SudokuSolver Forum

A forum for Sudoku enthusiasts to share puzzles, techniques and software
It is currently Sat Apr 27, 2024 2:58 pm

All times are UTC




Post new topic Reply to topic  [ 54 posts ]  Go to page Previous  1, 2, 3, 4, 5, 6  Next
Author Message
PostPosted: Sun Jul 31, 2011 4:18 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Puzzle rating table, with links to archive entries; each of these has a link to the puzzle thread.

Abbreviations used in Rating Table:
Est = Estimated rating by puzzle maker
E = Easy
H = Hard
Score = SudokuSolver v3.3 score, rounded to nearest 0.05
** in the Afmob column indicates that these puzzles were made by him,
for these ones the estimate is his rating.
+------------------------+-----------+-------+-------+-------+-----------------------+-------+
| Puzzle | Made By | Est | Afmob | Andrew| Other Raters | Score |
+------------------------+-----------+-------+-------+-------+-----------------------+-------+
| Tetris Killer | tarek | | 1.25 | H1.25 | | 1.75 |
| Tetris KillerV2 | tarek | | | H1.25 | | 1.20 |
| Assassin 146 | manu | | H1.25 | H1.25 | | 3.50 |
| JFFK4 | manu | | E1.50 | 1.50 | | 1.65 |
| Assassin 147 | tarek | | H1.00 | 1.25 | | 1.15 |
| Assassin 148 | Afmob | 1.25 | ** | 1.25 | (Ed) E1.50 | 1.35 |
| JFFK5 | manu | | 1.25 | E1.50 | | 1.40 |
| Assassin 149 | manu | | H1.25 | H1.50 | (Ed) E1.50 | 1.70 |
| Assassin 149V2 | manu | | H1.50 | H1.50 | | 2.15 |
+------------------------+-----------+-------+-------+-------+-----------------------+-------+


Some of the selected quotes in the puzzle entries have been edited to remove "spoilers"; the full rating comments are included with the walkthroughs. In some cases the puzzle makers gave hints; these are included in tiny text in the selected quotes.


Last edited by Andrew on Thu Aug 04, 2011 1:32 am, edited 4 times in total.

Top
 Profile  
Reply with quote  
PostPosted: Sun Jul 31, 2011 4:57 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Tetris Killer by tarek (March 2009) here
Puzzle Diagram:
Image
Images with "udosuk style Killer Cages" by Børge:
Image     Image
Code: Select, Copy & Paste into solver:
3x3::k:5382:2835:7188:5121:5121:5121:5383:5896:4869:5382:2835:7188:7188:5121:5383:5383:5896:4869:5382:2835:2835:7188:2562:5383:5896:5896:4869:5382:7698:7698:2562:2562:2562:4362:4362:4869:7698:7698:5137:5137:21:4105:4105:4362:4362:5392:5392:5137:5137:6404:4105:4105:4619:4619:5134:5392:5392:6404:6404:6404:4619:4619:5900:5134:3599:3599:4611:4611:4611:5901:5901:5900:5134:5134:3599:3599:4611:5901:5901:5900:5900:
81-character code string
LBSK<<LNJ^^^<^>^^^^^<^A^>^^^U<>^<H<^>^K<0G<^<L<^^P^^I<K^<>^<>^N^E<I<<N<^^<^<^>^>^
Solution:
+-------+-------+-------+
| 4 3 6 | 7 8 2 | 9 5 1 |
| 9 1 8 | 5 3 6 | 2 4 7 |
| 7 2 5 | 9 1 4 | 6 8 3 |
+-------+-------+-------+
| 1 6 7 | 4 2 3 | 5 9 8 |
| 8 9 4 | 6 7 5 | 3 1 2 |
| 3 5 2 | 8 9 1 | 7 6 4 |
+-------+-------+-------+
| 2 4 9 | 3 5 8 | 1 7 6 |
| 5 8 3 | 1 6 7 | 4 2 9 |
| 6 7 1 | 2 4 9 | 8 3 5 |
+-------+-------+-------+
Quote:
tarek: I'm not sure if this qualifies as an Assassin, it should prove difficult with an SSS=1.73 .... It follows the Tetris theme (I didn't have time to colour it :brickwall: , I'll be tempted if you like it :whistle: ) ...
Enjoy

rcbroughton: This thread gave rise to a great discussion on the nature of Assassins versus regular Killers - by popular demand, I've moved that portion of the discussion to a "sticky" topic here What is an Assassin

