SudokuSolver Forum

A forum for Sudoku enthusiasts to share puzzles, techniques and software
It is currently Thu Mar 28, 2024 11:22 pm

All times are UTC




Post new topic Reply to topic  [ 3 posts ] 
Author Message
 Post subject: Assassin 59 v1.5 Revisit
PostPosted: Sat May 15, 2021 6:46 pm 
Offline
Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
Attachment:
a59v15.JPG
a59v15.JPG [ 63 KiB | Viewed 4118 times ]
Assassin 59 v1.5 Revisit

The link above gets you to the archive of this puzzle. This gets a score of 1.80 (lowest of 4 rotations). JSudoku uses one 'complex intersection'.

Code: Select, Copy & Paste into solver:
3x3::k:3328:3328:3586:3586:3076:4613:4613:2567:2567:4361:4361:4361:3586:3076:4613:4623:4623:4623:2578:2578:3348:3586:4374:4613:2584:3865:3865:7195:2578:3348:4374:4374:4374:2584:3865:6947:7195:7195:7195:3879:3879:3879:6947:6947:6947:7195:4142:2607:5936:5936:5936:1843:2868:6947:4142:4142:2607:4409:5936:5179:1843:2868:2868:4415:4415:4415:4409:3139:5179:4933:4933:4933:1608:1608:4409:4409:3139:5179:5179:2639:2639:
Solution:
+-------+-------+-------+
| 4 9 2 | 8 5 6 | 1 3 7 |
| 8 3 6 | 1 7 2 | 9 4 5 |
| 1 7 5 | 3 4 9 | 6 2 8 |
+-------+-------+-------+
| 7 2 8 | 9 1 3 | 4 5 6 |
| 9 5 4 | 6 2 7 | 3 8 1 |
| 3 6 1 | 4 8 5 | 2 7 9 |
+-------+-------+-------+
| 2 8 9 | 7 6 4 | 5 1 3 |
| 6 4 7 | 5 3 1 | 8 9 2 |
| 5 1 3 | 2 9 8 | 7 6 4 |
+-------+-------+-------+
Cheers
Ed


Top
 Profile  
Reply with quote  
PostPosted: Sat May 22, 2021 9:59 pm 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
As with the earlier Revisits, I haven't checked how I originally solved this puzzle. However I doubt that I found the same breakthrough step back then.

Thanks Ed for pointing out that my step 4f was only partly correct; I've done detailed rework for steps 4f to 4j, 5d and 5f.
I've now added an alternative way for step 4f.
Here's my walkthrough for Assassin 59V1.5 Revisited:
Prelims

a) R1C12 = {49/58/67}, no 1,2,3
b) R12C5 = {39/48/57}, no 1,2,6
c) R1C89 = {19/28/37/46}, no 5
d) R34C3 = {49/58/67}, no 1,2,3
e) R34C7 = {19/28/37/46}, no 5
f) R67C3 = {19/28/37/46}, no 5
g) R67C7 = {16/25/34}, no 7,8,9
h) R89C5 = {39/48/57}, no 1,2,6
i) R9C12 = {15/24}
j) R9C89 = {19/28/37/46}, no 5
k) 10(3) cage at R3C1 = {127/136/145/235}, no 8,9
l) 11(3) cage at R6C8 = {128/137/146/236/245}, no 9
m) 19(3) cage at R8C7 = {289/379/469/478/568}, no 1
n) 14(4) cage at R1C3 = {1238/1247/1256/1346/2345}, no 9

1a. 45 rule on C1234 3 innies R456C4 = 19 = {289/379/469/478/568}, no 1
1b. 45 rule on C6789 3 innies R456C6 = 15 -> R456C5 = 11 = {128/146/236} (cannot be {137/245} which clash with R12C5 + R89C5, no 5,7,9
1c. R456C4 = {289/379/469/478} (cannot be {568} which clashes with R456C5), no 5
1d. 45 rule on N5 2 outies R37C5 = 10 = {19/28/37/46}, no 5
1e. 5 in C5 only in R12C5 = {57} or R89C5 = {57}, 7 locked for C5 (locking cages), clean-up: no 3 in R37C5
1f. 5 in N5 only in R456C6, locked for C6

