SudokuSolver Forum

A forum for Sudoku enthusiasts to share puzzles, techniques and software
It is currently Mon Dec 17, 2018 3:35 pm

All times are UTC




Post new topic Reply to topic  [ 3 posts ] 
Author Message
 Post subject: Assassin 364
PostPosted: Sat Dec 01, 2018 7:57 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 774
Location: Sydney, Australia
Attachment:
a364.JPG
a364.JPG [ 64.05 KiB | Viewed 62 times ]
This is the third version of this puzzle. The first two versions were one trick puzzles which just doesn't satisfy anymore. This one makes you work for much longer - and I found it quite difficult to break. Very satisfying to finally get a decent solution! SudokuSolver gives it 1.90 and JSudoku needs to use 6 chains.
code:
3x3::k:5632:5632:3585:3585:3585:5378:4099:4099:4099:7940:5632:5632:3585:3589:5378:4099:5382:5382:7940:1543:1543:4360:3589:5378:2313:2313:5382:7940:0000:0000:4360:4360:2315:2315:0000:5382:7940:7940:5645:5645:5645:5645:5645:0000:0000:4110:7940:2831:2831:3344:3344:3345:3345:0000:4110:1042:1042:5139:2324:3344:3349:3349:0000:4110:4110:6678:5139:2324:5642:3340:3340:0000:6678:6678:6678:5139:5642:5642:5642:3340:3340:
solution:
Code:
+-------+-------+-------+
| 6 7 5 | 3 2 8 | 4 1 9 |
| 3 1 8 | 4 9 6 | 2 5 7 |
| 9 4 2 | 1 5 7 | 6 3 8 |
+-------+-------+-------+
| 2 6 3 | 9 7 4 | 5 8 1 |
| 4 8 7 | 6 1 5 | 3 9 2 |
| 1 5 9 | 2 8 3 | 7 6 4 |
+-------+-------+-------+
| 8 3 1 | 7 6 2 | 9 4 5 |
| 5 2 4 | 8 3 9 | 1 7 6 |
| 7 9 6 | 5 4 1 | 8 2 3 |
+-------+-------+-------+

Cheers
Ed


Top
 Profile  
Reply with quote  
 Post subject: Re: Assassin 364
PostPosted: Fri Dec 07, 2018 10:44 pm 
Offline
Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 774
Location: Sydney, Australia
Here's how I solved it. Steps 8, 19 & 26 are my keys with one of those steps getting no (useful) eliminations!
WT 364:
Prelims courtesy of SudokuSolver
Preliminaries
Cage 4(2) n7 - cells ={13}
Cage 6(2) n1 - cells only uses 1245
Cage 14(2) n2 - cells only uses 5689
Cage 13(2) n9 - cells do not use 123
Cage 13(2) n6 - cells do not use 123
Cage 9(2) n56 - cells do not use 9
Cage 9(2) n8 - cells do not use 9
Cage 9(2) n3 - cells do not use 9
Cage 11(2) n45 - cells do not use 1
Cage 21(3) n2 - cells do not use 123
Cage 20(3) n8 - cells do not use 12
Cage 13(4) n9 - cells do not use 89
Cage 14(4) n12 - cells do not use 9
Cage 26(4) n7 - cells do not use 1

No routine clean-up done unless stated
1. "45" on n7: 1 outie r6c1 = 1
1a. "45" on n3: 1 outie r4c9 = 1

2. 4(2)n7 = {13} only: both locked for n7 and r7

3. "45" on n8: 1 innie r7c6 + 6 = 1 outie r9c7 = [28] only permutation
3a. r7c6 = 2 -> r6c56 = 11 (no 9)
3b. no 7 in 9(2)n8, no 6,8 in r8c5
3c. no 5 in 13(2)n9

4. 21(3)n2: {489} blocked by 14(2)n2 needing an 8 or 9
4a. = {579/678}(no 4)
4b. must have 7: 7 locked for n2 and c6
4c. no 4 in r6c5 (sp11(2))

5. 14(2)r23c5 = {59/68}; 9(2)r78c5 = [81]/[63]/{45}
5a. if 14(2) = {68} -> 9(2) = {45}; or 14(2) = {59}
5b. -> 5 locked in one of those two cages: locked for c5 (combined cages)
5c. no 6 in r6c6 (sp11(2))

6. "45" on n2: 1 innie r3c4 + 4 = 1 outie r1c3
6a. r1c3 = (5678), r3c4 = (1234)
6b. hidden quad 1,2,3,4 in n2 -> r123c4+r1c5 = {1234}
6c. 17(3)r3c4 can only have one of 1,2,3,4 -> no 2,3,4 in r4c45

7. 20(3)r7c4 = {389/479/569/578} = two of 6..9
7a. -> r456c4 must have two of 6..9 for c4
7b. r4c5 = (6789)
7c. sp11(2)r6c56 must have one of 6,7,8
7d. -> killer quad 6,7,8,9 in those four areas: all locked for n5 (hidden killer quad)
7e. r4c7 = (456)

