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 Post subject: Assassin 420
PostPosted: Fri Jul 01, 2022 8:12 pm 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 947
Location: Sydney, Australia
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Assassin 420

Nice hard one at 1.90. Very routine start then took one tough step to unlock it. Resists to the end. JSudoku uses just two 'advanced' steps which gave me courage.
triple click code:
3x3::k:8448:8448:2817:2817:6146:6146:6146:3331:3331:8448:8448:8448:2052:2052:3077:6146:6146:1798:1799:8448:8448:5640:5640:3077:1801:1801:1798:1799:3082:3082:5640:7947:6156:6156:4877:4877:3086:2575:5392:5640:7947:6156:6156:5649:4877:3086:2575:5392:7947:4626:7947:7947:5649:4877:5392:5392:7443:5392:4626:5649:5649:5908:5649:2581:4886:7443:4626:7443:4626:5908:5908:2839:2581:4886:4886:7443:7443:5908:5908:2839:2839:
solution:
+-------+-------+-------+
| 6 2 8 | 3 1 5 | 7 4 9 |
| 9 7 1 | 2 6 4 | 3 8 5 |
| 4 5 3 | 7 9 8 | 6 1 2 |
+-------+-------+-------+
| 3 8 4 | 5 7 9 | 1 2 6 |
| 5 9 2 | 1 4 6 | 8 3 7 |
| 7 1 6 | 8 2 3 | 9 5 4 |
+-------+-------+-------+
| 1 3 7 | 9 5 2 | 4 6 8 |
| 8 6 5 | 4 3 7 | 2 9 1 |
| 2 4 9 | 6 8 1 | 5 7 3 |
+-------+-------+-------+
Cheers
Ed


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 Post subject: Re: Assassin 420
PostPosted: Sun Jul 03, 2022 5:40 pm 
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Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1820
Location: Lethbridge, Alberta, Canada
Thanks Ed for your latest Assassin. My solving path was longer than recent ones but my only forcing chain was a fairly short one.

Here's my walkthrough for Assassin 420:
Prelims

a) R1C34 = {29/38/47/56}, no 1
b) R1C89 = {49/58/67}, no 1,2,3
c) R2C45 = {17/26/35}, no 4,8,9
d) R23C6 = {39/48/57}, no 1,2,6
e) R23C9 = {16/25/34}, no 7,8,9
f) R34C1 = {16/25/34}, no 7,8,9
g) R3C78 = {16/25/34}, no 7,8,9
h) R4C23 = {39/48/57}, no 1,2,6
i) R56C1 = {39/48/57}, no 1,2,6
j) R56C2 = {19/28/37/46}, no 5
k) R89C1 = {19/28/37/46}, no 5
l) 19(3) cage at R8C2 = {289/379/469/478/568}, no 1
m) 11(3) cage at R8C9 = {128/137/146/236/245}, no 9

1a. 45 rule on N1 2 innies R1C3 + R3C1 = 12 = [75/84/93] -> R1C4 = {234}, R4C1 = {234}
1b. Hidden killer quad 6,7,8,9 in R4C23, R56C1, R56C2 and R56C3 for N4, R4C23, R56C1 and R56C2 must each contain one of 6,7,8,9 -> R56C3 must contain at least one of 6,7,8,9
1c. 45 rule on N14 3 innies R1C3 + R56C3 = 16 = {169/178/268/367} (cannot be {259/349/358/347} because R1C3 = {789} and R56C3 must contain one of 6,7,8,9), no 4,5 in R56C3
1d. 5 in N4 only in R4C23 = {57} or R56C1 = {57} (locking cages), 7 locked for N4, clean-up: no 3 in R56C2

2a. 45 rule on N3 2 outies R1C56 = 6 = {15/24}
2b. Killer triple 4,5,6 in R1C89, R23C9 and R3C78, locked for N3
2c. R2C45 = {17/26} (cannot be {35} which clashes with R1C56 + R23C6), no 3,5
2d. Killer pair 1,2 in R1C56 and R2C45, locked for N2, clean-up: no 9 in R1C3, no 3 in R3C1 (step 1a), no 4 in R4C1
2e. R1C3 + R56C3 (step 1c) = {178/268/367} (cannot be {169} because R1C3 only contains 7,8), no 9
2f. Killer triple 3,4,5 in R1C4, R1C56 and R23C6, locked for N2