2a. 45 rule on C123 2 innies R19C3 = 5 = {14/23}
2b. 45 rule on C789 2 innie R19C7 = 8 = {17/26/35}, no 4,8,9
2c. 45 rule on C89 3 outies R258C7 = 20 = {389/479/569/578}, no 1,2
2d. 45 rule on R1234 2 innies R4C19 = 13 = {49/58/67}, no 1,2,3
2e. 45 rule on R6789 2 innies R6C19 = 12 = {39/48/57}, no 1,2,6
2f. 45 rule on N2 1 innie R3C5 = 2 outies R1C37 + 1
2g. Min R1C37 = 3 -> min R3C5 = 4, clean-up: no 8,9 in R7C5 (step 1d)

3a. 45 rule on N7 2 outies R6C23 = 1 innie R9C3 + 4
3b. Max R9C3 = 4 -> max R6C23 = 8, no 8,9 in R6C23, clean-up: no 1,2 in R7C3
3c. R6C23 = R9C3 + 4 -> no 4 in R6C2 (IOU)
3d. 45 rule on N3 2 outies R4C78 = 1 innie R1C7 + 8 -> no 8 in R4C8 (IOU)
3e. 45 rule on N9 2 outies R6C78 = 1 innie R9C7 + 2 -> no 2 in R6C8 (IOU)

4a. 45 rule on R8 3 innies R8C456 = 9 = {135/234} (cannot be {126} because no 1,2,6 in R8C5), no 6,7,8,9, 3 locked for R8 and N8, clean-up: no 4,5 in R9C5
4b. 1 in R8 only in 17(3) cage at R8C1 = {179} or R8C456 = {135} -> no 5 in 17(3) cage (locking-out cages)
4c. 45 rule on R89 2 outies R7C46 = 11 = {29/47}/[56], no 1,8, no 6 in R7C4
4d. 8 in N8 only in R9C456, locked for R9, clean-up: no 2 in R9C89
4e. Variable hidden killer pair 7,9 in R7C46 and R9C456 for N8, R7C46 cannot contain both of 7,9 -> R9C456 must contain at least one of 7,9
4f. Whichever of 6,7,8,9 in 19(3) cage at R8C7 must be in R9C456 for R6 -> 19(3) cage must contain at least one of 7,9 = {289/469/478} (cannot be {568} because R9C456 must contain one of 7,9, note that 19(3) cage = {568} forces R8C456 = {234}, 17(3) cage at R8C1 = {179}, 6(2) cage at R9C1 = {24}, R9C3 = 3 so {568} would have to be in R9C456), no 5
Alternative step 4f, in my normal style
19(3) cage at R8C7 = {289/469/478/568}, R9C12 = {15/24}
Consider combinations for R9C89 = {19/37/46}
R9C89 = {19}, locked for R9 and N9 => R9C12 = {24}, 2 locked for R9, 9 in N8 only in R7C46 = {29}, 2 locked for R7 => 2 in N9 only in 19(3) cage = {289}
or R9C89 = {37} => 9 in N9 only in 19(3) cage = {289/469}
or R9C89 = {46}, locked for N9 => 19(3) cage = {289} -> 19(3) cage = {289/469}
This actually achieves more than the first version of step 4f, including eliminating R9C89 = {19}, but I’ll leave the remaining steps unchanged.

[Fairly straightforward from here.]
4g. R8C456 = {135} (cannot be {234} which clashes with 19(3) cage), 1,5 locked for N8, 1 locked for R8, clean-up: no 9 in R3C5 (step 1d), no 6 in R7C6, no 8 in R9C5
4h. 17(3) cage at R8C1 = {269/278/467}
4i. R9C12 = {15} (cannot be {24} which clashes with 17(3) cage), locked for R9 and N7, clean-up: no 4 in R1C3 (step 2a), no 3,7 in R1C7 (step 2b), no 9 in R9C89
4j. 9 in N9 only in 19(3) cage = {289/469}, no 7, 9 locked for R8
4k. 9 in R9 only in R9C456, locked for N8, clean-up: no 2 in R7C46
4l. Naked pair {47} in R7C46, locked for R7 and N8 -> R9C5 = 9, R8C5 = 3, R8C46 = [51], clean-up: no 6 in R3C5 (step 1d), no 3,6 in R6C3, no 3 in R6C7
4m. R12C5 = {57} (hidden pair in C5), 7 locked for N2

