SudokuSolver Forum

A forum for Sudoku enthusiasts to share puzzles, techniques and software
It is currently Fri Mar 29, 2024 11:22 am

All times are UTC




Post new topic Reply to topic  [ 6 posts ] 
Author Message
 Post subject: Assassin 405
PostPosted: Mon Nov 15, 2021 8:23 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
Attachment:
a405.JPG
a405.JPG [ 105.31 KiB | Viewed 4461 times ]
NOTE: 1-9 cannot repeat on either diagonal. Note the disjoint cage 8(3)r3c7. r5c5 belongs to the 19(3).

Assassin 405

I found a nice way to get unstuck with this so very happy! SudokuSolver has a very hard time at 2.10 but JSudoku uses just 2 advanced steps which is why I tried it.
triple click code:
3x3:d:k:5912:5912:5912:4353:4353:4353:3074:3074:2819:5912:2071:2071:2820:4353:2821:2821:2819:4102:5912:3847:3080:2820:4361:4361:2058:4102:4102:2059:3847:3080:4876:4361:2058:5133:11534:4102:2059:3847:3855:3855:4876:5133:5133:5133:11534:5136:2833:2833:4876:6674:2058:3859:3859:11534:5136:5136:4372:6674:6674:6674:3093:3093:11534:5136:4372:7190:7190:6674:7190:11534:3093:11534:4372:2048:2048:7190:7190:7190:11534:11534:11534:
solution:
+-------+-------+-------+
| 7 4 8 | 5 1 2 | 3 9 6 |
| 3 6 2 | 8 9 4 | 7 5 1 |
| 1 9 5 | 3 7 6 | 4 8 2 |
+-------+-------+-------+
| 6 1 7 | 9 4 3 | 8 2 5 |
| 2 5 9 | 6 8 7 | 1 4 3 |
| 4 8 3 | 2 5 1 | 9 6 7 |
+-------+-------+-------+
| 5 3 1 | 4 6 9 | 2 7 8 |
| 8 7 4 | 1 2 5 | 6 3 9 |
| 9 2 6 | 7 3 8 | 5 1 4 |
+-------+-------+-------+
Cheers
Ed


Top
 Profile  
Reply with quote  
 Post subject: Re: Assassin 405
PostPosted: Sat Nov 20, 2021 4:29 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Thanks Ed for your new Assassin. Possibly the hardest puzzle we've had this year, either new Assassin or Revisit. I can see why SudokuSolver struggles; it's not really a 2.10 puzzle. I hope that Ed found a better, or more direct, solving path than I did.

Here's my walkthrough for Assassin 405:
Prelims

a) R1C78 = {39/48/57}, no 1,2,6
b) 11(2) cage at R1C9 = {29/38/47/56}, no 1
c) R2C23 = {17/26/35}, no 4,8,9
d) R23C4 = {29/38/47/56}, no 1
e) R2C67 = {29/38/47/56}, no 1
f) R34C3 = {39/48/57}, no 1,2,6
g) R45C1 = {17/26/35}, no 4,8,9
h) R5C34 = {69/78}
i) R6C23 = {29/38/47/56}, no 1
j) R6C78 = {69/78}
k) R9C23 = {17/26/35}, no 4,8,9
l) 8(3) disjoint cage at R3C7 = {125/134}
m) 19(3) cage at R4C4 = {289/379/469/478/568}, no 1

1a. 45 rule on N1 2 innies R3C23 = 14 = {59}/[68], clean-up: no 5,8,9 in R4C3
1b. 45 rule on C123 2 innies R58C3 = 13 = {67}/[85/94] -> R8C3 = {4567}
1c. 45 rule on N7 1 outie R6C1 = 1 innie R8C3 -> R6C1 = {4567}
1d. 45 rule on N78 2 outies R6C15 = 9 = {45}/[63/72], R6C5 = {2345}
1e. 45 rule on R6 using R6C15 3 innies R6C469 = 10 = {127/136/145/235}, no 8,9
1f. Hidden killer pair 8,9 in R6C23 and R6C78 for R6, R6C78 contains one of 8,9 -> R6C23 must contain one of 8,9 = {29/38}
1g. R6C469 = {127/136/145} (cannot be {235} which clashes with R6C23, alternatively must contain 1 for R6)

