6c2
4c. r7c3 = 9 -> r8c34 = 12 (cage sum) = [84/75](no 4,5,6 in r7c3)
4d. r8c8 = 2 -> r67c8 = 7 (cage sum) = {16/34}(no 5)

5. 9 in n9 only in 19(3) = {379/469}(no 5,8} = [3/4..]

6. 8(3)r9c6 = {125/134}
6a. but [1]{34} blocked by 19(3) = [3/4]
6b. [1]{25} blocked by no 2 in r89c7
6c. -> no 1 in r9c6
6d. 1 must be in 8(3) -> 1 locked in r89c7 for n9 and c7
6e. no 6 in r6c8 (h7(2)r67c8)
6f. 8 in n9 only in r7: 8 locked for r7
6g. no 4 in r6c2

7. 19(3)n9 = {379/469} and r7c8 = (346)
7a. {469}[3] in 19(3)+r7c8 or 19(3) = {379} -> 3 locked in 19(3) or r7c8 for n9 (Combined half-cage)

8. 8(3)r9c6 = {125/134}
8a. must have 2 or 3 which are only in r9c6
8b. -> r9c6 = (23)

[note: Andrew's step 13a & following is a simpler way to do the key groundwork than this next step]

9. "45" on n7: 3 remaining innies r7c12 + r8c3 = 17
9a. ={278/368/458/467}
9b. but r7c456 must have one of 4 or 5 for n8 since the only other place for both in n8 is in r8c4 (Hidden killer pair)
9c.->{45}[8] in h17(3)n7 blocked
9d. = {278/368/467}(no 5)
9e. the only permutation for 7 in r8c3 = [647]: also, when 7 in r8c3 -> 5 in r8c4 (h12(2)r8c34); but 4 in r7c2 + 5 in r8c4 leaves no 4 for n8 -> [647] blocked from h17(3)n7 (Locking out cages + combined half-cage)
9f. = {278/368}(no 4)
9g. must have 8 -> r8c3 = 8
9h. r8c4 = 4 (h12(2)r8c34)
9i. r8c3 = 8 -> r9c12 = 9(2) (h17(3) cage sum) = [27/63](no 3,4,7 in r7c1)
9j. r6c2 = (59)

10. 5 in n8 only in r7 in 29(6)r6c3: 5 locked for r7 and 29(6)
10a. no 5 in r6c34

11. 5 in n9 only in 8(3)r8c7 = {125} only
11a. r9c6 = 2, r89c7 = {15}: 5 locked for c7

12. Naked triple {135} in r7c456: 3 locked for r7 and 1,3 locked for 29(6)r6c3
12a. no 1,3 in r6c34
12b. no 4 in r6c8 (h7(2)r67c8)
12c. r67c2 = [57]
12d. r7c1 = 2 (h9(2)r7c12)

13. 29(6)r6c3 = {134579} only (no 2,6,8)
13a. r7c7 = 4
13b. r6c34 = [79]
13c. r67c8 = [16] (h7(2)r67c8)
13d. r7c9 = 8

14. 16(3)r6c5 = {268} only: all locked for r6

15. 15(2)r3c8 = {78} only: both locked for c8

16. 7 in n9 only in c9: locked for c9

17. "45" on c12: 1 innie r5c2 - 4 = 1 outie r9c3 = [84/95]
17a. r5c2 = (89), r9c3 = (45)

18. Naked pair {89} in r15c2: both locked for c2

19. 12(3)r2c2 = {246} only: all locked for c2

20. "45" on c89: 1 innie r5c8 + 3 = 1 outie r1c7 = [63/74/85]
20a. r5c8 = (345), r1c7 = (678)

21. "45" on r12: 1 innie r2c2 + 2 = 1 outie r3c7 = [46/68]
21a. r2c2 = (46), r3c7 = (68)

22. Naked triple {678} in r13c7 + r3c8: all locked for n3
22a. 6 locked for c7

23. 6 in c9 only in n6 in 25(5)r3c9
23a. 25(5) = {24568} only (no 1,3,9)
23b. r6c9 = 4, r6c1 = 3
23c. no 7 in r1c7 (IODc89=-3)

