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Ed
 Post subject: Assassin 263
PostPosted: Thu Jul 04, 2013 10:51 pm 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
A week late but hopefully worth the wait. I used one tricky step - tricky to spot but very enjoyable to find. Haven't used this technique in one of my puzzles for a long time. SudokuSolver gives it 1.50. JSudoku gets it out very quickly which is why I tried it.

Assassin 263
Note that this is an X killer ie 1-9 cannot repeat on the diagonals
Image

code: paste into solver:
3x3:d:k:6656:6401:6401:6401:6914:6914:6914:6914:4355:6656:6656:6656:6401:1028:1028:6914:4355:3077:7942:2567:3848:6401:3593:3593:4355:2826:3077:7942:2567:2315:3848:3593:3848:5388:2826:4365:7942:7942:2315:2315:3848:5388:5388:4365:4365:7942:2574:3855:3848:2832:3089:1810:1810:4365:7942:2574:3855:7955:2832:2832:3089:4628:4628:4373:4373:4373:7955:3094:3094:5655:2840:4628:4373:7955:7955:7955:5655:5655:5655:5655:2840:
solution: 
+-------+-------+-------+
| 7 2 3 | 4 8 6 | 5 1 9 |
| 6 8 5 | 9 3 1 | 7 2 4 |
| 4 9 1 | 7 5 2 | 6 3 8 |
+-------+-------+-------+
| 9 1 6 | 2 7 5 | 4 8 3 |
| 3 5 2 | 1 4 8 | 9 7 6 |
| 8 4 7 | 3 6 9 | 2 5 1 |
+-------+-------+-------+
| 2 6 8 | 5 1 4 | 3 9 7 |
| 5 7 4 | 8 9 3 | 1 6 2 |
| 1 3 9 | 6 2 7 | 8 4 5 |
+-------+-------+-------+
Cheerio
Ed
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wellbeback
 Post subject: Re: Assassin 263
PostPosted: Sat Jul 06, 2013 8:35 pm 
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Joined: Tue Jun 16, 2009 9:31 pm
Posts: 282
Location: California, out of London
Thanks Ed - I probably didn't find/use your tricky move. I used a very short contradiction chain (as is my wont :whistle: ) which solved it fairly quickly.

Hidden Text:
1. Starting Off

4/3@r2c5 = {13}
15/5@r3c3 = {12345}
Outies c1234 = r4c6+r5c5 = +9 = {45}
-> (r3c3,r4c4,r6c4) = {123}

Either whatever goes in r3c3 (from 123) goes in n5 in r5c4 or it doesn't.
If it does -> r456c4 = {123}
If it doesn't -> r5c4 = 6 -> r45c3 = {12} -> r3c3 = 3 and r46c4 = {12}

Either way -> (12) locked in c4 and n5 in r456c4.


2. Cracked

Outies n3 -> r1c56+r4c8 = +22
-> no 2 in r1c56
-> 2 in n2 in r3c56
-> 2 not in r3c8
-> (Given Outies n6 r3c8+r5c6 = +11) 9 not in r5c6
-> HS 9 in n5 in r6c6
-> r7c7 = 3, r6c4 = 3, r3c3 = 1, r4c4 = 2, r5c4 = 1


3. Finishing off

6 in n5 cannot go in r4c5 (no way to make 14/3@r3c5)
7 in n5 cannot go in r6c5 (no way to make 11/3@r6c5)

-> putting 6 in n5 in r5c6 would put 7 in n5 in r4c5
But that would put {25} in r3c56 and 5 in r3c8 -> contradiction
-> HS 6 in n5 -> r6c5 = 6

-> r7c56 = {14}
-> 4 in n2 in r123c4
-> 8 cannot be in r4c5
-> r4c5 = 7 and r3c56 = {25}
-> r5c6 = 8
-> 11/2@r3c8 = [38]
-> (Outies n3) r1c56 = +14 = [86]
-> r123c4 = {479} -> r1c23 = {23}
Also r789c4 = {568} -> r9c23 = {39}
-> 12/2@r8c5 = [93]
-> 4/3@r2c4 = [31]
-> r7c56 = [14]
-> r5c5 = 4, r4c6 = 5
-> (D\) 11/2@r8c8 = {56}
etc., etc.
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Andrew
 Post subject: Re: Assassin 263
PostPosted: Wed Jul 10, 2013 1:11 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Thanks Ed for your latest Assassin.