Andrew: It's good to see that you've now posted some puzzles with SS scores below two. Maybe next time you produce puzzles at this level you could sign up to post as Assassins. IMHO, just from glancing at the puzzles before I try them, the easier one could have been posted as an Assassin with the harder one as a V2 provided that there was already a volunteer for the following week's Assassin.
Maybe it's a good thing that you didn't colour it. I've just done that on my Excel worksheet and it immediately highlights the hole in the middle.
It was also interesting to note that the first puzzle has four cages which are immediately naked quads but the lighter version doesn't have any. Despite that, the lighter version is definitely the easier of the two.

Afmob: I have to agree with Andrew that it would have been better to use these Killers as Assassins. By the way, you might want to use the recent SudokuSolver version (3.3.0) for the ratings.
Rating: 1.25.

tarek: So I missed my chance for an Assassin :brickwall:
I would probably want to sign up for 1 assassin & then disappear to improve Generated puzzles design before returning :cheesey:
So ,, where should I sign up ?!

manu: I won't post any WT for this "V1" because there are many steps similar to Afmob. On the other hand, I 'd like to point out a decisive move that enables me to crack this puzzle in a different way.

Andrew (in 2010): Here is another puzzle from my unsolved backlog; I managed to solve the Lite version when it was active but had got stuck on the original Tetris Killer. Having gone through Afmob's walkthrough it looks as if some parts of the solving path are fairly narrow but my key breakthrough ... was very different.
I'll rate my walkthrough for Tetris Killer at least Hard 1.25.

Walkthrough by Afmob:
I have to agree with Andrew that it would have been better to use these Killers as Assassins. By the way, you might want to use the recent SudokuSolver version (3.3.0) for the ratings.

Edit: I made a logical mistake (forgot a combo). Thanks for finding it, manu! My walkthrough should be ok now.

Tetris Killer Walkthrough:

1. R1234 !
a) 11(4) = {1235} locked for N1
b) Innies+Outies C123: -13 = R4C1 - R12C3 -> R4C1 = (1234), R12C3 <> 4
c) 4 locked in 21(4) @ N1 for C1
d) ! Outies R123 = 18(5) = {12348} since R4C1456 = {1234} -> R4C9 = 8; 1,2,3,4 locked for R4; 4 also locked for N5+10(4)
e) 10(4) = {1234} -> CPE: R56C5 <> 1,2,3
f) 28(4): R23C4 <> 6,7 since 4,5 only possible there and R12C3 = {89} blocked by Killer pair (89) of 21(4) @ N1

2. R456
a) Innie of grid = R5C5 = 7
b) 30(4) = {6789} locked for N4; 7 also locked for R4; 8 also locked for R5
c) 5 locked in 17(4) @ R4 for N6 -> 17(4) = 25{19/46} -> 2 locked for R5+N6; R5C89 = (124)

3. R789
a) Innies+Outies N7: -11 = R9C4 - R7C23 -> R9C4 <> 7,8; R7C23 <> 1,2
b) Innies+Outies N9: 1 = R9C6 - R7C78 -> R9C6 <> 1,2,3; R7C78 <> 8,9
c) Outies N9 = 19(2+1): R9C6 <> 5 because R6C89 <> 5,8
d) Outies N9 = 19(2+1): R9C6 <> 4 because R6C89 = {69} blocked by R4C78 = (569)
e) R9C6 <> 8 since it sees all 8 of N9

4. C456 !
a) ! 7 locked in Innies C1234 = 15(4) = 17{25/34} -> 1 locked for C4
b) Killer pair (45) locked in Innies C1234 + 28(4) for C4
c) Innies+Outies N8: -2 = R6C5 - R9C46 -> R6C5 <> 5 since R9C46 >= 8
d) 5 locked in 16(4) @ N5 for C6 -> 16(4) = 5{128/137/146/236} <> 9
e) Innies+Outies N8: -2 = R6C5 - R9C46 -> R9C4 <> 6 because R9C6 >= 6
f) 6 locked in R56C4 @ C4 for N5
g) Killer pair (23) locked in Innies C1234 + R9C4 for C4
h) Naked triple (689) locked in R56C4+R6C5 for N5
i) R6C6 <> 3 since it sees all 3 of N6