24. Hidden single 7 in n3 -> r3c8 = 7, r4c8 = 8
24a. r6c7 = 2
24b. r6c56 = {68} only: both locked for n5

25. Naked pair {56} in r45c9: locked for n6 and c9
25a. r5c8 = 3, r1c7 = 6 (IODc89=-3)
25b. r3c7 = 8 -> r2c2 = 6 (IODr12=-2)
25c. r3c9 = 2

26. "45" on r5: 2 innies r5c19 = 10 = [46] only permutation

very routine from there with nakeds and a few cage sums.
solution:
+-------+-------+-------+
| 7 9 3 | 8 2 5 | 6 4 1 |
| 8 6 2 | 1 7 4 | 3 5 9 |
| 1 4 5 | 6 3 9 | 8 7 2 |
+-------+-------+-------+
| 9 2 6 | 3 4 1 | 7 8 5 |
| 4 8 1 | 2 5 7 | 9 3 6 |
| 3 5 7 | 9 6 8 | 2 1 4 |
+-------+-------+-------+
| 2 7 9 | 5 1 3 | 4 6 8 |
| 5 3 8 | 4 9 6 | 1 2 7 |
| 6 1 4 | 7 8 2 | 5 9 3 |
+-------+-------+-------+
Cheerio
Ed


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 Post subject: Re: Assassin 267
PostPosted: Sun Aug 25, 2013 9:17 pm 
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Grand Master
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Joined: Tue Jun 16, 2009 9:31 pm
Posts: 282
Location: California, out of London
Thank you Ed - You made it seem too easy!

My solving path was almost identical to yours - with a few minor differences in the details of some of the stages. So I won't bother writing it all out and posting it.
We'll see if I can get a happy medium between the two I've posted for the next one :)

Cheers, Wellbeback


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 Post subject: Re: Assassin 267
PostPosted: Wed Sep 25, 2013 3:56 am 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Continuing to catch up after my holiday; I'm trying to do the Assassins in the order they were posted.

Please keep Assassins and other puzzles coming. I'm sure that Ed, Frank, wellbeback and others will be happy to have new ones to solve, before I've caught up and am ready to try them.

Ed and I found the key breakthrough in the same area, although we used the 45s is somewhat different ways. Unfortunately I found the later part of the puzzle harder and it was only after going through Ed's walkthrough and then checking my walkthrough again that I realised that I'd missed a key clean-up step which would have given the same simple ending that Ed used.

Here is my walkthrough for Assassin 267:
Thanks Ed for your comments and corrections.

Prelims

a) R34C8 = {69/78}
b) R67C2 = {39/48/57}, no 1,2,6
c) 24(3) cage at R1C1 = {789}
d) 9(3) cage at R6C8 = {126/135/234}, no 7,8,9
e) 21(3) cage at R7C3 = {489/579/678}, no 1,2,3
f) 8(3) cage at R8C7 = {125/134}
g) 19(3) cage at R8C9 = {289/379/469/478/568}, no 1
h) 30(4) cage at R8C5 = {6789}

1. 24(3) cage at R1C1 = {789}, locked for N1
1a. Max R12C3 = 11 -> min R1C4 = 2

2. 30(4) cage at R8C5 = {6789}, locked for N8
2a. 21(3) cage at R7C3 = {489/579} (cannot be {678} because R8C4 only contains 4,5), no 6, 9 locked for C3 and N7, clean-up: no 3 in R6C2
2b. R8C4 = {45} -> no 4,5 in R78C3

3. 19(5) cage at R3C1= {12349/12358/12367/12457/13456}, 1 locked for C1

4. 19(5) cage at R8C1 = {12358/12367/12457/13456}, 1 locked for N7
4a. Caged X-Wing for 1 in 19(5) cage and 8(3) cage at R8C7, no other 1 in R89

5. 45 rule on R12 1 outie R3C7 = 1 innie R2C2 + 2, no 1,2,9 in R3C7

6. 45 rule on R89 1 outie R7C3 = 1 innie R8C8 + 7 -> R7C3 = 9, R8C8 = 2, R67C8 = 7 = {16/34}, no 5
6a. Min R89C7 = 4 -> max R9C6 = 4

7. 9 in N9 only in 19(3) cage at R8C9 = {379/469}, no 5,8
7a. 8 in N9 only in R7C79, locked for R7, clean-up: no 4 in R6C2