I've a feeling that I didn't use your tricky move. My breakthrough (step 11) was equivalent to wellbeback's step 2, but I saw it very differently.
I used:
iteration of innies-outies; something I haven't used for a long time. Then in the re-worked steps I used simple "clones".
Thanks Ed for pointing out that I'd made a silly mistake in step 1a. I've re-worked my walkthrough and also amended my rating comment.
Here is my walkthrough for Assassin 263:
Prelims

a) R2C56 = {13}
b) R23C9 = {39/48/57}, no 1,2,6
c) R34C2 = {19/28/37/46}, no 5
d) R34C8 = {29/38/47/56}, no 1
e) R67C2 = {19/28/37/46}, no 5
f) R67C3 = {69/78}
g) 12(2) cage at R6C6 = {39/48/57}, no 1,2,6
h) R6C78 = {16/25/34}, no 7,8,9
i) R8C56 = {39/48/57}, no 1,2,6
j) 11(2) cage at R8C8 = {29/38/47/56}, no 1
k) 9(3) cage at R4C3 = {126/135/234}, no 7,8,9
l) 21(3) cage at R4C7 = {489/579/678}, no 1,2,3
m) 11(3) cage at R6C5 = {128/137/146/236/245}, no 9
n) 26(4) cage at R1C1 = {2789/3689/4589/4679/5678}, no 1
o) 15(5) cage at R3C3 = {12345}

1. Naked pair {13} in R2C56, locked for R2 and N2, clean-up: no 9 in R3C9
1a. Min R3C56 = {24} = 6 -> max R4C5 = 8
1b. 9 in N5 only in R56C6, locked for C6, clean-up: no 3 in R8C5

2. 45 rule on C1234 2 outies R4C6 + R5C5 = 9 = {45}, locked for N5, D/ and 15(5) cage at R3C3, no 4,5 in R3C3, clean-up: no 7,8 in R7C7
2a. Naked triple {123} in R3C3 + R46C4, CPE no 2 in R3C4, no 3 in R6C6, clean-up: no 9 in R7C7
2b. 1 on D\ only in R3C3 + R4C4, locked for 15(5) cage at R3C3, no 1 in R6C4
[I overlooked the CPE no 1 in R4C3, which I got in step 3d from a slightly different set of 1s.]
2c. Killer quint 1,2,3,4,5 in R3C3 + R4C4, R5C5, R7C7 and 11(2) cage at R8C8, locked for D\

3. 45 rule on N5 4 innies R4C5 + R5C6 + R6C56 = 3 outies R345C3 + 21
3a. Min R345C3 = 6 -> min R4C5 + R5C6 + R6C56 = 27 and contains 7,8,9 -> R4C5 + R5C6 + R6C56 = {3789/6789}, no 1,2
3b. Min R6C5 = 3 -> max R7C56 = 8, no 8 in R7C67
3c. 1,2 in N5 only in R456C4, locked for C4
3d. 1 in N5 only in R45C4, CPE no 1 in R4C3

4. 45 rule on R12 3 outies R3C479 = 21 = {489/579/678}, no 1,2,3, clean-up: no 9 in R2C9
4a. 1 in N3 only in R1C789, locked for R1

5. 45 rule on R89 3 outies R7C489 = 21 = {489/579/678}, no 1,2,3
5a. Min R7C3 + R7C489 = 27 must contain 9, locked for R7, clean-up: no 1 in R6C2

6. 45 rule on R89 1 outie R7C4 = 1 innie R8C9 + 3, no 7,8,9 in R8C9

7. 45 rule on N6 1 outie R5C6 = 1 innie R4C8 -> R4C8 = {6789}, clean-up: R3C8 = {2345}

8. 17(3) cage at R1C9 = {179/269/368} (cannot be {278} which clashes with R23C9)
8a. 1,3 of {179/368} must be in R1C9 -> no 7,8 in R1C9

9. 14(3) cage at R3C5 = {239/248/257/347/356}
9a. 3 of {356} must be in R4C5 -> no 6 in R4C5
9b. 8 of {248} must be in R4C5 -> no 8 in R3C56

10. 11(3) cage at R6C5 = {128/137/146/236} (cannot be {245} because no 2,4,5 in R6C5), no 5
10a. 7 of {137} must be in R67C5 (R67C5 cannot be [31] which clashes with R2C5), no 7 in R7C6

11. 45 rule on N3 2 outies R1C56 = 1 innie R3C8 + 11
11a. Min R3C8 = 2 -> min R1C56 = 13, no 2 in R1C56, no 4 in R1C5
11b. 2 in N2 only in R3C56, locked for R3, clean-up: no 8 in R4C2, no 9 in R4C8, no 9 in R5C6 (step 7)
11c. Min R3C8 = 3 -> min R1C56 = 14, no 5 in R1C5, no 4 in R1C6

