SudokuSolver Forum

A forum for Sudoku enthusiasts to share puzzles, techniques and software
It is currently Thu Mar 28, 2024 12:40 pm

All times are UTC




Post new topic Reply to topic  [ 4 posts ] 
Author Message
 Post subject: Assassin 387
PostPosted: Fri Nov 01, 2019 7:58 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
Attachment:
a387.JPG
a387.JPG [ 67.39 KiB | Viewed 6602 times ]
x-puzzle: 1 to 9 cannot repeat on each diagonal

Assassin 387
I had to pick away at this puzzle but in the end, found a decent way through. Not my favourite type but interesting in its own way. JSudoku can't solve it without a 'recursive' step and uses 20 chains!! but SS gives it 1.55.
triple click code:
3x3:d:k:9216:3073:3330:3330:3330:6915:4868:4868:4868:9216:3073:3073:6915:6915:6915:3333:3333:4868:9216:9216:9216:9216:6915:6406:6406:6406:4868:4871:7944:7944:3337:3337:3337:6406:4627:4627:4871:4871:7944:7944:2572:2572:6406:4627:4627:5133:3086:7944:7944:2572:3855:3855:8976:8976:5133:3086:2833:2833:8210:3855:8976:8976:8976:5133:3086:7691:7691:8210:8210:8210:8210:8976:5133:5133:7691:7691:8210:3594:3594:3594:3594:
solution:
Code:
+-------+-------+-------+
| 6 5 2 | 4 7 8 | 3 1 9 |
| 7 3 4 | 1 9 6 | 8 5 2 |
| 9 8 1 | 5 3 2 | 6 7 4 |
+-------+-------+-------+
| 4 1 5 | 2 8 3 | 9 6 7 |
| 8 7 9 | 6 4 5 | 1 2 3 |
| 2 6 3 | 7 1 9 | 5 4 8 |
+-------+-------+-------+
| 5 4 8 | 3 2 1 | 7 9 6 |
| 3 2 6 | 9 5 7 | 4 8 1 |
| 1 9 7 | 8 6 4 | 2 3 5 |
+-------+-------+-------+
Cheers
Ed


Top
 Profile  
Reply with quote  
 Post subject: Re: Assassin 387
PostPosted: Sun Nov 10, 2019 8:16 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
Steps 4 & 9 are the key ones. There will surely be alternatives to 9. Thanks to Andrew for checking my WT and for some corrections.
A387 WT:
Preliminaries
Cage 13(2) n3 - cells do not use 123
Cage 11(2) n78 - cells do not use 1
Cage 10(3) n5 - cells do not use 89
Cage 19(3) n4 - cells do not use 1
Cage 30(4) n78 - cells ={6789}
Cage 14(4) n89 - cells do not use 9

1. "45" on n12: 1 innie r3c6 = 2
1a. "45" on n3: 2 outies r45c7 = 10 = {19/37/46}(no 5,8)

2. "45" on c1234: 4 innies r1c3 + r124c4 = 9
2a. min. r124c4 = 6 -> max r1c3 = 3
2b. max. r124c4 = 8 -> no 6,7,8,9, no 5 in r4c4

3. "45" on n1: 1 innie r1c3 + 3 = 1 outie r3c4 = [14/25/36]

First hard step
4. from step 2, r1c3 + r134c4 = 9 and from step 3, r1c3 + r3c4 = [14/25/36]
4a. -> r1c3 + r1234c4: [2]+[1..] blocked by can't reach 13(3)r1c345
4b. = [1][5142]/[2][4152]/[3][1362]
4c. r1c4 = (145), r2c4 = (13)
4d. r4c4 = 2, placed for d\
4e. -> r4c56 = 11 = {38/47/56}(no 1,9)
4f. and r1c345 = [157/247/319]
4g. -> r1c5 = (79)
4h. 1 must be in r12c4: locked for c4 and n2

5. "45" on r6789: 3 innies r6c345 = 11 (no 9)

6. "45" on n5: 3 innies r56c4 + r6c6 = 22 = {589/679}(no 1,3,4)

7. 10(3)n5 = {136/145}(no 7): if it has 4, also has 5
7a. r6c345 = 11 (step 5): but {245} as [254] only, blocked by 5 in 10(3) cage
7b. h11(3) = {128/137/146/236}(no 5)
7c. h22(3)n5 = {589/679} -> 8 in {589} must be in r6c4 -> no 8 in r5c4 nor r6c6