2a. 45 rule on D/ 2 outies R4C4 + R6C6 = 10 = [64/73/82/91], R4C4 = {6789}, R6C6 = {1234}
2b. R4C4 + R6C6 = [64/82/91] (cannot be [73] because R5C5 + R6C4 = 12 = [84] clashes with 8(3) disjoint cage at R3C7 = {134}), no 7 in R4C4, no 3 in R6C6
2c. 17(3) cage at R7C3 = {179/269/278/368/458} (cannot be {359} which clashes with 8(3) disjoint cage, cannot be {467} which clashes with R8C3 + R9C23, killer ALS block)
2d. 17(3) cage at R7C3 = {179/269/278/368} (cannot be {458} because 11(2) cage at R1C9 + 19(3) cage at R4C4 cannot be {29}+6{67}), no 4,5
2e. 19(3) cage at R4C4 = {289/379/469/478/568}
2f. Consider placement for 1 on D/
1 in R3C7 + R4C6, locked for 8(3) disjoint cage => R4C4 + R6C6 = [64/82] => 19(3) cage = {478/568} (cannot be {289/469} = [892/694] which clash with R4C4 + R6C6, CCC)
or 1 in 17(3) cage = {179}, 7,9 locked for D/ => 19(3) cage = {289/469/568}
-> 19(3) cage = {289/469/478/568}, no 3
2g. {289/469} must be [982/946/964], no 2,9 in R5C5
2h. {478} must be [847] (cannot be [874] because R6C46 cannot be [42], step 1g), no 7 in R5C5
2i. {568} must be [685] (cannot be 8{65} which clashes with 8(3) disjoint cage = {15}2), no 5 in R5C5
2j. 9 on D/ only in 11(2) cage at R1C9 = {29}
or 17(3) cage = {179/269}
-> 17(3) cage = {179/269/368} (cannot be {278}, locking-out cages)
2k. 45 rule on N1478 2 outies R5C4 + R6C5 = 11 = [65/83/92] (cannot be [74] which clash with 19(3) cage = {469/478}, while R5C4 = 6 for 19(3) cage = {289} and R5C4 = 9 for 19(3) cage = {568}), no 7 in R5C4, no 4 in R6C5, clean-up: no 8 in R5C3, no 5 in R6C1 (step 1d), no 5 in R8C3 (step 1b)
2l. 19(3) cage = {469} must be [964] (cannot be [946] which clashes with R5C4 + R6C15 = [863], step 1d), no 6 in R6C4
2m. Combined cage 19(3) cage + R5C4 + R6C3 = {289}[65]/{469}[83]/{478}[65](because of R4C4 + R6C6)/{568}[92] -> 8 in R4C4 + R5C45, locked for N5
2n. Combined cage R34C3 + R58C3 = [57][94]/[84]{67}/[93]{67}, 7 locked for C3, clean-up: no 1 in R2C2, no 1 in R9C2
2o. R6C469 (step 1g) = {127/145} (cannot be {136} because only 2,4,5,7 in R6C4), no 3,6

3a. 45 rule on N2 1 innie R2C6 = 1 outie R4C5 -> no 8 in R2C6, no 1 in R4C5, clean-up: no 3 in R2C7
3b. 45 rule on N69 1 outie R5C6 = 1 innie R4C9 + 2, no 6,8,9 in R4C9, no 1,2 in R5C6
3c. 1 in N5 only in R46C6, locked for C6 and 8(3) disjoint cage, no 1 in R3C7