12. R6C6 = 9 (hidden single in N5), R7C7 = 3, both placed for D\, R3C3 = 1, R4C4 = 2, placed for D\, R6C4 = 3, placed for D/, clean-up: no 8 in R3C2, no 9 in R4C2, no 7 in R6C2, no 4 in R6C78, no 1,7 in R7C2, no 6 in R7C3, no 8 in 11(2) cage at R8C8
12a. R5C4 = 1 (hidden single in N5), R45C3 = 8 = [35/53/62], no 4, no 6 in R5C3
[This step has been slightly edited]

[Because of my careless error in step 1a, I’ve had to re-work from here.]
13. 14(3) cage at R3C5 (step 9) = {248/257} -> R3C56 = {24/25}

14. 8 on D\ only in R1C1 + R2C2, locked for N1
14a. 26(4) cage at R1C1 must contain 8 and one of 6,7 for D\ = {2789/5678}, no 4

15. 11(3) cage at R6C5 (step 10) = {128/146}, no 7, 1 locked for R7 and N8
15a. R6C5 = {68} -> no 6 in R7C56

16. R5C6 = R4C8 (step 7), 7 in N5 only in R4C5 + R5C6 -> 7 in R4C58, locked for R4, clean-up: no 3 in R3C2
16a. R5C6 = R4C8, 6 in N5 only in R5C6 + R6C5 -> 6 in R4C8 + R6C5, CPE no 6 in R6C789, clean-up: no 1 in R6C78

17. Naked pair {25} in R6C78, locked for R6 and N6, clean-up: no 8 in R7C2

18. 45 rule on N6 3 innies R4C78 + R5C7 = 21 = {489/678}, 8 locked for N6

19. Moved to step 12a

20. 1 in N6 only in R46C9, locked for C9
20a. 17(3) cage at R1C9 (step 8) = {269} (only remaining combination), locked for N3 and D/, clean-up: no 6 in R6C3
20b. Naked triple {178} in R7C3 + R8C2 + R9C1, locked for N7
20c. Naked pair {78} in R67C3, locked for C3

21. R7C489 (step 5) = {489/579} (cannot be {678} which clashes with R7C3), no 6
21a. 6 in R7 only in R7C12, locked for N7

22. 1 in N7 only in 17(4) cage at R8C1 = {1358/1457} (cannot be {1259/1349} because 2,3,4,5,9 only in R8C13), no 2,9

23. 9 in N7 only in R9C23, locked for R9 and 31(5) cage at R7C4, no 9 in R78C4
23a. R8C5 = 9 (hidden single in N8), R8C6 = 3, R2C56 = [31]
23b. 17(4) cage at R8C1 (step 22) = {1457} (only remaining combination), locked for N7, 4,5 also locked for R8 -> R67C3 = [78], clean-up: no 6 in R6C2, no 6,7 in R9C9
23c. Naked pair {26} in R7C12, locked for R7 and N7 -> R7C56 = [14], R6C5 = 6 (cage sum), R4C6 = 5, R5C5 = 4, placed for D\, R3C56 = [52], R9C9 = 5, R8C8 = 6, placed for D\, R8C9 = 2, clean-up: no 7 in R23C9, no 3 in R5C3 (step 12a)

24. Naked pair {48} in R23C9, locked for C9 and N3 -> R3C8 = 3, R4C8 = 8, R4C5 = 7, R5C6 = 8, R4C7 = 4 (hidden single in N6), R5C7 = 9 (cage sum)

25. R9C23 = {39} = 12 -> R789C4 = 19 = {568} (only remaining combination) = [586]

and the rest is naked singles, without using the diagonals.

Rating Comment:
I'll rate my walkthrough for A263 at Easy 1.5; my re-worked step 16 is equivalent to "clone" steps.
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Ed
 Post subject: Re: Assassin 263
PostPosted: Wed Jul 17, 2013 7:02 am 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
So, we all did the key eliminations for every part of this puzzle differently. This Assassin worked out really well. My "tricky step" from my intro to the puzzle was thinking of my step 4a. Then, my middle went in a completely different direction to both wellbeback and Andrew who both found shorter ways.

Assassin 263 Walkthrough
19 steps:
Preliminaries courtesy of SudokuSolver
Cage 4(2) n2 - cells ={13}
Cage 15(2) n47 - cells only uses 6789
Cage 7(2) n6 - cells do not use 789
Cage 12(2) n3 - cells do not use 126
Cage 12(2) n59 - cells do not use 126
Cage 12(2) n8 - cells do not use 126
Cage 10(2) n47 - cells do not use 5
Cage 10(2) n14 - cells do not use 5
Cage 11(2) n36 - cells do not use 1
Cage 11(2) n9 - cells do not use 1
Cage 9(3) n45 - cells do not use 789
Cage 21(3) n56 - cells do not use 123
Cage 11(3) n58 - cells do not use 9
Cage 26(4) n1 - cells do not use 1
Cage 15(5) n15 - cells ={12345}