8. 45 rule on C12 1 innie R5C2 = 1 outie R9C3 + 4, R5C2 = {56789}, R9C3 = {12345}

9. 45 rule on C89 1 outie R1C7 = 1 innie R5C8 + 3, R1C7 = {46789}, R5C8 = {13456}

10. 45 rule on R5 2 innies R5C19 = 10 = {19/28/37/46}, no 5

11. 45 rule on N7 3 remaining innies R7C12 + R8C3 = 17 = {278/368/458/467}
11a. 2,6 of {278/467} must be in R7C1 -> no 7 in R7C1
11b. 3 of {368} must be in R7C2 -> no 3 in R7C1

12. Hidden killer pair 6,7 in R7C789 and 19(3) cage at R8C9 for R7, 19(3) cage (step 7) contains one of 6,7 -> R7C789 must contain one of 6,7
12a. Hidden killer pair 6,7 in R7C123 and R7C789 for R7, R7C789 contains one of 6,7 -> R7C12 must contain one of 6,7
12b. R7C12 + R8C3 (step 11) = {278/368/467} (cannot be {458} which doesn’t contain 6 or 7), no 5, clean-up: no 7 in R6C2
12c. 2,6 only in R7C1 -> R7C1 = {26}

13. 45 rule on N7 2 remaining innies R7C12 = 1 outie R8C4 + 5
13a. R8C4 = {45} -> R7C12 = 9,10 -> R7C12 + R8C4 = [274/634/645], CPE no 4 in R7C456 + R8C12
13b. R7C456 = {123/125/135} (cannot be {235} which clashes with R7C12 + R8C4), 1 locked for R7, N8 and 29(6) cage at R6C3, no 1 in R6C34, clean-up: no 6 in R6C8 (step 6)
13c. 1 in N9 only in R89C7, locked for C7
13d. 4 in N8 only in R8C4 + R9C6, CPE no 4 in R8C7
13e. 5 in N8 only in R7C456 + R8C4, CPE no 5 in R6C4

14. R7C8 = {346}, 19(3) cage at R8C9 (step 7) = {379/469} -> combined cage R7C8 + 19(3) = 3{469}/{46}{379}, 3 locked for N9

15. 8(3) cage at R8C7 = {125/134}
15a. 2,3 only in R9C6 -> R9C6 = {23}

16. R8C4 = 4 (hidden single in N8), R8C3 = 8 (cage sum), R7C12 (step 13) = 9 = [27/63], no 4, clean-up: no 8 in R6C2
16a. 4 in N7 only in R9C123, locked for R9

17. Naked pair {15} in R89C7, locked for C7 and N9, R9C6 = 2 (cage sum)
17a. Naked triple {135} in R7C456, locked for R7 and 29(6) cage at R6C3, no 3,5 in R6C34 -> R7C2 = 7, R7C1 = 2 (hidden single in R7), R6C2 = 5, clean-up: no 6 in R5C2, no 1,3 in R9C3 (both step 8), no 8 in R5C9 (step 10), no 4 in R6C8 (step 6)
17b. Naked triple {468} in R7C789, locked for N9
17c. 7 in N1 only in R12C1, locked for C1, clean-up: no 3 in R5C9 (step 10)

18. 1 in N7 only in R89C2, locked for C2
18a. 12(3) cage at R2C2 = {246} (only remaining combination), locked for C2
18b. Naked pair {13} in R89C2, locked for N7
18c. 6 in N7 only in R89C1, locked for C1, clean-up: no 4 in R5C9 (step 10)
[I missed clean-up after steps 17 and 18a, using step 5, which would have eliminated 3 from R2C2 and 5 from R3C7 and later given naked triple {678} in R1C7 + R3C78, locked for N3, leading to a much simpler ending. OOPS! :oops: I should also have used step 5 clean-up after step 19 to eliminate 5 from R2C2.
This note has been expanded, after I worked through my steps again while looking at Ed's comments.]