8. 10(3)n5 = {136/145}: if it has 3, also has 6
8a. h11(3)r6c345: but {236} as [263] only, blocked by 6 in 10(3)
8b. h11(3) = {128/137/146}
8c. must have 1: locked for r6
8d. can only have one of 6,7,8 -> no 6,7,8 in r6c35

This step was originally much more complicated but now manageable I hope.
9. "45" on n36: 3 innies r6c789 = 17: but {368} blocked by h11(3)r6 needing one of those (step 8b)
9a. = {269/278/359/458/467}(no eliminations yet)
9b. if 9 in r6c6 -> 15(3)r6c6 = [951/924] -> combined with h17(3)r6c789 -> r6c6789 = [95]{48}/[92]{78}
9c. ie, 9 in r6c6 must have 8 in r6c89
9d. h22(3)n5 = {589/679}: but [589] blocked by 8 in r6c89
9e. -> no 5 in r5c4

10. naked quad 6789 in r5689c4: all locked for c4
10a. no 3 in r1c3 (iodn1=-3)

11. 13(3)r1c3 = [157/247]
11a. r1c5 = 7, r1c4 = (45)

12. naked pair {45} in r13c4: both locked for n2 and c4
12a. r7c34 = [83], 8 placed for d/, r2c4 = 1

13. h22(3)n5 = {679} only: 6 & 7 both locked for n5

14. r4c56 = 11 = [83] only permutation, 3 placed for d/

15. h11(3)r6c345 = {137/146}(no 2)

16. 1 in n4 only in 31(6) = {135679} only (no 2,4)
16a. 3 & 5 locked for n4, no 9 in r5c12 since it sees all 9 in 31(6) (Common Peer Elimination CPE)

17. 5 in r6 only in n6 in h17(3) = {359/458}(no 2,6,7)

18. 2 in r6 only in n4: locked for n4

19. 2 in n47 only in two cages -> both must have 2
19a. -> 12(3)r6c2 = {129/246}(no 5,7,8)

20. 20(5)r6c1 must have 2 for n4/7 and 5 for n7
20a. = {12359/12458/23456}(no 7)

21. 7 in n7 only in r89c3: locked for c3 and 30(4)cage

22. 7 in c4 only in r56c4: locked for n5 and 31(6)

23. 7 in n4 only in 19(3) = {478} only: 4 and 8 locked for n4: 8 for r5

24. 8 in r6 only in r6c789 in h17(3) = {458} only: 4 locked for r6 and no 4,5 in r7c7 since it sees all of r6c789 (CPE), 4,5 locked for n6
24a. h11(3)r6c345 = [371], 7 placed for d/

25. naked pair {45} in r5c56: both locked for r5
25a. r4c1 = 4 (Hsingle n4)
25b. 7 in n4 only in r5c12: locked for r5

26. 2 and 4 in c3 only in n1: both locked for n1

27. r3c4 = (45) -> in n1, 12(3) must have at least one of 4 or 5
27a. {246} blocked by both 2 & 4 are only in r2c3
27b. = {147/156/345}(no 2,8,9)

28. hsingle 2 in n1 -> r1c3 = 2, r1c4 = 4 (cage sum), r3c4 = 5
28a. 36(6) = {16789/34789}[5]
28b. -> 7 locked for n1

29. r2c9 = 2 (hsingle n3), r5c8 = 2 (hsingle n6)

30. 2 on d/ only in n7: locked for n7

31. r7c5 = 2 (hsingle r7), r9c7 = 2 (hsingle n9), r8c2 = 2 (hsingle n7)
31a. -> r67c2 = 10 = [64/91]: note, has 6 in r6c2 or 1 in r7c2

32. 15(3)r6c6: {168} as [681] only, blocked by r67c2 (step 31a)
32a. = {159/456}(no 7,8)

33. 7 on d\ only in n9, locked for n9
33a. -> r7c7 = 7 (hsingle r7)

34. 7 in n6 only in 18(4) = {2367}: r5c9 = 3, 6 locked for n6 and r4

35. naked pair {19} in r45c7: both locked for c7 and not in r3c8

35. 2 innies n3 = 13 = [67] only: 6 placed for d/

36. r2c78 = [85/49]

37. 12(3)n1 = {156/345}
37a. 1 in {156} must be in r1c2 -> no 6 in r1c2

Last key step
38. 6 in r1 only in r1c16 -> no 6 in r6c6 (CPE)
38a. r6c6 = 9 (placed for d\), -> 15(3) = [951]

39. hsingle 4 on d/ -> r5c5 = 4: placed for d\

lots of naked stuff now.
Cheers
Ed


Top
 Profile  
Reply with quote  
 Post subject: Re: Assassin 387
PostPosted: Mon Nov 11, 2019 12:04 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Thanks Ed for your latest Assassin; I'm up to date again! :)

It's a long time since I've solved an Assassin without using any forcing chains. This time it was combination analysis with one fairly hard step; maybe that's why it wasn't Ed's favourite type of puzzle. I also found lots of hidden singles in my solving path.

