SudokuSolver Forum

A forum for Sudoku enthusiasts to share puzzles, techniques and software
It is currently Sat Apr 27, 2024 7:46 pm

View unanswered posts | View active topics


Board index » Puzzles and Solutions » Killer Puzzles

All times are UTC




Post new topic Reply to topic  Page 1 of 1
  [ 4 posts ] 
  Print view Previous topic | Next topic 
Author Message
Ed
 Post subject: Assassin 440
PostPosted: Tue Aug 15, 2023 6:38 pm 
Offline
Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Attachment:
a440.png
a440.png [ 56.26 KiB | Viewed 13708 times ]
Assassin 440
This started as a plenty-hard-enough 1.40 but couldn't help myself and toughened the middle up a touch to get it to 1.65. JSudoku had to work on both versions so am getting really fussy here. Enjoyed the making and solving challenges!
triple click code:
3x3::k:3840:3840:3840:5121:5121:5121:4866:4611:5892:4357:4614:4631:4118:2312:5121:4866:4611:5892:4357:4614:4631:4118:2312:2312:4866:4611:5892:4614:4631:4631:8457:8457:8457:4866:7178:5892:4614:4631:8459:8457:8457:2316:2316:7178:7178:8459:8459:8459:8459:8457:1293:1293:7178:7178:8459:2574:2575:2575:4624:3345:3345:7178:3858:2574:3859:2575:4624:4624:4884:4884:4884:3858:3859:3859:3349:3349:3349:4884:2823:2823:3858:
solution: 
+-------+-------+-------+
| 2 7 6 | 3 5 4 | 1 9 8 |
| 9 3 4 | 7 1 8 | 5 6 2 |
| 8 5 1 | 9 2 6 | 4 3 7 |
+-------+-------+-------+
| 4 8 3 | 5 7 2 | 9 1 6 |
| 6 2 5 | 4 9 1 | 8 7 3 |
| 7 1 9 | 8 6 3 | 2 5 4 |
+-------+-------+-------+
| 3 9 2 | 1 4 7 | 6 8 5 |
| 1 4 7 | 6 8 5 | 3 2 9 |
| 5 6 8 | 2 3 9 | 7 4 1 |
+-------+-------+-------+
Cheers
Ed
Top
 Profile  
Reply with quote  
wellbeback
 Post subject: Re: Assassin 440
PostPosted: Wed Aug 23, 2023 5:39 pm 
Offline
Grand Master
Grand Master

Joined: Tue Jun 16, 2009 9:31 pm
Posts: 282
Location: California, out of London
Thanks Ed! I enjoyed this one a lot. I had a couple of small chains but since they opened up the puzzle so well I kept them in.
Assassin 440 WT:
1. 17(2)n1 = {89}
Innies n1 = r23c23 = +13(4) - Must contain a 1
-> 1 not in r45c2
18(5)r2c3 must contain a 1
-> 1 in r234c3

2. 18(5)r2c3 does not contain a 9
-> 9 in 33(6) in n4
16(2)n2 = {79}
Outies n14 = r6c4 + r7c1 = +11(2)
-> [r6c4,r7c1] from [83], [47], {56}
Innies r789 = r7c18 = +11(2)
-> r6c4 = r7c8

3. Innies c9 = r56c9 = +7(2)
Innies c89 = r89c8 = +6(2) = [15] or {24}
-> r8c8,r9c78 from [165], [274], or [492]

4! Outies n3 = r4c78 = +15(2) = {69} or {78}
-> If r7c8 < 6 that value goes in n6 only in r5c7
-> Trying r6c4 = r7c8 from (45) puts r5c7 = (45)
It also puts the other of (45) in r89c8 and in r5c6
Since it also puts r7c1 from (76) - this leaves no solution for 13(2)r7
-> r6c4 = r7c8 from (68)