5a. R8C4 = 5 -> 17(4) cage at R7C4 = {2357/2456}, no 8
5b. R9C6 = 8 (hidden single in N8)
5c. R89C6 = [18] = 9 -> R7C6 + R9C7 = 11 = [47], R7C4 = 7, R1C7 = 1 (step 2b), clean-up: no 9 in R1C89, no 3,9 in R34C7, no 6 in R67C7, no 4 in R9C3 (step 1a), no 3 in R9C89
5d. Naked pair {46} in R9C89, locked for N9, 6 locked for R9 -> R9C4 = 2, R19C3 = [23], R7C5 = 6 -> R3C5 = 4 (step 1d), clean-up: no 8 in R1C89, no 9 in R4C3, no 6 in R4C7, no 4,7 in R6C3, no 8 in R7C3
5e. R67C3 = [19], clean-up: no 4 in R4C3
5f. R7C12 = {28}, locked for R7 and N7, R6C2 = 6 (cage sum), clean-up: no 7 in R1C1, no 7 in R3C3, no 7 in R4C9 (step 2d)
5g. Naked triple {128} in R456C5, 2,8 locked for N5
5h. R456C4 (step 1a) = 19 = {469} (only remaining combination), 6 locked for C4, 6,9 locked for N5
5i. R7C6 = 6 -> 23(4) cage at R6C4 = {4568} (only possible combination, cannot be {2678} because 2,8 only in R6C5, cannot be {3569} because R6C5 only contains 2,8) -> R6C456 = [485], R6C7 = 2 -> R7C7 = 5, clean-up: no 8 in R34C7, no 7 in R6C19 (step 2e)
5j. R34C7 = [64], clean-up: no 4 in R1C89, no 9 in R4C19 (step 2d), no 7 in R4C3
5k. 45 rule on N4 2 remaining innies R4C23 = 10 = [28] -> R3C3 = 5, clean-up: no 5 in R4C19 (step 2d)
5l. R4C19 = [76], R4C2 = 2 -> R3C12 = 8 = [17]
5m. Naked pair {37} in R1C89, locked for R1 and N3

and the rest is naked singles.


Top
 Profile  
Reply with quote  
PostPosted: Tue May 25, 2021 6:43 pm 
Offline
Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
Great shortcut by Andrew! Here's what I had to go through to get to his step 4i. [Thanks to Andrew for checking my WT and suggesting some improvements]
Start to a59 v1.5R:
Preliminaries courtesy of SudokuSolver
Cage 6(2) n7 - cells only uses 1245
Cage 7(2) n69 - cells do not use 789
Cage 12(2) n8 - cells do not use 126
Cage 12(2) n2 - cells do not use 126
Cage 13(2) n14 - cells do not use 123
Cage 13(2) n1 - cells do not use 123
Cage 10(2) n47 - cells do not use 5
Cage 10(2) n36 - cells do not use 5
Cage 10(2) n9 - cells do not use 5
Cage 10(2) n3 - cells do not use 5
Cage 10(3) n14 - cells do not use 89
Cage 11(3) n69 - cells do not use 9
Cage 19(3) n9 - cells do not use 1
Cage 14(4) n12 - cells do not use 9

NOTE: no clean-up done unless stated

1. "45" on c123: 2 innies r19c3 = 5 = {14/23}

2. "45" on r8: 3 innies r8c456 = 9 = and must have one of 3,4,5 for r8c5 = {135/234}(no 6,7,8,9)
2a. 3 locked for r8 and n8
2b. r9c5 = (789)

3. 17(3)n7: {458} blocked by 6(2)n7 needing one of 4 or 5
3a. = {179/269/278/467} = 1 or 2 or 4
3b. -> {24}[1] blocked from r9c123
3c. -> no 1 in r9c3
3d. -> no 4 in r1c3 (h5(2)r19c3)