4a. R3C23 (step 1a) = {59}/[68], 19(3) cage at R4C4 (step 2f) = {289/469/478/568}, R4C4 + R6C6 (step 2b) = [64/82/91]
4b. Consider combinations for 8(3) disjoint cage at R2C7 = {125/134}
8(3) disjoint cage = 5{12} => R3C23 = [68], 8 placed for D\ => 19(3) cage = {469}
or 8(3) disjoint cage = [251] => R4C4 = 9 => 19(3) cage = {289/469}
or 8(3) disjoint cage = {134}, 4 locked for N5 using D/ => 19(3) cage = {289/568}
-> 19(3) cage = {289/469/568}, no 7
4c. 7 in N5 only in R4C5 + R5C6, CPE no 7 in R3C6
4d. 45 rule for N5 using R5C4 + R6C5 = 11 (step 2k), 4 remaining innies R4C56 + R56C6 = 15 containing 1,7 for N5 = {1257/1347}, no 6,9, clean-up: no 6,9 in R2C6 (step 3a), no 2,5 in R2C7, no 4,7 in R4C9 (step 3b)
4e. R2C6 = R4C5 (step 3a) -> R2456C6 = {1257/1347}, 7 locked for C6
4f. 9 in N5 only in R45C4, locked for C4, clean-up: no 2 in R23C4
4g. 19(3) cage = {289/469/568} = [982/964/685] -> R4C4 = {69}, R5C5 = {68}, clean-up: no 2 in R6C6 (step 2b)
4h. Killer pair 6,8 in R5C34 and R5C5, locked for R5, clean-up: no 2 in R4C1
4i. 17(3) cage at R7C3 (step 2j) = {179/269} (cannot be {368} which clashes with R5C5 on D/), no 3,8, 9 locked for N7 and D/, clean-up: no 2 in 11(2) cage at R1C9

5a. 8(3) disjoint cage at R2C7 = [314]/{25}1/{34}1, 1 on D/ only in R4C6 or 17(3) cage at R7C3 = {179}, 7 on D/ only in 11(2) cage at R1C9 = {47} or 17(3) cage at R7C3 = {179}
5b. Consider combinations for R1C78 = {39/48/57}
R1C78 = {39}, 3 locked for N3 => 11(2) cage at R1C9 = {47/56}, killer pair 4,5 in 11(2) cage and 8(3) disjoint cage => R6C4 = 2, placed for D/
or R1C78 = {48/57} => 11(2) cage at R1C9 = {38/56}, no 7
-> 17(3) cage at R7C3 (step 2j) = {179}, 1,7 locked for N7 and D/, clean-up: no 4 in 11(2) cage at R1C9, no 6 in R5C3 (step 1b), no 9 in R5C4, no 7 in R6C1 (step 1c), no 2 in R6C5 (step 1d)
5c. R4C4 + R6C6 = [91] (hidden pair in N5), placed for D\, clean-up: no 5 in R3C2 (step 1a), no 3 in R4C3
5d. R4C4 = 9 -> R5C5 + R6C4 = 10 = [64/82]
5e. 7 in C3 only in R45C3, locked for N4, clean-up: no 1 in R45C1
5f. 1 in N4 only in R45C2, locked for C2
5g. 15(3) cage at R3C2 = [681]/9{15}, no 2,3,4, no 6 in R4C2, no 9 in R5C2
5h. 6 in N4 only in R46C1, locked for C1
5i. R6C469 (step 2o) = {127/145} -> R6C9 = {57}
5j. 7 in R6 only in R6C789, locked for N6
5k. 12(3) cage at R7C7 = {138/147/156/237/246/345} (cannot be {129} because 1,9 only in R7C8), no 9
5l. 1 of {138} must be in R7C8 -> no 8 in R7C8
5m. 9 in N9 only in R7C9 + R8C79 + R9C78, locked for 45(9) cage at R4C8, no 9 in R5C9