5! Trying r6c4 = r7c8 = 6 puts r7c1 = 5 and r89c8 = {24} (since r7c8 = 6 prevents r89c8 = [15])
It also puts remaining Innies n5 = r56c6 = +6(2) = {24}. (Cannot be [51] since that puts r56c7 both 4)
-> this again leaves no solution for 13(2)r7
-> r6c4 = r7c8 = 8

6. -> r7c1 = 3
-> (38) in n4 in 18(5)
-> 18(5) = {12348}
Also 10(3)r7c3 = 1 in r7c4 and r78c3 from {27} or {45}
-> (Remaining Innie n7) 13(3)r9 = [8{23}]
Also -> r45c2 = {28} or {48} and r4c3 = 3
-> In the first case 2 in n1 in r1c1 -> 15(3)n1 = [276], 18(4)n12 = [{35}{46}], r23c3 = {14}
and in the second case 4 in n1 in r1c1 -> 15(3)n1 = [456], 18(4)n12 = [{37}{26}], r23c3 = {24}
-> in both cases 33(6)r5c3 = [{1579}83]

7. r145c1 = {246}
-> 10(2)n7 not {46}
-> 10(2)n7 = [91]
-> Innies c89 = r89c8 = [24]
-> r9c7 = 7
-> Remaining Innies n9 = r78c7 = +9(2) = [63]
-> r7c6 = 7
Also 15(3)n9 = [591]
-> (HS 9 in r9) r89c6 = [59]
Also -> Innies c9 = r56c9 = +7(2) = {34}
-> Remaining Innies n5 = r56c6 = +4(2) = [13]
-> r56c7 = [82]
-> Outies n3 = r4c79 = +15(2) = [96]
Also 5 in r9 in r9c12 -> r78c3 = [27]
etc.
Top
 Profile  
Reply with quote  
Andrew
 Post subject: Re: Assassin 440
PostPosted: Fri Aug 25, 2023 3:51 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Thanks Ed for your latest Assassin. From wellbeback's comments and a glance at his WT, we either solved it very differently or saw some steps differently. After my routine step 1, my steps 2a-2c were heavy going, then it started getting easier again. Maybe Ed will have found a third way to solve it.

Here's how I solved Assassin 440:
Prelims

a) R23C1 = {89}
b) R23C4 = {79}
c) R5C67 = {18/27/36/45}, no 9
d) R6C67 = {14/23}
e) 10(2) cage at R7C2 = {19/28/37/46}, no 5
e) R7C67 = {49/58/67}, no 1,2,3
f) R9C78 = {29/38/47/56}, no 1
g) 9(3) cage at R2C5 = {126/135/234}, no 7,8,9
h) 10(3) cage at R7C3 = {127/136/145/235}, no 8,9
i) 18(5) cage at R2C3 = {12348/12357/12456}, no 9

1a. Naked pair {89} in R23C1, locked for C1 and N1, clean-up: no 1,2 in R7C2
1b. Naked pair {79} in R23C4, locked for C4 and N2
1c. 9 in R1 only in R1C789, locked for N3
1d. 15(3) cage at R1C1 = {267/357/456}, no 1
1e. 1 in N1 only in R23C23, CPE no 1 in R45C2
1f. 18(5) cage at R2C3 = {12348/12357/12456}, 1 locked for C3
1g. 18(5) cage at R2C3 = {12348/12357/12456}, CPE no 2 in R56C3
1h. 10(3) cage at R7C3 = {127/136/145/235}
1i. 1 of {136/145} must be in R7C4 -> no 4,6 in R7C4
1j. 45 rule on N3 2 outies R4C79 = 15 = {69/78}
1k. 45 rule on C9 2 innies R56C9 = 7 = {16/25/34}, no 7,8,9
1l. 45 rule on C89 2 innies R89C8 = 6 = [15]/{24} -> R9C7 = {679}
1m. 45 rule on N14 2 outies R6C4 + R7C1 = 11 = [47/56/65/83]
1n. 45 rule on R789 2 innies R7C18 = 11 = [38/56/65/74]
1o. 45 rule on N5 2 outies R56C7 = 1 innie R6C4 + 2, IOU no 2 in R5C7, clean-up: no 7 in R5C6
1p. Min R6C4 = 4 -> min R56C7 = 6, max R6C7 = 4 -> no 1 in R5C7, clean-up: no 8 in R5C6
1q. 45 rule on N7 2 innies R7C1 + R9C3 = 1 outie R7C4 + 10
1r. Min R7C1 + R9C3 = 11, max R7C1 = 7 -> min R9C3 = 4
1s. 9 in N4 only in 33(6) cage at R5C3 = {135789/145689/234789/235689/245679} (cannot be {126789} which clashes with R6C67)
1t. Killer pair 1,2 in 33(6) cage and R6C67, locked for R6, clean-up: no 5,6 in R5C9
1u. Consider combinations for R7C18 = [38/56/65/74]
R7C18 = [38] => 10(3) cage at R7C3 = {127/145} => R7C4 = 1
or R7C18 = {56}, locked for R7
or R7C18 = [74] => R7C67 = {58}, 5 locked for R7
-> no 5 in R7C4