Here is my walkthrough for Assassin 387:
This is a Killer-X.

Prelims

a) R2C78 = {49/58/67}, no 1,2,3
b) R7C34 = {29/38/47/56}, no 1
c) 19(3) cage at R4C1 = {289/379/469/478/568}, no 1
d) 10(3) cage at R5C5 = {127/136/145/235}, no 8,9
e) 30(4) cage at R8C3 = {6789}
f) 14(4) cage at R9C6 = {1238/1247/1256/1346/2345}, no 9

1a. 45 rule on N12 1 innie R3C6 = 2
1b. 45 rule on N3 2 innies R3C78 = 13 = {49/58/67}, no 1,3
1c. 45 rule on N3 2 remaining outies R45C7 = 10 = {19/37/46}, no 5,8

2. 45 rule on N47 5 outies R56789C4 = 33 = {36789/45789}, no 1,2, 7,8,9 locked for C4
2a. R4C4 = 2 (hidden single in C4), placed for D\
2b. 45 rule on N5 3 innie R56C4 + R6C6 = 22 = {589/679}, 9 locked for N5
2c. 10(3) cage at R5C5 = {136/145}, no 7, 1 locked for N5
2d. Killer pair 5,6 in R56C4 + R6C6 and 10(3) cage
2e. R4C4 = 2 -> R4C56 = 11 = {38/47}
2f. R56789C4 = {36789/45789} -> R7C4 = {34}, R7C3 = {78}
2g. 2 in C5 only in R789C5, locked for 32(6) cage at R7C5

3a. 45 rule on N1 1 outie R3C4 = 1 innie R1C3 + 3 -> R1C3 = {123}, R3C4 = {456}
3b. 45 rule on C1234 1 outie R1C5 = 1 remaining innie R2C4 + 6 -> R1C5 = {79}, R2C4 = {13}
3c. 1 in C4 only in R12C4, locked for N2
3d. Min R1C35 = 8 -> max R1C4 = 5
3e. 45 rule on N2 3 innies R1C45 + R3C4 = 16 = {169/457} (cannot be {349} which clashes with R7C4, cannot be {367} = [37]6 because 13(3) cage at R1C3 cannot be [337]), no 3

4. 45 rule on N457 4(1+3) innies R6C6 + R789C3 = 30
4a. Max R789C3 = 24 -> min R6C6 = 6
4b. Min R6C6 = 6 -> max R6C7 + R7C6 = 9, no 9 in R6C7 + R7C6

5. 45 rule on R6789 3 innies R6C345 = 11 = {128/137/146} (cannot be {236} = [263] which clashes with 10(3) cage = {136}, cannot be {245} = [254] which clashes with 10(3) cage = {145}), no 5,9, 1 locked for R6
5a. R6C4 = {678} -> no 6,7,8 in R6C35
5b. R56C4 + R6C6 (step 2b) = {589/679}
5c. 8 of {589} must be in R6C4 -> no 8 in R5C4 + R6C6

6. R56C4 + R6C6 (step 2b) = {589/679}
6a. R56C4 + R6C6 = {589} must be [589] when 15(3) cage at R6C6 = [924/951]
6b. 45 rule on N1236 3 innies R6C789 = 17 = {278/359/368/458/467} (cannot be {269} which clashes with R56C4 + R6C6)
6c. R6C789 = {278/359/368/458} (cannot be {467} because R56C4 + R6C6 = {589} + 15(3) cage = [924/951] doesn’t include 4,6,7 in R6C7 and {467} clashes with R56C4 + R6C6 = {679})
6d. R56C4 + R6C6 = {679} (cannot be {589} = [589] which clashes with R6C789), 6,7 locked for N5
6e. R4C56 (step 2e) = {38}, locked for R4, 3 locked for N5
6f. R5689C4 = {6789} -> R7C4 = 3 (step 2), R7C3 = 8, placed for D/, R4C6 = 3, placed for D/, R4C5 = 8, R2C4 = 1
6g. R13C4 = {45} (hidden pair in C4), locked for N2, R1C45 + R3C4 = 16 (step 3e) -> R1C5 = 7, R1C34 = 6 = [15/24]
6h. Naked pair {45} in R13C4, CPE no 4,5 in R1C1
6i. 8 in C4 only in R89C4, locked for N8
6j. R6C345 (step 5) = {137/146}, no 2
6k. R6C789 = {278/359/458} (cannot be {368} which clashes with R6C345), no 6
6l. Combined cages R6C345 + R6C789 = {137}{458}/{146}{278}/{146}{359}, 4 locked for R6
Clean-ups: no 5 in R2C7, no 5 in R3C8 (step 1b), no 7 in R5C7 (step 1c)