19. R7C456 = {135} (step 18a) -> 29(6) cage at R6C3 = {134579} (only remaining combination) -> R7C7 = 4, R6C34 = [79], R7C8 = 6, R6C8 = 1 (step 6), R7C9 = 8, clean-up: no 9 in R1C7 (step 9), no 9 in R34C8, no 9 in R5C1 (step 10)
19a. Naked pair {78} in R34C8, locked for C8
19b. 7 in N9 only in R89C9, locked for C9, clean-up: no 3 in R5C1 (step 10)

20. 16(3) cage at R6C5 = {268} (only remaining combination), locked for R6

21. 8 in C9 only in 25(5) cage at R3C9 = {24568} (only remaining combination, cannot be {12589} because R6C9 only contains 3,4, cannot be {13489} which clashes with 19(3) cage at R8C9) -> R6C9 = 4, R345C9 = {256}, locked for C9, R6C1 = 3, clean-up: no 7 in R1C7 (step 9), no 1 in R5C1 (step 10)
21a. 9 in N6 only in R45C7, locked for C7

22. 2,3 in C1 only in 19(5) cage at R3C1 = {12349/12358}
22a. R5C1 = {48} -> no 4,8 in R34C1
22b. 8 in N4 only in R5C12, locked for R5

23. 45 rule on N3 4 innies R2C7 + R3C789 = 20 = {2378/2567}
23a. 2 of {2378} must be in R3C9, 5 of {2567} must be in R3C9 -> R3C9 = {25}
23b. 2 of {2567} must be in R2C7 -> no 6 in R2C7

24. 6 in C9 only in R45C9, locked for N6
24a. 6 in R6 only in 16(3) cage at R6C5, locked for N5

25. 5 in C9 only in R34C9
25a. 45 rule on R1234 4(2+2) innies R34C19 = 17, R34C9 = {25/56} = 7,11 -> R34C1 = 6,10 = [51/19]
25b. Only permutations for R34C19 are [19]{25} (cannot be [51][25] which doesn’t total 17) -> R34C1 = [19], R5C12 = [48], R34C9 = {25}, R5C9 = 6, R1C2 = 9
25c. R9C3 = 4 (hidden single in N7)
25d. 9 in N3 only in R2C89, locked for R2
25e. R5C7 = 9 (hidden single in R5)
25f. 7 in N6 only in R4C78, locked for R4

26. 13(3) cage at R1C3 = {238/256}, no 7
26a. Hidden killer pair 3,5 in 13(3) cage and R3C3 for C3, 13(3) cage contains one of 3,5, which must be in C3 -> R3C3 = {35}, no 3,5 in R1C4

27. 13(3) cage at R4C3 = {148/238/346} (cannot be {256} which clashes with R4C2), no 5
27a. 1,2 of {148/238} must be in R4C3 -> no 1,2 in R4C45
27b. 4 in R4 only in R4C56, CPE no 4 in R3C5
[I think this CPE has been there for a while.]

28. 15(3) cage at R2C6 = {267/348/357} (cannot be {168} which clashes with R1C7, cannot be {258} which clashes with R6C7, cannot be {456} because 4,5 only in R2C6)
28a. 4,5 of {348/357} must be in R2C6, 7 of {267} must be in R2C6 (R23C7 cannot be {27} because R23C7 + R3C89 = {27}[85] totals more than 20) -> R2C6 = {457}

29. Consider combinations for 13(3) cage at R1C3 (step 27) = {238/256}
13(3) cage = {238} => R12C3 = {23}, locked for C3 => R5C3 = 1
or 13(3) cage = {256} => R3C3 = 3 => 3 in R4 only in 13(3) cage at R4C3 (step 27) = {238/346}, no 1
-> no 1 in R4C2
29a. Naked pair {26} in R4C23, locked for R4 and N4 -> R34C9 = [25], R5C8 = 3, R1C7 = 6 (step 9)
29b. Naked pair {78} in R4C78, locked for R4 and N6 -> R4C45 = [34], R4C3 = 6 (cage sum), R4C6 = 1

30. 13(3) cage at R1C3 (step 26) = {238} (only remaining combination) -> R1C4 = 8, R12C3 = {23}, locked for N1 -> R3C3 = 5, R12C1 = [78]

31. R3C3 = 5, R4C6 = 1, 9 in R3 only in R3C56 -> 31(6) cage at R3C3 = {135679} (only remaining combination) -> R4C7 = 7, R3C4 = 6, R3C56 = {39}, locked for R3 and N3, R23C7 = [38], R2C6 = 4 (cage sum)

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough for A267 at Easy 1.5. However if I hadn't missed the important clean-up after step 18b, I'd have rated it at 1.25 or Hard 1.25.


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