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 Post subject: Assassin 385
PostPosted: Tue Oct 01, 2019 7:59 am 
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Posts: 1040
Location: Sydney, Australia
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x-puzzle. 1 to 9 cannot repeat on either diagonal

Assassin 385
SudokuSolver and JSudoku both make a hash of this puzzle. Hope I haven't! I used two advanced steps - one I really like and is very powerful. Unfortunately, they are both available quite early in an optimised WT and so the ending feels a big dragged out. Sorry about that.
triple-click code:
3x3:d:k:3328:1537:0000:0000:0000:6403:6403:6403:5892:3328:1537:4101:4101:0000:0000:7431:6403:5892:3848:3848:4101:4101:0000:7431:7431:7431:5892:4617:4617:7434:7434:7434:7431:7431:5892:5892:4617:4363:7434:7434:10508:10508:10508:10508:10508:4617:4363:4363:2573:2573:10508:10508:10508:3086:4879:4879:3088:3088:2573:4369:8722:8722:3086:4879:2835:2835:3092:4369:1542:1542:8722:3086:4879:2562:2562:3092:4369:8722:8722:8722:8722:
solution:
Code:
+-------+-------+-------+
| 4 5 2 | 6 1 7 | 9 3 8 |
| 9 1 3 | 5 8 4 | 2 6 7 |
| 8 7 6 | 2 9 3 | 4 5 1 |
+-------+-------+-------+
| 3 4 1 | 8 7 9 | 6 2 5 |
| 5 8 9 | 4 2 6 | 7 1 3 |
| 6 2 7 | 1 3 5 | 8 9 4 |
+-------+-------+-------+
| 1 9 5 | 7 6 8 | 3 4 2 |
| 2 3 8 | 9 4 1 | 5 7 6 |
| 7 6 4 | 3 5 2 | 1 8 9 |
+-------+-------+-------+
Cheers
Ed


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 Post subject: Re: Assassin 385
PostPosted: Thu Oct 10, 2019 6:40 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
Don't get to post the first WT often! Steps 6 & 10 are my keys.
WT for a385:
Preliminaries courtesy of SudokuSolver
Cage 6(2) n1 - cells only uses 1245
Cage 6(2) n89 - cells only uses 1245
Cage 15(2) n1 - cells only uses 6789
Cage 12(2) n8 - cells do not use 126
Cage 12(2) n78 - cells do not use 126
Cage 13(2) n1 - cells do not use 123
Cage 10(2) n7 - cells do not use 5
Cage 11(2) n7 - cells do not use 1
Cage 10(3) n58 - cells do not use 89
Cage 41(8) n56 - cells ={12356789}

1. "45" on n7: 1 innie r7c3 = 5, placed for D/, r7c4 = 7

2. 12(2)n8 = {39/48}(no 5) = 3 or 4

3. "45" on n78: 3 innies r7c5 + r89c6 = 9
3a. but {234} blocked by 12(2)n8
3b. = {126/135}(no 4,8,9)

4. "45" on r789: 1 outie r6c9 + 2 = 1 innie r7c5 = [13/46]

5. 10(3)r6c4 must have 3 or 6 for r7c5 = {136/235}(no 4,7)

A straight forward forcing chain but took me a long time to find.
6. {48} in 12(2)n8 -> 4 in r5 is only in n4, locked for n4 -> 4 in r6 in r6c9 -> 6 in r7c5 (step 4)
or {39} in 12(2)n8 -> 6 in r7c5
6a. -> r7c5 = 6 -> r6c9 = 4 and r89c6 = {12} only (step 3b), both locked for n8 and c6 and no 1,2 in r8c8 (Common Peer Elimination CPE)
6b. r6c45 = 4 = {13} only: both locked for r6 and n5
6c. r78c9 = 8 = [17/26/35]
6d. r8c7 = (45)

7. 41(8)r5c5 must have 1 & 3 which are only in r5c789: both locked for n6 and r5

8. 3 in n1 only in c3: locked for c3

9. "45" on n4: 2 innies r45c3 = 10 (no 7)

Final key step
10. "45" on r56789 including the h10(2)r45c3 -> 3 outies r4c123 - 4 = 1 innie r5c4
10a. 3 outies must have 1 & 3 for r4 = 4 -> 1 remaining outie = r5c4
10b. since r4c3 and r5c4 are in the same cage they cannot be the two equal cells -> r4c3 must have the 1 or 3
10c. -> r4c3 = 1, r5c3 = 9 (h10(2))

11. r45c3 = 10 -> r4c45 + r5c4 = 19 = {478/568}(no 2)
11a. must have 8, locked for n5