[Now I was running out of ideas so did some fairly heavy combination analysis, something I try to avoid doing these days.]
2a. 28(6) cage at R4C8 = {123589/134569/134578/234568} (cannot be {123679} which clashes with R4C79, cannot be {124579} = {1479}{25} which clashes with R89C8, cannot {124678} = {2478}{16} which clashes with R4C79), 3 locked for N6, clean-up: no 6 in R5C6, no 2 in R6C6
2b. 28(6) cage = {1389}[25]/{1569}{34}/{1578}{34}/{3468}[25] (cannot be {3459}[16]/{2568}{34} which clash with R89C8), no 2 in R45C8, no 1 in R5C9, no 6 in R6C9
2c. 4 of {134569/134578} is in R56C9, 4 of {234568} must be in R456C8 (cannot be {368}[25]4 which clashes with R4C79) -> no 4 in R7C8, clean-up: no 7 in R7C1 (step 1n), no 4 in R6C4 (step 1m)
2d. Killer pair 1,4 in 28(6) cage and R89C8, locked for C8
2e. 18(3) cage at R1C8 = {279/369/378/567}
2f. 9 of {279} must be in R1C8 -> no 2 in R1C8
2g. Consider placement for 2 in N6
2 in R5C9
or 2 in R6C7 => R6C6 = 3, R6C9 = 4
-> R56C9 = [25/34]
2h. 45 rule on N5 3 innies R5C6 + R6C46 = 12 = {138/345} (cannot be {156} = [561] because 9(2) cage at R5C6 is 4 more than 5(2) cage at R6C6), cannot be {246} = [264] which clashes with R56C9), no 2,6, 3 locked for C6 and N5, clean-up: no 7 in R5C7, no 5 in R7C1 (step 1m), no 6 in R7C8 (step 1n)
2i. R6C4 = {58} -> no 5 in R5C6, no 4 in R5C7
2j. 10(3) cage at R7C3 = {127/145/235} (cannot be {136} which clashes with R7C1), no 6
2k. R7C67 = {49/67} (cannot be {58} which clashes with R7C8), no 5,8
2l. R56C6 = {13/34} -> R56C7 must contain one of 2,6
2m. 28(6) cage = {1389}[25]/{1569}{34}/{1578}{34} (cannot be {3468}[25] which clashes with R56C7), 1 locked for C8 and N6, clean-up: no 4 in R6C6, no 5 in R9C8 (step 1l), no 6 in R9C7
2n. Naked pair {24} in R89C8, locked for C8 and N9, clean-up: no 9 in R7C6
2o. Naked pair {24} in R89C8, CPE no 2,4 in R9C6
2p. 4 in N6 only in R6C79, locked for R6
2q. 15(3) cage at R7C9 = {159/168} (cannot be {357} which clashes with R56C9), no 3,7, 1 locked for C9 and N9
2r. R8C7 = 3 (hidden single in N9), clean-up: no 7 in R7C2
2s. 7 in N9 only in R79C7, locked for C7, clean-up: no 8 in R4C9 (step 1j)
2t. Max R8C78 = 7 -> min R89C6 = 12, no 1,2 in R89C6