6a. 45 rule on N23 3 remaining outies R4C569 = 12 = {147/237/345}
6b. 7 of {147/237} only in R4C5 -> no 2 in R4C5, clean-up: no 2 in R2C6 (step 3a), no 9 in R2C7
6c. 2 in N5 only in R4C6 + R6C4, locked for D/
6d. 1,2 in N3 only in R2C9 + R3C89, locked for 16(4) cage at R2C9, no 1,2 in R4C9, clean-up: no 3,4 in R5C6 (step 3b)
6e. Combined cage R1C78 + 11(2) cage at R1C9 = {39}{56}/{48}{56}/{57}{38}, 5 locked for N3
6f. 8(3) disjoint cage at R2C7 = {34}1 (only remaining combination), 3,4 locked for D/, clean-up: no 8 in 11(2) cage
6g. Naked pair {34} in R3C7 + R4C6, CPE no 3,4 in R3C6 + R4C7
6h. Naked pair {56} in 11(2) cage, locked for N3 and D/, R5C5 = 8, placed for D\, clean-up: no 7 in R1C78, no 5 in R2C6, no 5 in R4C5 (step 3a)
6i. R4C569 = 12 = {345} -> R4C9 = 5, R4C56 = {34}, locked for R4, 3 locked for N5, R34C3 = [57], 5 placed for D\, R3C2 = 9 (step 1a), R4C1 = 6 -> R5C1 = 2, R5C34 = [96], naked pair {38} in R6C23, 8 locked for R6 and N4, R6C9 = 7, R45C2 = [15], R6C5 = 5, R5C6 = 7, R6C1 = 4 -> R8C3 = 4 (step 1c), R7C3 = 1, R8C2 = 7, R9C1 = 9, clean-up: no 3 in R2C23, no 6 in R2C4, no 4 in R2C7, no 3 in R9C23
6j. R1C2 = 4 (hidden single in C2), clean-up: no 8 in R1C78
6k. Naked pair {39} in R1C78, locked for R1 and N3 -> R3C7 = 4 -> R4C45 = [43], R2C6 = 4, R2C7 = 7, R1C9 = 6, R2C8 = 5, clean-up: no 7 in R3C4
6l. R4C5 = 4 -> R3C56 = 13 = [76]
6m. Naked pair {38} in R23C4, locked for C4 and N2
6n. R7C8 = 7 (hidden single in N9) -> R7C7 + R8C8 = 5 = {23}, locked for N9, 2 placed for D\, R2C23 = [62], R9C23 = [26]
6o. R4C8 + R5C9 = [23] (hidden singles in 45(9) cage at R4C8) -> R8C8 = 3, R7C7 = 2, R89C7 = [65] (hidden singles in 45(9) cage at R4C8), R9C6 = 8
6p. R6C5 = 5, R7C46 = [49] -> R78C5 = 8 = [62]

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


Top
 Profile  
Reply with quote  
 Post subject: Re: Assassin 405
PostPosted: Sat Nov 20, 2021 7:33 pm 
Offline
Grand Master
Grand Master

Joined: Tue Jun 16, 2009 9:31 pm
Posts: 280
Location: California, out of London
Thanks Ed! A new Assassin! :)
Took me a while but once I found the first breakthrough it went pretty smoothly.
Here's an optimized WT of how I did it. Quite different start from Andrew's WT.
Thanks to Andrew for checking & correcting!
Assassin 405 WT:
1. For n5...
19(3) - No 1
Outies n1478 = r5c4 + r6c5 = +11(2) - No 1
IOD n69 r5c6 = r4c9 + 2 -> r5c6 not (12)
Outies n2 = r2c7 + r4c5 = +11(2) - No 1
-> 1 in n5 in r46c6
-> 1 not in r3c7

2. For r6...
Innies n14 = r5c3 + r6c1 = +13(2) - No 123
-> 1 in r6 in r6c69

3! Outies n9 = r4c8, r56c9 = +12(3) = Same three values as in 12(3)n9
-> Whatever is in r78c8 goes in n6 in r56c9 -> also goes in n3 in r123c7
Since 1 cannot be in r123c7 -> 1 not in r56c9
-> (HS 1 in r6) r6c6 = 1