12. r5c5 = 2 (hsingle n5), Placed for both diagonals

13. "45" on n1: 3 innies r123c3 = 11 and must have 3 for n1 = {236} only: 2 & 6 locked for n1 and c3

14. 6(2)n1 = {15} only: both locked for c2 and 5 for n1

15. 15(2)n1 = {78}: both locked for r3 and n1
15a. 13(2)n1 = {49} both locked for c1

16. hidden pair 1,2 in r8 -> r8c1 = (12)

17. 4 in c3 only in n7: locked for n7
17a. 11(2)n7 = [38/74]

18. 10(2)n7: [37] blocked by r8c2 = (37)
18a. = [28/64]

19. naked pair {48} in r89c3: 8 locked for n7 and c3
19a. r6c3 = 7
19b. -> r56c2 = 10 = [46/82]

20. naked pair {26} in r69c2: both locked for c2

21. hsingle 9 in r7c2

22. 7 in n7 only on d/: locked for d/

23. 9 in n5 only in c6: locked for c6

24. "45" on c6789: 2 innies r27c6 = 12 = {48} only: both locked for c6

25. 17(3)n8 must have 4 or 8 for r7c6 = {458} only: 4 & 8 locked for n8
25a. 12(2)n8 = {39}: both locked for c4
25b. r6c45 = [13]: 1 placed for d/

26. 4 in n5 only in h19(3) = {478} only -> r4c5 = 7
26a. 4 locked for c4

27. naked triple {569} in r456c6: 5 & 6 locked for c6, 5 locked for 41(8)
27a. r3c6 = 3, r3c3 = 6 (placed for d\)

28. hsingle 6 in r8 -> r8c9 = 6, r7c9 = 2 (cage sum)

29. 4 on d/ only in n3: 4 locked for n3

30. 34(7)r7c7 = {1234789} (no 5)
30a. r8c7 = 5 (hsingle n9), r8c6 = 1

31. 8 on d/ only in n3: locked for n3

32. 25(4)r1c6: [7]{459} blocked by r3c7 = (49)
32a. [7]{468} blocked by 4 & 8 only in r2c8
32b. = [7]{19}[8]/[7]{369}(no 2,4,5)

33. r3c7 = 4 (hsingle n3)

34. 5 in n6 only in r4c89: locked for r4 and 23(5)
34a. r3c8 = 5 (hsingle n3), r4c9 = 5 (hsingle n6)

etc, lots of naked stuff from here. Thanks to Andrew's suggestion to get step 34 added to make the final bit simpler.
Cheers
Ed


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 Post subject: Re: Assassin 385
PostPosted: Sun Oct 13, 2019 8:41 pm 
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Joined: Tue Jun 16, 2009 9:31 pm
Posts: 280
Location: California, out of London
Thanks Ed. No apologies necessary! Our solution paths are almost identical (for the important first half at least) except we resolved the two key steps slightly differently.
Don't know why the programs had so much trouble.
Here's how I saw it...
Assassin 385 WT:
1. Innies n7 -> 12(2)r7c3 = [57]

2. Remaining Innies n8 = r7c5,r89c6 = +9(3)
Since 1 in n8 not in 17(3) or 12(2) -> H9(3)n8 = {126} or {135}

3. Outies r789 = r6c459 = +8(3)
Outies n9 = r6c9 + r89c6 = +7(3)
-> Only possibilities are:
10(3)r6c4 = [{13}6] and outies n9 = [4{12}]
10(3)r6c4 = [{25}3] and outies n9 = [1{15}]

But since 41(8) has no 4 ...
-> the latter possibility would put 4 in r4c789 and 12(2)n8 = {48} which leaves no place for 4 in n5
-> 10(3)r6c4 = [{13}6] and outies n9 = [4{12}]
-> 5 in r89c5

4. Innies n1 = r123c3 = +11(3)
3 in n1 not in 13(2) or 15(2) or 6(2) -> 3 in n1 in r123c3
(13) in 41(8) in r5c789
-> 3 in n4 in r4c12 and 1 in n4 in r4c123

5! Innies n4 = r45c3 = +10(2)
Innies r56789 = r56c1 + r5c34 = +24(4)
Since r5c34 cannot be +10(2) -> r56c1 cannot be 14(2) -> r4c12 cannot be +4(2)
-> Since 3 already in r4c12 -> 1 not in r4c12
-> r4c3 = 1