3a. R1C34 = [74/83], R1C89 = {49/58/67} -> combined cage R1C34 + R1C89 = [83]{49}/[83]{67} (cannot be [74]{58} which clashes with R1C56) -> R1C34 = [83], R3C1 = 4 (step 1a), R4C1 = 3, clean-up: no 5 in R1C89, no 8,9 in R2C6, no 3 in R2C9, no 9 in R3C6, no 3 in R3C78, no 4,9 in R4C2, no 9 in R4C3, no 8,9 in R56C1, no 6,7 in R89C1
3b. Naked pair {57} in R56C1, locked for C1 and N4 -> R4C23 = [84], clean-up: no 2,6 in R56C2
3c. Naked pair {19} in R56C2, locked for C2, 1 locked for N4
3d. Naked pair {26} in R56C3, locked for C3 and 21(5) cage at R5C3
3e. 6 in N7 only in 19(3) cage at R8C2 = {469} -> R9C3 = 9, R89C2 = {46}, locked for C2, clean-up: no 1 in R89C1
3f. Naked pair {28} in R89C1, locked for C1 -> R7C1 = 1
3g. R56C3 = {26}, R7C1 = 1 -> R7C24 = 12 = [39/57/75], no 4,8
3h. Combined half cage R7C234 = [359/379/537/735], 3 locked for R7 and N7
3i. 29(5) cage at R7C3 = {23789/25679/34589/34679/35678} (cannot be {14789/15689/24689} because R78C3 must contain two of 3,5,7), no 1
3j. 29(5) cage = {23789/34589/35678} (cannot be {25679} because R78C3 = {57} so R8C5 + R9C45 = {269} clashes with R7C234 = [359/379], cannot be {34679} which clashes with R9C2), 8 locked for N8
3k. 9 of {23789/34589} must be in R8C5 -> no 2,4 in R8C5

4a. 9 in N2 only in R3C45, min R3C45 = {69} = 15 -> max R45C4 = 7, no 7,8,9 in R45C4
4b. Killer pair 6,9 in R1C1 and R1C89, locked for R1
4c. 45 rule on N3 3 innies R1C7 + R7C78 = 18 = {189/378} (cannot be {279} which clashes with R1C89), no 2
4d. R1C7 = {17} -> no 1,7 in R2C78

5a. 45 rule on N9 4(2+2) outies R56C8 + R79C6 = 11
5b. Min R56C8 = 3 -> max R79C6 = 8, no 9 in R7C6, no 7 in R9C6
5c. Min R79C6 = 3 -> max R56C8 = 8, no 8,9 in R56C8
5d. 45 rule on N9 2 innies R7C79 = 1 outie R9C6 + 11
5e. R7C234 (step 3h) = [359/379/537/735]
5e. Min R56C8 + R7C6 = 6 -> max R7C79 = 15 (cannot be {79} which clashes with R7C234) -> max R9C6 = 4
5f. Min R7C79 = 12, no 2 in R7C79
5g. 2 in R7 only in R7C568, CPE no 2 in R9C6

6a. R1C56 (step 2a) = {15/24}, R23C6 = [48/57/75]
6b. R2C45 = {26} (cannot be {17} which clashes with R1C56 + R23C6), locked for R2 and N2 -> R12C1 = [69], clean-up: no 4 in R1C56, no 7 in R1C89, no 1,5 in R3C9
6c. R2C6 = 4 (hidden single in N2) -> R3C6 = 8, clean-up: no 3 in R3C9
6d. Naked pair {15} in R1C56, locked for R1 -> R1C27 = [27]
6e. Naked pair {38} in R2C78, 3 locked for R2
6f. Naked pair {79} in R3C45, 7 locked for R3
6g. R3C45 = {79} = 16 -> R45C4 = 6 = [15/24/51]