Ready for the first advanced step - which totally cracked one of the previous versions of this puzzle
8. 21(3)n2 = {579}/678}
8a.if {579} -> 14(2)n2 = {68} (combined cage)
8b. r9c7 = 8 -> r89c6 + r9c5 = 14 = {149/167/347/356}
8c. if {149} -> 9(2)n8 = {36} only (combined cage)
8d. 9 in c6 in one of 21(3)n2 or r89c6 -> 14(2)n2 = {68} or 9(2)n8 = {36}
8e. must have 6: 6 locked for c5
8f. no 5 in r6c6 (sp11(2))

9. 6 in c5 in 14(2)n2 = {68} or 6 in 9(2)n8 -> no {18} in 9(2)n8 since it would block all 6 in c5 (locking-out cages)
9a. 9(2) = [63]/{45}

10. 8 in n8 only in 20(3) = {389/578}(no 4,6) = 3 or 5
10a. 8 locked for c4

11. 9(2)n8 = [63]/{45} = 3 or 5
11a. killer pair 3,5 with 20(3) (step 10): both locked for n8

12. 3 in c6 only in n5: 3 locked for n5
12a. no 8 in r6c6 (sp11(2))

13. 8 in c6 only in 21(3)n2 = {678} only: 6,8 locked for n2, 6 for c6

14. 14(2)n2 = {59}: both locked for c5
14a. r78c5 = [63]
14b. 13(2)n9 = {49} only: both locked for n9 and r7

15. "45" on n9: 2 remaining innies r78c9 = 11 = [56] only permutation

16. 16(4)r6c1: must have 7 or 8 for r7c1 = [1]{258} only
16a. R7C1 = 8
16b. r8c12 = {25} both locked for r8
16c. r7c4 = 7

17. r8c4 = 8 (hidden single n8)
17a. r9c4 = 5 (cage sum)

18. 17(3)r3c4 must have 6 or 9 for r4c4, and 7 or 8 for r4c5 = {179/368/467}(no 2)
18a. no 6 in r1c3 (IODn2=-4)

Next key step
19. "45" on n2: 3 outies r1c3 + r4c45 = 21 = [5][97]/[7][68]/[8][67]:
19a. note: must have 5 in r1c3 or 6 in r4c4
19b. note2: must have 7 in r1c3 or r4c5
19c. note: no eliminations yet (can take 7 from r4c3 but not important to this optimised solution)

20. 11(2)r6c3: [56] blocked by step 19a
20a. = {29}/[74] = 4 or 9

21. 13(2)n6: {49} blocked by 11(2)n4
21a. = [58]/{67}(no 4,9; no 5 in r6c8)

22. hidden pair 5,6 in r6. 13(2)n6 can only have one of 5,6 -> r6c2 = (56)

23. "45" on r6: 2 remaining innies r6c29 = 9 = [54/63]

24. hidden pair 2,9 in r6 -> 11(2)r6c3 = {29} only

25. "45" on n1: 3 innies r1c3 + r23c1 = 17
25a. but {458} blocked by 6(2)n1 needing 4 or 5
25b. must have 5,7,8 for r1c3 = {278/359/368/467}
25c. note: if has 7 in r1c3 must have {46} in r23c1
25d. note: no eliminations yet

The final crack by removing 6 from r6c2
26. from step 19b. must have 7 in r1c3 or r4c5
26a. if in r1c3 -> r23c1 = {46} (step 25c) -> no 6 in r6c2 (same cage)
26b. if in r4c5 -> 7 in r6 only in 13(2)r6c78 = {67}
26c. -> both places have 6 -> no 6 in r6c2

27. r6c2 = 5
27a. r6c9 = 4 (h9(2)r6c29), r6c56 = [83], r4c5 = 7 -> r34c4 = 10 = [19/46] (no 3)
27b. no 7 in 1c3 (IODn2=-4)
27b. r8c12 = [52]

28. 31(6)r2c1 = {23489}[5]/{23678}[5]
28a. must have 8 -> r5c2 = 8
28b. must have 2 & 3 which are only in c1: locked for c1

29. naked pair {14} in r3c24: both locked for r3

30. naked pair {67} in r6c78: locked for n6
30a. r4c67 = [45], naked pair {19} in r89c6: 1 locked for n8 and c6, r9c5 = 4, r5c6 = 5

31. 22(5)r5c3 must have 1 for n5 = {13459/13567}(no 2)
31a. must have 3: 3 locked for r5
31b. r5c5 = 1

32. naked pair {29} in r5c89: both locked for r5 and n6

Straightforward now.
Cheers
Ed


Top
 Profile  
Reply with quote  
 Post subject: Re: Assassin 364
PostPosted: Sat Dec 08, 2018 9:22 pm 
Offline
Master
Master