7a. 36(6) cage at R1C1 = {156789/246789/345789}, 7,8,9 locked for N1
7b. 12(3) cage at R1C2 = {156/246/345}

8. 31(6) cage at R4C2 = {135679/234679}, 3 locked for C3 and N4
8a. 3 in R6 only in combined cages R6C345 + R6C789 (step 6l) = {137}{458}/{146}{359}, no 2
8b. R6C789 = {359/458}, 5 locked for R6 and N6
8c. 2 in R6 only in R6C12, locked for R6 -> 31(6) cage = {135679}, no 4, 5 locked for N4
8d. 2,4 in C3 only in R123C3, locked for N1
8e. 12(3) cage at R1C2 (step 7b) = {156/345} (cannot be {246} because 2,4 only in R2C3), no 2
8f. R1C3 = 2 (hidden single in N1) -> R1C4 = 4 (cage sum), R3C4 = 5
8g. R3C78 (step 1b) = {49/67}, no 8
8h. R45C7 (step 1c) = {19}/[73] (cannot be {46} which clashes with R3C78), no 4,6
8i. 25(5) cage at R3C6 = 2{49}[73]/2{67}{49}, CPE no 7,9 in R12C7, clean-up: no 4,6 in R2C8
8j. R2C9 = 2 (hidden single in N3)
8k. R5C8 = 2 (hidden single in N6)
8l. R9C7 = 2 (hidden single in N9)
8m. R8C2 = 2 (hidden single on D/) -> R67C2 = 10 = [64/91]
8n. R6C1 = 2 (hidden single in C1)
8o. Naked triple {679} in R6C246, locked for R6
8p. R6C789 = {458}, 4 locked for R6, 4,8 locked for N6 -> R6C35 = [31], R6C4 = 7 (step 6j), placed for D/
8q. Naked pair {45} in R5C56, locked for R5
8r. R4C1 = 4 (hidden single in N4) -> R5C12 = {78} (hidden pair in N4), 7 locked for R5
8s. 30(4) cage at R8C2 = {6789}, 7 locked for C3 and N7
8t. Min R6C67 = 10 -> max R7C6 = 5
8u. 7 in R7 only in R7C789, locked for N9
8v. R2C1 = 7 (hidden single in R2) -> R5C12 = [87]
8w. R3C2 = 8 (hidden single in N1)
8x. R7C7 = 7 (hidden single on D\), R45C7 (step 8h) = {19}, locked for C7 and N6, 9 locked for 25(5) cage at R3C6) -> R3C78 (step 8g) = [67], 6 placed for D/, R4C8 = 6, R5C9 = 3
8y. R7C5 = 2 (hidden single in N8)
8z. Naked triple {689} in R126C6, 6,9 locked for C6

9a. R5C5 = 4 (hidden single on D/), placed for D\ -> R5C6 = 5
9b. 5 in C5 only in R89C5, locked for 32(6) cage at R7C5
9c. Naked triple {159} on D/, CPE no 1 in R1C1 + R9C9
9d. Naked pair {14} in R7C26, locked for R7
9e. 14(4) cage at R9C6 = {1238/2345} (cannot be {1247} because R9C9 only contains 5,6,8, cannot be {1256} which clashes with R7C78), no 6,7
9f. 14(4) cage at R9C6 = {1238/2345} -> R9C8 = 3
9g. R8C6 = 7 (hidden single in N8) -> R9C3 = 7 (hidden single in N7)
9h. 32(6) cage contains 2,5,7 = {125789/245678}, 8 locked for R8 and N9
9i. R9C9 = 5, placed for D\, R9C78 = [23] -> R9C6 = 4 (cage sum), R7C6 = 1, R7C2 = 4 -> R6C2 = 6 (cage sum), R6C6 = 9, placed for D\, R6C7 = 5 (cage sum), R7C89 = [96]
9j. Naked pair {19} in R9C12, locked for N7, 9 locked for R9
9k. R2C8 = 5 -> R2C7 = 8, R1C8 = 1, R1C9 = 9, placed for D/

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

Rating Comment:
I'll rate my WT for A387 at Hard 1.25 for my hardest analysis step.