7a. R7C234 (step 3h) = [359/379/537/735]
7b. R9C6 = {13} -> R7C79 (step 5d) = 12,14 = {48/68} (cannot by {57/59} which clash with R7C234), no 5,7,9, 8 locked for N9
7c. 9 in N9 only in 23(5) cage at R7C8 = {12569/23459} (cannot be {12479} which clashes with R7C79 + R9C6 = {48}1, cannot be {13469} which clashes with R7C79), no 7
7d. 7 in N9 only in 11(3) cage at R8C9 = {137}, 1,3 locked for N9
7e. Naked pair {137} in R9C689, 3,7 locked for R9, 7 locked for N9
7f. 22(5) cage at R5C8 = {12478/12568/13468/23458}
7g. 4 of {12478/23458} must be in R7C79, 1,3 of {13468} must be in R56C8 -> no 4,6 in R56C8

8a. 8 in N8 only in R8C5 + R9C45
8b. 45 rule on N5689, R45C4 = 6 (step 6g) -> 4 remaining innies R7C4 + R8C5 + R9C45 = 26 = {3689/4589/5678} (cannot be {2789} because R9C45 = {28} clashes with R9C1), no 2

9a. R7C79 = R9C6 + 11 (step 5d)
9b. Consider combinations for 22(5) cage at R5C8 (step 7f) = {12478/12568/13468/23458}
22(5) cage = {12478/12568/13468}, 1 locked for C8 => 1 in N9 only in R89C9
or 22(5) cage = {23458} => R7C79 = {48} => R9C6 = 1 => R8C9 = 1 (hidden single in N9)
-> 1 in R89C9, locked for C9 and N9 -> R2C9 = 5, R3C9 = 2, R2C23 = [71], clean-up: no 5 in R7C4 (step 3g)
9c. Naked pair {79} in R37C4, locked for C4
9d. 7 in C3 only in R78C3, locked for 29(5) cage at R7C3
9e. 29(5) cage at R7C3 (step 3j) = {35678}, no 4,9, 6 locked for N8
9f. 6 in R7 only in R7C789, locked for N9

10a. 19(4) cage at R4C8 = {1369/2368/2467} (cannot be {1279/1459/1567/2359/2458} because 1,2,5 only in R4C8, cannot be {1378/3457} which clashes with R89C9, ALS block, cannot be {1468} which clashes with R7C9)
10b. 1,2 only in R4C8 -> R4C8 = {12}
10c. 19(4) cage = {1369/2368/2467}, 6 locked for C9 and N6

11a. 45 rule on N78 using R7C124 = 13 (step 3g), 2 remaining innies R79C6 = 1 outie R6C5 + 1
11b. R79C6 cannot total 2,4,7,9 -> no 1,3,6,8 in R6C5
11c. 18(4) cage at R6C5 = {2349/2457} (cannot be {1359} which clashes with R9C6), no 1
11d. R9C6 = 1 (hidden single in N8) -> R1C56 = [15], R7C79 (step 5d) = 12 = {48}, 4 locked for R7 and N9
11e. R9C6 = 1 -> R6C5 = R7C9 = {27}
11f. R9C2 = 4 (hidden single in R9) -> R8C2 = 6
11g. R8C4 = 4 (hidden single in R8) -> R45C4 (step 6g) = {15}, locked for N5
11h. R8C4 = 4 -> 18(4) cage = {2457} -> R7C5 = 5, R8C6 = {27}
11i. Naked pair {27} in R78C6, locked for C6, 7 locked for N8 -> R7C4 = 9, R7C2 = 3, R78C3 = [75], R7C6 = 2, R8C6 = 7 -> R6C5 = 2, R2C45 = [26], R9C45 = [68], R8C5 = 3, R3C45 = [79]
11j. R45C5 = [74], R6C4 = 8 -> R6C67 = 12 = {39}, locked for R6
11k. R6C9 = 4 (hidden single in R6), R17C9 = [98], R4C9 = 6 -> R4C8 + R5C9 = 9 = [27]
11l. R7C679 = [248] -> R56C8 = 8 = [35]

and the rest is naked singles.


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