Joined: Tue Jun 16, 2009 9:31 pm
Posts: 172
Location: California, out of London
Thanks Ed! This was the puzzle that kept on giving. As you wrote - several key steps needed.
As usual I wrote my WT before reading yours. Some similarities and some differences. Where there were similarities we often approached each step from opposite directions.
Assassin 364 WT:
1. Outies n3 -> r4c9 = 1
Outies n7 -> r6c1 = 1
-> 1 in n5/r5 in r5c456

2. 4(3)n7 = {13}
Outies - Innies n8 -> r9c7 = r7c6 + 6
-> [r7c6,r9c7] = [28]

3. Innies n2 -> r1c45 + r23c4 = +10(4) = {1234}
-> 21(3)n2 = {7(68|59)}
Also Since Max r3c4 = 4 -> both r4c45 are Min 5.

4! 1 in c6 only in r589c6
9 in c6 in one of:
a) r123c6 -> 14(2)n2 = {68}
b) r5c6 -> 1 in r89c6
c) r89c6 -> 22(4)n8 = [{149}8]
In none of those cases can 9(2)n8 be {18}
-> 8 in n8 in 20(3)n8
-> 20(3)n8 = {8(57|39)}

5! 6 in c4 only in n5 in r456c4
Also -> 1 in n8 in 22(4)n8
-> 3 in n8 in 20(3) or 9(2)
-> 3 in c6 in n5 in r456c6
-> 13(3) r6c5 from [832] or [742]
If the former -> 14(2)n2 = {59} -> 9(2)n8 = [63] -> 20(3)n8 = {578}
If the latter -> 7 in 20(3)n8 = {578} -> 9(2)n8 = [63] -> 14(2)n2 = {59}
Either way 20(3)n8 = {578}, 9(2)n8 = [63], 14(2)n2 = {59}, 21(3)n2 = {678}, 22(4)n8 = [{149}8]
-> 9 in c4 in n5 in r456c4
Also 5 in c6 in n5 in r45c6
Also -> r46c5 = {78}

(Having read Ed's WT the next step is more complicated than it need be since 13(2)n9 can already only be {49})!

6! Remaining Innies n9 -> r78c9 = +11(2)
3 in r9 only in r9c89
-> 13(4)n9 cannot contain a 6
-> 6 in n9 in 13(2) or H11(2)
-> 6 in r9 in n7 in r9c123
-> 2 in n7 in r8c12
-> 2 in r9 in r9c89
-> 13(4)n9 = [{17}{23}]
-> 13(2)n9 = {49}
-> r78c9 = [56]
-> 16(4)r6c1 can only be [18{25}]
-> 20(3)n8 = [785]
Also 26(4)n7 = {4679} with r8c3 from (49)
Also 22(4)n8 = [{149}8] with r8c6 from (49)

7. (27) already in c6 and 1 already in r4c9 -> 9(2)r4 from {36} or {45}
r4c4 from (69) and r4c5 from (78)
-> 17(3)r3c4 from [197], [368], [467]
The first of these -> r6c56 = [83]
-> In all cases 9(2)r4 can only be {45}

8. 8 in n5 in r46c5 and 3 in n5 in r56c6
-> 11(2)r6 cannot be {38}
Remaining Innies r6 -> r6c29 = +9(2) (No 9)
-> 9 either in 11(2)r6c3 = {29} or 13(2)r6 = {49}
-> 11(2)r6 cannot be {47}
-> 11(2)r6c3 from {29} or [56]

9. 5 in r7c9 prevents H9(2)r6c29 = [45]
-> 4 in n4 in r5c123
-> 4 in n5 only in r46c6
-> 22(4)n8 = [9418]
-> 26(4)n7 = [4{679}]
-> 4 in n4 in r5c12
-> 31(6) = {2349(58|67)}

10. Innies n1 = r1c3 + r23c1 = +17(3)
Innies - Outies n2 -> r1c3 = r3c4 + 4
Since r3c4 from (134) -> r1c3 from (578)
But r1c3 = 7 -> r23c1 = +10(2) for which there is no solution
-> r1c3 from (58)
-> r3c4 from (14)
-> 17(3)r3c4 from [197] or [467]
-> r4c5 = 7
-> 13(3)r6c5 = [832]

(This next step is essentially Ed's Step 19a).

11! 5 in r6 only in r6c23
r1c3 from (58)
If r1c3 = 5 puts 5 in r6c2
If r1c3 = 8 puts 17(3)r3c4 = [467] -> 5 not in r6c3
Either way r6c2 = 5

12. -> r6c9 = 4
-> 9(2)r4 = [45]
Also 13(2)n6 = {67}
-> 11(2)r6 = {29}
Also r8c12 = [52]
Also -> 31(6) = {234589}
-> r5c2 = 8
-> r5c1 = 4
-> r234c1 = {239}
-> Innies n1 can only be r1c3 = 5, r23c1 = {39}
-> r4c1 = 2 and r3c4 = 1
-> r4c4 = 9
-> 11(2)r6 = [92]
-> r5c456 = [615]
Also 6(2)n1 = [42]
etc.


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 10 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