4. Outies D/ = r4c4,r6c6 = +10(2) -> r4c4 = 9
Also 1 in D/ only in n7 -> 17(3)n7 = {179}

5! -> r5c5,r6c4 from {28} or {46}
In the latter case this puts 11(2)n3 = {38}, 12(2)n3 = {57}, [r3c7,r4c6] = [25]
It also puts r5c4,r6c5 (Outies n1478) = [83] and r5c3 = 7
But since r5c6 is Min 3 this leaves no value for it!
-> r5c5,r6c4 = {28}

6. Outies n78 = r6c15 = +9(2) -> remaining Innies r6 = r6c467 = +10(3) (No 8)
-> 19(3)n5 = [982]
-> 15(2)r5 = [96]
-> Remaining Innie n14 = r6c1 = 4
-> Remaining Outie n78 = r6c5 = 5
Also -> r6c467 = [217]
-> 15(2)r6 = {69}
-> 11(2)r6 = {38}

7. Innies n1 = r3c23 = +14(2)
Since 12(2)r3c3 cannot be [84] or [66] and 9 already in D\ -> r3c3 cannot be from (689) -> r3c23 = [95]
-> 12(2)r3c3 = [57]
Also -> 15(3)r3c2 = [9{15}]
-> 8(2)n4 = [62]

8. Also (HS 7 in n5) -> r5c6 = 7
-> r4c9 = 5
-> r45c2 = [15]

10. r3c7,r4c6 = {34}
Given r4c9 = 5 -> r23c7 = +11(2)
This cannot be [83] since 12(2)n3 from {39} or {48}
-> r23c7 = [74]
-> r4c56 = [43] and r2c6 = 4
Also 12(2)n3 = {39}
Also 11(2)n3 = [65]
Also 11(2)r2c4 = {38}
-> 17(3)r3c5 = [764]
-> 17(4)n2 = [{125}9]
-> r1c123 = [7{48}]
-> 8(2)n1 = {26} and r23c1 = {13}
-> 17(3)n7 = [179]
-> r78c1 = {58} and r7c2 = 3
Also 8(2)n7 = {26}, r8c3 = 4
etc.


Last edited by wellbeback on Tue Nov 23, 2021 12:25 am, edited 2 times in total.

Top
 Profile  
Reply with quote  
 Post subject: Re: Assassin 405
PostPosted: Mon Nov 22, 2021 11:29 pm 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
wellbeback's step 3 shows a much better way to solve this puzzle! Clearly my comment about its difficulty only applies to my solving path.

Andrew


Top
 Profile  
Reply with quote  
 Post subject: Re: Assassin 405
PostPosted: Wed Nov 24, 2021 8:26 pm 
Offline
Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
Sorry to put Andrew through the grinder. Clearly, there is a very narrow start to this puzzle. I saw that differently to wellbeback. Even with finding the start, it's still no gimme. My middle is very different, though I end up getting the same key elimination (wellbeback's step 5) at step 15. [Big thanks to Andrew for checking my WT so quickly!]

I have a few more V1 Assassins in the pipeline. My daily commute has changed slightly so have more puzzling time.
a405 WT:
Preliminaries from SudokuSolver
Cage 15(2) n6 - cells only uses 6789
Cage 15(2) n45 - cells only uses 6789
Cage 8(2) n7 - cells do not use 489
Cage 8(2) n4 - cells do not use 489
Cage 8(2) n1 - cells do not use 489
Cage 12(2) n3 - cells do not use 126
Cage 12(2) n14 - cells do not use 126
Cage 11(2) n4 - cells do not use 1
Cage 11(2) n3 - cells do not use 1
Cage 11(2) n2 - cells do not use 1
Cage 11(2) n23 - cells do not use 1
Cage 8(3) n35 - cells do not use 6789
Cage 19(3) n5 - cells do not use 1


This is a highly optimised solution so any clean-up, if required, is stated.