Top
 Profile  
Reply with quote  
 Post subject: Re: Assassin 387
PostPosted: Sat Nov 30, 2019 8:55 pm 
Offline
Grand Master
Grand Master

Joined: Tue Jun 16, 2009 9:31 pm
Posts: 280
Location: California, out of London
Better late than never! Thanks Ed for another interesting and tricky puzzle :applause:
Ed's way of eliminating one possibility (his step 9) is much better than my way of doing the equivalent I think (My step 4).
Here's how I did it.
Assassin 387 WT:
1. Innies n12 -> r3c6 = 2
Innies n3 -> r3c78 = +13(2)
-> r45c7 = +10(2)
-> r6c789 = +17(3)

2. IOD n1 -> r3c4 = r1c3 + 3
Innies c1234 = r1c3 + r124c4 = +9(4)
-> r1234c4 = +12(4) = {1236} or {1245}
-> r4c4 = 2

3. Innies n5 = +22(3) = {589} or {679}
30(4)r8c3 = {6789}
Innies r6789 = r6c345 = +11(3)

(Ed's way of removing one possibility (his Step 9 ) is better than mine!)

4. Trying r1234c4 = [{136}2] puts ...

r1c3 = 3 and r123c4 = [136]
HP r23c9 = [13] and 2 in n3 in r1
Also puts 1 in n1 in r3
puts HS 2 in n1 r2c3 = 2 (Since 36(6) cannot contain both 1 and 2, and 2 already on D\)

Also HS 4 in c4 puts 11(2)r7c3 = [74]
puts 7 in r89c4
puts H+22(3)n5 = {589}
puts 10(3)n5 = {136}

which leaves no solution for r6c345 = +11(3)

-> r123c4 = {145}

5. 13(3)r1 cannot contain both (12)
-> [r1c3][r123c4] from [1][514] or [2][415]
-> HS 3 in c4 -> 11(2)r7c3 = [83]
-> 8 in r89c4
-> Innies n5 = {679}
-> 10(3)n5 = {145}
-> 13(3)n5 = [283]

6. r6c345 = +11(3) from [371] or <164>
r6c789 = +17(3)
The only way 2 could be in there is if it is {278}
which puts r56c4 = [76]
which leaves no place for both (67) in n4
-> 2 in r6c12
-> 2 in c3 in r12c3

7. r6c126 = +17(3) and r6c6 from (679)
For r6c345 = [371] -> r6c126 = {269} -> 19(3)n4 = {478}
For r6c345 = <164> -> r6c126 = [{28}7] -> r5c4 = 9 -> 19(4) = {469}
Either way 4 in 19(3)n4
-> 4 in c3 in r123c4

8. -> For the case where r1c3,r123c4 = [1][514] -> No room for both (24) in n1
-> r1c3 = 2, r123c4 = [415]
-> r1c5 = 7
Also -> HS 2 in n3 r2c9 = 2
-> HS 2 in n6 r5c8 = 2
2 in n8 in r789c5
-> HS 2 in c7/n9 -> r9c7 = 2
-> HS 2 in D/ -> r8c2 = 2
-> HS 2 in n4 -> r6c1 = 2
-> HS 2 in n8 -> r7c5 = 2
Also r6c2 cannot be 8 -> r6c26 = {69}
-> r6c345 = [371]
-> r6c789 = {458}
Also r5c56 = {45}
-> 19(3)n4 = [4{78}]

9. This finishes it off
5 in r3c4 -> 5 in n1 in 12(3) = {156} or {345}
-> 7 in D\ in n9
r6c6 from (69) and r6c7 from (458} -> r7c6 cannot be 7
-> 7 in r7 in n9
-> r7c7 = 7

10. -> 35(6)r6c8 contains a 7 and not a 2
-> 35(6) = [{48}7{169}]
Also r45c7 = {19}
-> r3c78 = [67]
Also r6c7 = 5
-> r67c2 and r67c6 are between them [91] and [64]
-> r8c9 = 1
-> r1c8 = 1
-> HS 1 in D/ -> r9c1 = 1
-> 12(3)r6c2 = [642] and 15(3)r6c6 = [951]
Also HS 1 in D\ -> r3c3 = 1
Also 9 in r1 in r1c9
-> 13(2)r2c7 = [85]
etc.


Top
 Profile  
Reply with quote  
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 4 posts ] 

All times are UTC


Who is online

Users browsing this forum: No registered users and 4 guests


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  
cron
Powered by phpBB® Forum Software © phpBB Group