6. -> r5c3 = 9
Also HS 1 in n1 -> 6(2)n1 = {15}
-> H11(3)n1 = r123c3 = {236}
-> 15(2)n1 = {78}
-> 13(2)n1 = {49}
-> 4 in c3 only in r89c3
-> 11(2)n7 -> r89c3 cannot be {47} -> HS 7 in c3 -> r6c3 = 7
-> NP r89c3 = {48}

7. Cells of 29(5) in n5 can only be {478} or {568}
-> HS 2 in n5 -> r5c5 = 2

8. 11(2)n7 and 10(2)n7 from [74][28] or [38][64]
But the former leaves no place for 2 in n8
-> 11(2)n7 = [38]
-> 10(2)n7 = [64]
-> 17(3)n4 can only be [827]
-> 18(4)n4 = [34{56}]
Also r7c2 = 9 and r789c1 = {127}
Also 15(2)n1 = [87]

9. r23c3 = two of (236)
Since 7 already in c4 -> Only possible solution for 16(4)r2c3 is {2356} with 5 in r23c4
-> Since 5 in n8 in r89c5 -> 5 in n5 in r456c6
-> 29(5)r4c3 can only be [18794]
-> 12(2)n8 = [93]
-> r6c45 = [13]
-> r123c4 = {256} with 5 in r23c4
-> 3 in r23c3
-> r1c34 = {26}

10. Whichever of (12) is in r9c6 goes in n9 in r78c9
-> r78c9 = [17] or [26]
But 7 in D\ only in r8c8 or r9c9
-> r78c9 = [26]
-> r9c6 = 2
-> r789c1 can only be [127]
Also 6(2)r8c6 = [15]
-> r8c8 = 7
Also r9c5 = 5
-> 17(3)n8 = [845]
-> r7c78 = {34}
-> r9c789 = {189}

11. 2 in n3 only in r2c7 or r3c8
-> HS 2 in r4 -> r4c8 = 2
-> r2c7 = 2
-> IOD c9 -> r59c9 = +12(2) can only be [39]
-> NS r4c9 = 5
-> r123c9 = {178}
-> HS 8 in D/ -> r1c9 = 8
-> r23c9 = [71]

12. 9 in r9c9 -> 13(2)n1 = [49]
-> r7c78 = [34]
-> NS r3c3 = 6
-> r12c3 = [23]
-> r123c4 = [652] (Thanks Ed)
-> 6(2)n1 = [51]
-> NS D\ -> r6c6 = 5
-> r56c1 = [56]
-> r45c6 = [96]
-> r4c7 = 6
etc.


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 Post subject: Re: Assassin 385
PostPosted: Sat Nov 02, 2019 4:32 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
I'm getting a bit behind with Assassins and, it would appear, out of practice as I missed Ed's step 6, wellbeback's step 3; I'd looked at the various parts of the latter but had failed to follow them through as in the final part of that step. Therefore my solving path was very different.

Loved Ed's final key step, particularly step 10b, and wellbeback's step 5! Each of those depended on that earlier step which I'd missed.

Here is my walkthrough for Assassin 385:
This is a Killer-X.

Prelims

a) R12C1 = {49/58/67}, no 1,2,3
b) R12C2 = {15/24}
c) R3C12 = {69/78}
d) R7C34 = {39/48/57}, no 1,2,6
e) R8C23 = {29/38/47/56}, no 1
f) R89C4 = {39/48/57}, no 1,2,6
g) R8C67 = {15/24}
h) R9C23 = {19/28/37/46}, no 5
i) 10(3) cage at R6C4 = {127/136/145/235}, no 8,9
j) 41(8) cage at R5C5 = {12356789}, no 4

1a. 45 rule on N7 1 innie R7C3 = 5 -> R7C4 = 7, 5 placed for D/, clean-up: no 6 in R8C23, no 5 in R89C4
1b. 45 rule on N89 1 remaining innie R7C5 = 1 outie R6C9 + 2 -> R6C9 = {124}, R7C5 = {346}
1c. 45 rule on N8 3 remaining innies R7C5 + R89C6 = 9 = {126/135} (cannot be {234} which clashes with R89C4), no 4,8,9, 1 locked for C6 and N8, clean-up: no 2 in R6C9, no 2 in R8C7
1d. R7C5 = {36} -> no 3,6 in R9C6
1e. 45 rule on N89 3 outies R6C459 = 8 = {125/134}, no 6,7, 1 locked for R6
1f. 5 of {125} must be in R6C5 -> no 2 in R6C5
1g. 10(3) cage at R6C4 = {136/235} (cannot be {145} because R7C5 only contains 3,6), no 4
1h. 10(3) cage = {136/235}, CPE no 3 in R45C5
1i. 41(8) cage at R5C5 = {12356789}, 1 locked for R5
1j. 1 in N4 only in R4C123, locked for R4