4. "45" on c789: 2 innies r19c7 = 8 (no 4,8,9)

5. "45" on n2: 2 outies r1c37 + 1 = 1 innie r3c5
5a. min. r1c37 = 3 -> min. r3c5 = 4

6. "45" on n5: 2 outies r37c5 = 10 (no 5)
6a. min. r3c5 = 4 -> max. r7c5 = 6

7. "45" on r89: 2 outies r7c46 = 11 {29/47/56}(no 1,8)

8. "45" on n8: 4 remaining innies r7c5 + r9c456 = 25 and must have 8 for n8
8a. = {1789/2689/4678}(no 5)
8b. 1 in {1789} must be only in r7c5 -> no 1 in r9c46
8c. 8 locked for r9

First key step
9. "45" on c1234: 3 innies r456c4 = 19 (no 1)
9a. -> 1 in c4 in 14(4)r1c3 or in r8c4 with r8c456 = [1]{35}(step 2)
9b. 4 in r9c3 -> 1 in r1c3 -> [1]{35} in r8c456
9c. -> r8c4 + r9c3 = [14] blocked since r79c4 <> 12 (Combo Crossover Clash (CCC) with step 9b ie; can't be {39} because of 3 in r8c56; can't be {48} because 4 is already in r9c3; can't be {57} because of 5 in r8c56)
9d. -> no 4 in r9c3
9e. -> r19c3 = {23}: both locked for c3

10. "45" on n8: 1 innie r7c5 + 4 = 2 outies r9c37
10a. = [1]{23}/[426/435]/[637]
10b. no 2 in r7c5, no 1 in r9c7

11. r37c5 = 10 = [91]/{46}(no 7,8) (h10(2)r37c5)

12. "45" on c5: 3 remaining innies r456c5 = 11
12a. ie, can't have both 5 & 7
12b. so both 5 & 7 must be in one of 12(2) in c5: both locked for c5 (Locking cages)
12c. -> r456c5 = 11 and must have 2 for c5 ={128/236}(no 4,9) = 6 or 8
12d. 2 locked for n5

13. h19(3)r456c4: {568} blocked by r456c5
13a. = {379/469/478}(no 5)

14. 5 in n5 only in c6: locked for c6
14a. no 6 in r7c4 (h11(2)r7c46)

Now things get harder to see
15. 5 in n8 only in 12(2) = [57] or in 17(4)
15a. -> 7 in 17(4) must also have 5 (locking-out cages)
15b. -> {1367} blocked
15c. {1268} blocked by 6,8 are only in r9c4
15d. {1457} blocked since no 2,3 for r9c3
15e. {2456} as {45}[26] only puts [91] in r37c5 (h10(2)) and [39] in r89c5: ie two 9's in c5
15f. {1259/1358} blocked since [1]{35} is in r8c456 (CCC)
15f. = {1349/2348/2357}(no 6)

16. from step 10, iodn8 = -4
16a. 6 in r7c5 -> r9c37 = 10 = [37]
16b. or 6 in n8 in 20(4)
16c. -> no 6 in r9c7

17. r9c37 from {2357} -> {37} blocked from 10(2)n9 since iodn8 = -4 can't be [325]

18. "45" on r9: 5 innies r9c34567 = 29 and must have 378 = 18 for r9
18a. -> other two cells = 11 = {29/56} (can't have two 7 or two 8 in r9 so can't be {38/47}
18b. if other two are {56}, they are only in r9c67 in 20(4)r7c6 -> r78c6 = 9 = [72] only but makes h11(2)r7c46 = [47] and h9(3)r8c456 = {34}[2]; ie, two 4 in n8
18c. -> no 6 in r9c6, no 5 in r9c7

cracked
19. 5 in r9 only in 6(2)n7 = {15}: both locked for n7, 1 for r9
19a. 6 in r9 only in 10(2)n9 = {46}: both locked for n9, 4 for r9

Much easier from here with last combos, locked candidates, basic "45"s etc
Cheers
Ed


Top
 Profile  
Reply with quote  
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 3 posts ] 

All times are UTC


Who is online

Users browsing this forum: No registered users and 13 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:  
Powered by phpBB® Forum Software © phpBB Group