3a. Consider combination for R7C67 = [49]/{67}
R7C67 = [49] => R56C6 = {13}, R6C4 = 8 (step 2h) => R7C1 = 3 (step 1m)
or R7C67 = {67}, 6 locked for R7
-> R7C1 = 3, R6C4 = 8 (step 1m), R56C6 = {13} (step 2h), 1 locked for C6 and N5, clean-up: no 5 in R5C7, no 7 in R8C1
[Cracked, the rest is fairly straightforward]
3b. 10(3) cage at R7C3 (step 2j) = {127/145} -> R7C4 = 1
3c. R7C4 = 1 -> R7C1 + R9C3 = 11 (step 1q), R7C1 = 3 -> R9C3 = 8, R9C45 = 5 = {23}, locked for R9 and N8, R9C8 = 4 -> R9C7 = 7, R8C8 = 2, clean-up: no 6 in R7C6
3d. R7C3 = 2 (hidden single in N7) -> R8C3 = 7 (cage sum)
3e. R7C1 = 3 -> R7C8 = 8 (step 1n) -> 15(3) cage at R7C9 (step 2q) = {159}, 5,9 locked for C9, 9 locked for N9, R7C7 = 6 -> R7C6 = 7, clean-up: no 4 in R8C1
3f. R6C79 = [24] -> R6C6 = 3, R5C679 = [183], R4C7 = 9 -> R4C9 = 6 (step 1j)
3g. Naked triple {157} in R456C8, 5,7 locked for C8
3h. 1 in R6 only in R6C12, locked for N4
3i. 1 in C3 only in R23C3, locked for N1

4a. R6C4 + R7C1 = [38], 1,9 in N4 only in 33(6) cage at R5C3 -> {135789} (only possible combination), 7 locked for R6 and N4 -> R56C8 = [75], R56C3 = [59], R6C5 = 6, R5C5 = 9 (hidden single in N5)
4b. 18(3) cage at R7C5 = {468} (only remaining combination) -> R7C5 = 4, R8C45 = [68], R7C2 = 9, R8C1 = 1, R6C12 = [71]
4c. Naked pair {56} in R9C12, 5 locked for R9 and N7 -> R8C2 = 4, R89C6 = [59]
4d. Naked pair {24} in R4C16, locked for R4 -> R4C2345 = [8357]
4e. R4C23 = [83] = 11 -> R23C3 + R5C2 = 7 = {124} -> R23C3 = {14}, 4 locked for N1, R5C2 = 2
4f. R45C1 = [46] = 10 -> R23C2 = 8 = {35}, locked for N1, R4C6 = 2
4g. 15(3) cage at R1C1 = [276] -> R1C69 = [48]
4h. R3C6 = 6 -> R23C5 = 3 = {12}, locked for C5

and the rest is naked singles.
Top
 Profile  
Reply with quote  
Ed
 Post subject: Re: Assassin 440
PostPosted: Sun Aug 27, 2023 5:07 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
I saw some of the fun features that wellbeback used but couldn't see as far ahead as he does. My way is closer to Andrew but think it definitely is a 'third way'. [Big thanks to Andrew for finding a mistake I made at the end]

This is how I got started.
My start:
Preliminaries
Cage 16(2) n2 - cells ={79}
Cage 17(2) n1 - cells ={89}
Cage 5(2) n56 - cells only uses 1234
Cage 13(2) n89 - cells do not use 123
Cage 9(2) n56 - cells do not use 9
Cage 10(2) n7 - cells do not use 5
Cage 11(2) n9 - cells do not use 1
Cage 9(3) n2 - cells do not use 789
Cage 10(3) n78 - cells do not use 89
Cage 18(5) n14 - cells do not use 9