1. "45" on n14: 2 innies r5c3 + r6c1 = 13 (no 1,2,3)
1a. r6c1 = (4567)

2. "45" on n78: 2 outies r6c15 = 9 = [72/63]/{45}(r6c5 = (2345)

3. "45" on n2: 2 outies r2c7 + r4c5 = 11 (no 1)

4. "45" on n69: 1 outie r5c6 - 2 = 1 innie r4c9
4a. -> no 1,2 in r5c6, no 8,9 in r4c9

5. 1 in n5 only in r46c6 in 8(3)r3c7: 1 locked for c6 and no 1 in r3c7

key step
6. "45" on n9: 3 outies r4c8 + r56c9 = 12
6a. those 3 cells see all n9 apart from the 12(3)n9 so must exactly repeat there
6b. but r4c8 sees r78c8 so r4c8 = r7c7
6c. and 1 in r6 only in r6c69
6d. -> r4c8 and r7c7 <> 1
6e. -> no 1 in r4c8 nor r7c7

7. 1 in c7 only in r4589c7 -> no 1 in r56c9 (Common Peer Elimination CPE)

8. r6c6 = 1 (hsingle r6): placed for d\

9. "45" on d/: 1 remaining outie r4c4 = 9: placed for d\
9a. no 6 in r5c3
9b. -> no 7 in r6c1 (h13(2)n4)
9c. -> no 2 in r6c5 (h9(2)r6)

10. 1 on d/ only in 17(3)n7 = {179} only, 1 locked for n7, 7,9 for n7 and d/

11. "45" on n1: 2 innies r3c23 = 14 = [95/68]
11a. r4c3 = (47)
11b. 15(3)r3c2 = [6]{18/27/45}/[9]{15/24}(no 3, no 6 or 9 in r45c2)

12. 3 in n4 only in 8(2) = {35} or 11(2) = {38}
12a. -> {58} blocked from h13(2)n4
12b. = {49/67}(no 5,8) = 4 or 7
12c. no 7 in r5c4

13. killer pair 4,7 in r4c3 and h13(2)n4: both locked for n4
13a. no 1 in 8(2)n4

14. 1 in n4 only in 15(3) = [9]{15}/[6]{18}(no 2): 1 locked for c2

Love finding these ones.
15. "45" on n14: 1 outie r5c4 - 2 = 1 innie r6c1 = [64/86]
15a. must have 6 -> no 6 in r6c4 nor r5c1
15b. no 2 in r4c1

16. r5c5 + r6c4 = 10 (cage sum) = {28}/[64]

17. "45" on r6 including h9(2)r6c15: 2 remaining innies r6c49 = 9 = [27/45]
17a. no 2 in r5c5 (sp10(2)n5)
17b. -> h12(3)n6 must have 5,7 for r6c9 = {237/345}(no 6,8,9)
17c. must have 3: locked for n6 and 45(9)
17d. note: must have 2 or 5

18. naked pair {68} in r5c45: both locked for r5 and n5

19. 1 in n3 only in 16(4) -> no 1 in r4c9

20. "45" on n69: 1 outie r5c6 - 2 = 1 innie r4c9 = [42/75]

21. killer pair 2,5 in h12(3)n6 and r4c9: both locked for n6

22. hidden triple 2,3,5 in r5c129
22a. -> r5c2 = 5
22b. -> r34c2 = 10 = [91]
22b. r5c19 = {23}
22c. r45c1 = [62]
22d. r5c9 = 3

23. r6c1 = 4
23a. -> h9(2)r6c49 = [27] (2 placed for d/)
23b. -> r4c8 = 2 (h12(3))
23c. -> 12(3)n9 = [2]{37}(hidden single, then hidden pair): 2 placed for d\, 3,7 locked for c8

24. r34c3 = [57] (5 placed for d\)

Much easier now
Cheers
Ed


Top
 Profile  
Reply with quote  
 Post subject: Re: Assassin 405
PostPosted: Tue Dec 07, 2021 11:32 pm 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Don't worry about me! Ed and wellbeback both showed that there's a preferred start for this puzzle which I missed and clearly SudokuSolver isn't programmed to spot, hence the high score. In most puzzles there are always other ways to solve them. That's one of the beauties of Assassins!


Top
 Profile  
Reply with quote  
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 6 posts ] 

All times are UTC


Who is online

Users browsing this forum: No registered users and 8 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