2a. R12C1 = {49/58} (cannot be {67} which clashes R3C12), no 6,7
2b. Killer pair 4,5 in R12C1 and R12C2, 4 locked for N1
2c. Killer pair 8,9 in R12C1 and R3C12, locked for N1
2d. 45 rule on N1 3 innies R123C3 = 11 = {137/236}, 3 locked for C3, clean-up: no 8 in R8C2, no 7 in R9C2

3a. 45 rule on N4 2 innies R45C3 = 10 = [19]/{28/46}, no 7, no 9 in R4C3
3b. 45 rule on N4 3 outies R4C45 + R5C4 = 19 = {289/379/469/478/568}
3c. 2 of {289} must be in R45C4 (R45C4 cannot be {89} which clash with R89C4), no 2 in R4C5
3d. 29(5) cage must contain 9 in R4C45 + R5C34, CPE no 9 in R5C56
[Note. 29(5) contains 9 because R4C45 + R5C4 = {478/568} clash with R45C3 = {28/46}]

4. 45 rule on N3456789 2 outies R13C6 = 10 = {28/37/46}, no 5,9

5. 45 rule on C1 3 outies R347C2 = 20 = {389/479/569/578}, no 1,2
5a. 5 of {569} must be in R4C2 -> no 6 in R4C2
5b. 1 in C2 only in R12C2 = {15}
or R9C23 = [19]
-> R347C2 = {569} must be [956], no 6 in R3C2, clean-up: no 9 in R3C1

6. 45 rule on C12 3 outies R689C3 = 19 = {289/469/478}, no 1, clean-up: no 9 in R9C2

7. 45 rule on C9 2 innies R59C9 = 1 innie R4C8 + 10
7a. Min R4C8 = 2 -> min R59C9 = 12, no 1,2 in R59C9
7b. Max R59C9 = 17 -> max R4C8 = 7

8. R347C2 (step 5) = {389/479/569/578}, R12C1 (step 2a) = {49/58}, R12C2 = {15/24}, R3C12 = [69]/{78}
8a. Consider combinations for R12C1 = {49/58}
R12C1 = {49} => R12C2 = {15}, 5 locked for C2 => R347C2 = {389/479}
or R12C1 = {58} => R3C12 = [69] => R347C2 = {389/479/569}
-> R347C2 = {389/479/569}, 9 locked for C2, clean-up: no 2 in R8C3
8b. 17(3) cage at R5C2 = {278/359/368/458/467} (cannot be {269} which clashes with R45C3)
8c. 17(3) cage = {278/368/458/467} (cannot be {359} = {35}9 which clashes with R12C2 + R347C2), no 9
8d. 18(4) cage at R4C1 = {1278/1359/1467/2358/2367/2457/3456} (cannot be {1269/1368/1458/2349} which clash with R45C3)
8e. Hidden killer pair 1,9 in 18(4) cage and R45C3 for N4, 1,9 must both be in 18(4) cage or both in R45C3 = [19] -> 18(4) cage = {1359/2358/2367/2457/3456} (cannot be {1278/1467} which only contain 1 but not 9)
8f. 1 of {1359} must be in R4C1 -> no 9 in R4C1

9. R12C2 = {15/24}, R123C3 (step 2d) = {137/236}, R45C3 (step 3a) = [19]/{28/46}
9a. Consider placement for 1 in C3
R123C3 = {137}, 1 locked for N1 => R12C2 = {24}, 2 locked for C2
or R45C3 = [19]
-> R8C23 = [38]/{47}, no 2,9
9b. R9C23 = [19]/{28/46} (cannot be [37] which clashes with R8C23)
9c. R689C3 (step 6) = {289/469/478}
9d. 9 of {289/469} must be in R9C3 -> no 2,6 in R9C3, clean-up: no 4,8 in R9C2
9e. Consider combinations for 17(3) cage at R5C2 (step 8c) = {278/368/458/467}
17(3) cage = {278/458} and {467} with 6 in R56C2 => no 6 in R6C3 => R689C3 = {289/478}
or 17(3) cage = {368}, locked for N4 => R45C3 = [19] => R689C3 = {478}
or 17(3) cage = {47}6, 4,7 locked for C2 => R8C23 = [38] => R689C3 = {289/478}
-> R689C3 = {289/478}, no 6, 8 locked for C3
9f. R45C3 = [19]/{46}, no 2