1. 17(2)n1 = {89}: both locked for c1 and n1

2. 16(2)n2 = {79}: both locked for c4 and n2

3. 2 outies n14: r6c4 + r7c1 = 11 = [47]/{56}/[83]
3a. r6c4 = (4568), r7c1 = (3567)

4. "45" on r789: 2 innies r7c18 = 11
4a. -> r7c8 = (4568)

5. "45" on c89: 2 innies r89c8 = 6 = [15]/{24}
5a. -> r8c8 + r9c78 = [165/274/492]

6. "45" on n3: 2 outies r4c79 = 15 = {69/78}

7. "45" on c9: 2 innies r56c9 = 7 = {16/25/34}
7a. -> r4567c8 = h21(4)

Key steps
8. if combined cage {78/16} in r4c79 + r56c9 -> h21(4)?
8a. note: can't have 1 or 6 since it sees both {16} in r56c9
8b. can't be {2379} since none are in r7c8
8c. can't be {2478} which must have 7 in n6
8d. can't be {3459} which clashes with h6(2)r89c9
8e. -> can't have that combined cage -> can't have {16}
8f. -> h7(2) = {25/34}

9. 15(3)n9: {249/357} blocked by h7(2)n6
9a. {258/456} blocked by h6(2)n9
9b. {348} + [165] with r8c8 + r9c78 (step 5a) blocked by r7c8 = (4568)
9c. = {159/168/267}(no 3,4) = 1 or 5 or 6
9d. -> r8c7 = 3 (hsingle n9)

10. from step 5a, r8c8 + r9c78 = [165] blocked by 15(3)n9
10a. = [274/492]
10b. -> {24} in r89c8 locked for c8 and n9 and no 2,4 in r9c6 (Common Peer Elimination CPE)
10c. no 6 in r9c7
10d. no 9 in r7c6

The original puzzle was stone dead now so from here is the toughened up middle.
11. h11(2)r7c18 = [38]/{56}(no 7) = 5 or 8

12. 13(2)r7c6: {58} blocked by h11(2)
12a. = [49]/{67} (no 5,8)

13. 5 in n9 only in r7c8 or 15(3)
13a. -> no 5 in r56c9 (CPE)
13b. -> h7(2)r56c9 = {34} only: both locked for c9 and n6

14. h21(4)r4567c8 = {1569/1578}: 1 & 5 locked for c8, 1 for n6
14a. -> r6c56 = [32]
14b. r56c9 = [34]

15. "45" on n5: 2 remaining innies r5c6 + r6c4 = 9 = [18/45]

16. "45" on c789: 2 remaining outies r57c6 - 6 = 1 remaining innie r8c8
16a. r8c8 = (24) -> r57c6 = 8/10 = [17/46]

17. 13(2)r7c6 = {67} only: both locked for r7
17a. -> h11(2)r7 = [38] only
17b. -> r6c4 = 8 (outiesn12=11)

18. r7c8 = 8 -> h21(4)c8 = {157}[8]
18a. 5,7 locked for n6: 7 for c8

19. 9(2)r5c6 = [18] only permutation
19a. -> r7c6 = 7, r8c8 = 2 (step 16a)
19b. r9c78 = [74]

20. r8c78 = 5 -> r89c6 = 14 = {59/68}

21. "45" on n7: 3 outies r7c4 + r9c45 = 6 = {123}, 1,2 locked for n8
21a. r9c45 = {13/23} = 4 or 5 -> r9c3 = (89)

Looks I messed up this last part. I'll fix it up later. Thanks Andrew!
On from there
Cheers
Ed
Top
 Profile  
Reply with quote  
Display posts from previous:  Sort by  
Post new topic Reply to topic  Page 1 of 1
  [ 4 posts ] 

Board index » Puzzles and Solutions » Killer Puzzles

All times are UTC


Who is online

Users browsing this forum: No registered users and 56 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