1. 4(2)n2 = {13} only: both locked for r2 and n2
1a. no 9 in r3c9
1b. min. r3c56 = {24} = 6 -> max. r4c5 = 8 (no 9)

2. "45" on c1234: 2 outies r4c6+r5c5 = 9 = {45} only: both locked for n5, D/ and 15(5)r3c3 (no 4,5 in r3c3)
2a. r4c6+r5c5 = 9 -> rest of 15(5)r3c3 = 6 = {123} only
2b. no 7,8 in r7c7

3. "45" on n36: 3 outies r1c56 + r5c6 = 22
3a. -> min. r1c56 = 13 (no 2)

4. 2 in n2 only in c4 or r3, also 2 must be in h6(3)r3c3, r4c4, r4c6 ie, must be in c4 or r3
4a. both only have 2 in r3 or c4 -> 2 locked for c4 and r3 (Grouped X-wing or perhaps Turbot fish?) (no 2 in r3c1278, nor r789c4: this last should also have included r5c4 but I missed that one: Thanks Andrew!)
4b. no 8 in r4c2
4c. no 9 in r4c8

5. "45" on n6: 1 innie r4c8 = 1 outie r5c6 = (678) only (no 2,3,4,5,9)
5a. no 6,7,8,9 in r3c8

6. Hidden single 9 in n5 -> r6c6 = 9, Placed for D\, r7c7 = 3, Placed for D\
6a. no 1 in r7c2
6b. no 6 in r7c3
6c. no 7 in r6c2
6d. no 4 in r6c8
6e. no 2 nor 8 in 11(2)n9

Pretty routine from here, but takes quite a few steps to completely crack it.
7. Naked pair {12} in r3c3 + r4c4: locked for D\ and no 1,2 in r6c4 (same cage)
7a. r3c4+r4c3 see both of r3c3 and r4c4 -> no 1,2 in either r3c4 nor r4c3
7b. r6c4 = 3: placed for D/
7c. no 7 in r7c2
7d. min. r45c3 = [31] = 4 -> max. r5c4 = 5 (no 6)

8. Naked pair {12} in r45c4: locked for c4 and n5

9. 2 in n2 only in r3: 2 locked for r3
9a. 2 in n2 only in 14(3)r3c5 = {248/257}(no 6,9 )
9b. 7 or 8 must be in r4c5 -> no 7,8 in r3c56
9c. r3c3 = 1
9d. r45c4 = [21]
9e. no 9 in r4c2
9f. no 8 in r3c2
9g. r5c4 = 1 -> r45c3 = 8 = {35}[62](no 4, no 6 in r5c3)

10. 11(3)r6c5 must have 6/7/8 for r6c5 = {128/146}(no 5,7)
10a. cannot have both 6 & 8 -> no 6,8 in r7c56
10b. must have 1, 1 locked for r7 & n8

11. "45" on r89: 1 outie r7c4 - 3 = r8c9
11a. no 7,8,9 in r8c9
11b. no 6 in r7c4

12. 18(3)n9: {567/468/459} all blocked by 11(2)n9 = {47/56}
12a. 18(3) = {189/279}(no 4,5,6)
12b. must have 9, 9 locked for n9 & r7
12c. can't have both 1 & 2 -> no 2 in r7c89
12d. r8c9 = (12) -> r7c4 = (45)(IODr89 = +3)
12e. no 6 in r6c3
12f. no 1 in r6c2

13. 6 in r7 only in n7: 6 locked for n7

14. 6 in D/ only in n3: 6 locked for n3
14a. 6 must be in 17(3)n3 = {269} only: locked for n3 and D/
14b. no 3 in r3c9

15. Naked triple {178} in r7c3+r8c2+r9c1: locked for n7
15a. no 2 in r6c2

16. "45" on n9: 2 remaining outies r9c56 = 9
16a. but {45} blocked by r7c4
16b. h9(2) = {27/36}(no 4,5,8,9)

17. 31(5)r7c4: must have 4 or 5 for r7c4
17a. but {34789/45679} blocked by h9(2)r9c56 (step 16b)
17b. 31(5) = {25789/35689}(no 4)
17c. must have 8 which is only in r89c4: locked for c4 and n8
17d. r7c4 = 5
17e. r8c56 = [93](only permutation)
17f. h9(2)r9c56 = {27} only: locked for r9, n8 and 22(5)r8c7
17g. no 2,7 in r8c7

18. Naked pair {68} in r89c4: locked for c4
18a. Hidden pair 6,8 in n2 -> r1c56 = {68} only: locked for r1 and 27(5)r1c5 (no 8 in r2c7)

19. "45" on n36: 3 outies r1c56+r5c6 = 22. r1c56 = {68} = 14 -> r5c6 = 8

On from there.
Cheerio
Ed
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