10. 18(4) cage at R4C1 (step 8e) = {1359/2358/2367/2457/3456}}, R45C3 (step 9f) = [19]/{46}, R689C3 (step 9e) = {289/478}
10a. Consider combinations for R6C459 (step 1e) = {125/134}
R6C459 = {125}, 2 locked for R6 => R689C3 = {478}, 4 locked for C3 => R45C3 = [19]
or R6C459 = {134}, 3 locked for R6 => 41(8) cage at R5C5 = {12356789}, 3 locked for R5 => 3 in R4 only in 18(4) cage = {2358/2367/3456} (cannot be {1359} = [13]{59} which clashes with R12C1), no 1
-> no 1 in R4C1
[Almost cracked.]
10b. R4C3 = 1 (hidden single in N4), R5C3 = 9 => R4C45 + R5C4 (step 3b) = {478/568}, no 2,3, 8 locked for N5, R689C3 = {478}, no 2, 7 locked for C3
10c. 1 in N1 only in R12C2 = {15}, locked for C2, 5 locked for N1
10d. R12C1 = {49}, locked for C1, 9 locked for N1
10e. R3C12 = {78}, locked for R3, clean-up: no 2,3 in R1C6 (step 4)
10f. Killer pair 4,8 in R8C23 and R9C3, locked for N7
10g. R7C2 = 9 (hidden single in N7)
10h. R347C2 (step 5) = 20, R7C2 = 9 -> R34C2 = 11 = [74/83]
10i. Combined half-cage R34C2 + R8C2 = [743/834/837], 3 locked for C2
10j. 17(3) cage at R5C2 (step 8c) = {278/467}, 7 locked for N4

11. 16(4) cage at R2C3 = {2356} (only possible combination, cannot be {1249/1258/1348/1456} because R23C3 only contain 2,3,6), 5 locked for C4 and N2
11a. R4C45 + R5C4 (step 10b) = {478/568}
11b. 5,7 only in R4C5 -> R4C5 = {57}, R45C4 = {48/68}, 8 locked for C4
11c. R89C4 = {39}, locked for C4 and N8
11d. R7C5 = 6 -> R6C45 = 4 = [13], R6C9 = 4, 1 placed for D/
11e. 17(3) cage at R7C6 = {458} (only remaining combination), 5 locked for C5 and N8, clean-up: no 1 in R8C7
11f. R4C5 = 7 -> R45C4 = {48}, 4 locked for C4 and N5
11g. R5C5 = 2, placed for both diagonals
11h. Naked pair {12} in R89C6, 2 locked for C6, clean-up: no 8 in R1C6 (step 4)
11i. 5 in C6 only in R56C6, locked for 41(8) cage at R5C5
11j. 5 in N6 only in R4C789, locked for R4
11k. 4 in C3 only in R89C3, locked for N7, clean-up: no 7 in R8C3
11l. R6C3 = 7 (hidden single in C3) -> R56C2 = 10 = [46/82]
11m. Naked pair {48} in R5C24, 8 locked for R5
11n. R5C789 = {137} hidden triple in 41(8) cage, 3 locked for R5 and N6

12. 45 rule on R56789 3 remaining outies R4C124 = 15 = {348} (only remaining combination), no 2,6, 8 locked for R4

13. Naked triple {569} in R456C6, 6,9 locked for C6 -> R13C6 (step 4) = 10 = [73], R3C3 = 6, placed for D\
13a. 16(4) cage at R2C3 = {2356} -> R2C3 = 3, R1C34 = [26]

14. Consider position of 2 in C6
R8C6 = 2 => R8C7 = 4 => R8C23 = [38]
or R9C6 = 2 => R9C23 = [64] => R8C23 = [38]
-> R8C23 = [38], 3 placed for D/, R9C23 [64]
14a. R1C6 = 7, 3 in R1 only in R1C78 -> 25(4) cage at R1C6 = {3679} -> R2C8 = 6, placed for D/, R1C78 = {39}, 9 locked for R1 and N3
14b. R1C1 = 4, placed for D\, R1C2 = 5 (hidden single in R1) -> R2C2 = 1, placed for D\
14c. R3C7 = 4, R8C7 = 5 -> R8C6 = 1

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

Rating Comment:
I'll rate my WT for A385 at 1.5. I used several forcing chains.

Don't know why the programs had so much trouble:
The SS score, not posted by Ed, is 2.10. One reason SS has trouble is that it isn't programmed to apply 45 rule to N3456789, which I found useful in the later stages of my solving path. I don't know JSudoku but assume the same reason applies for it.
I doubt that either solver is programmed so that it's capable of finding Ed's step 10 or wellbeback's step 5; SS will be able to find the component parts of the latter but may not be able to chain them together.


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