5. R456 !
a) Naked triple (689) locked in R5C124 for R5
b) 16(4) = 5{137/146/236} -> R6C7 = (67)
c) ! Innies R6789 = 18(4) <> 5 because R6C47 >= 13
d) 16(4) = 5{137/146/236} -> R5C6 = 5; R5C7 = (34)
e) 20(4) = 6{149/239/248} (step 4f); R6C3 <> 3 since 2 only possible there
f) Innies R6789 = 18(4) = 1{269/278/467} -> 1 locked for R6
g) 1 locked in 17(4) @ N6 = {1259} for R5 -> 9 locked for R4+N6
h) 30(4) = {6789} -> R5C12 = {89} locked for R5
i) R5C4 = 6
j) 3 locked in 10(4) @ N5 for R4+10(4)

6. N478
a) Killer pair (12) locked in 20(4) + R4C1 for N4
b) 5 locked in R6C12 @ N4 for 21(4) -> 21(4) = 35{49/67}
c) Outies N7 = 10(2+1) = 2+{35} -> R9C4 = 2; 3 locked for R6+N4+21(4)
d) Innies+Outies N8: R6C5 = R9C6 = 9
e) R5C3 = 4, R6C4 = 8 -> R6C3 = 2, R6C6 = 1, R5C7 = 3 -> R6C7 = 7, R4C1 = 1
f) 21(4) @ N1 = {1479} -> 7,9 locked for C1+N1
g) Hidden Single: R7C3 = 9 @ C3
h) 21(4) @ N7 = {3459} -> R7C2 = 4
i) 14(4) = 12{38/56} -> 1 locked for N7
j) R5C1 = 8
k) 20(4) @ N7 = {2567} since (78) only possible @ R9C2 -> R9C2 = 7; 5,6 locked for C1+N7

7. C4567
a) 28(4) = {5689} -> 6,8 locked for C3; 5 locked for C4+N2
b) Innies N3 = 11(2) = {29/56}
c) Killer pair (59) locked in Innies N3 + R4C7 for C7
d) 18(4) @ N9 = {1467} since R6C89 = {46} and R7C7 <> 3,5 -> R7C7 = 1, R7C8 = 7
e) 25(4) = {3589} -> R7C4 = 3, R7C6 = 8, R7C5 = 5
f) 23(4) @ N8 = {2489} locked for N9 because R89C7 <> 3,5; 2 also locked for R8

8. N238
a) 10(4) = {1234} -> R3C5 = 1
b) 18(4) = {1467} -> R8C4 = 1, R8C6 = 7; 4,6 locked for C8
c) Outies N3 = 10(2) = {46} locked for C6+N2+21(4)
d) Innies N3 = 11(2) = {29} locked for C7+N3

9. Rest is singles.

Rating: 1.25. I used Killer pairs of large Innies.
manu's decisive move:
I won't post any WT for this "V1" because there are many steps similar to Afmob. On the other hand, I 'd like to point out a decisive move that enables me to crack this puzzle in a different way. It' something similar to Ed's technic IOE, but one only obtains an inequality (similar to IOI technic I have used for JFF1)

Following Afmob's WT for instance, one can obtain r56c4=(689) and r6c5=(89) and obtain a naked triple {689}
for n5.

From this situation, using Innies-Outies for n7, we have r7c23 = 11+r9c4 so r7c2, r7c3 <>r9c4. We deduce that digit at r9c4 is locked for n7 and c1 at r78c1, so r9c4 <>r4c1.
Using now Innies-Outies for n47, we have r5c3+r6c3 = 5 + r9c4 - r4c1, so r5c3+r6c3 <> 5 since r9c4 <>r4c1.
We deduce that r56c4 <> 15 , so r6c5<>8 since r56c4<>{69} : r6c5=9, and so on.. . The puzzle becomes smoother from this point.
Walkthrough by Andrew (in 2010):
Here is another puzzle from my unsolved backlog; I managed to solve the Lite version when it was active but had got stuck on the original Tetris Killer. Having gone through Afmob's walkthrough it looks as if some parts of the solving path are fairly narrow but my key breakthrough using 45 rule on N69 was very different.

Rating Comment. I'll rate my walkthrough for Tetris Killer at least Hard 1.25 because of my combination/permutation work and because I used a couple of hidden killer quads, although they might not have been necessary.

Here is my walkthrough for Tetris Killer.

Prelims

a) 11(4) cage in N1 = {1235}
b) 28(4) cage at R1C3 = {4789/5689}, no 1,2,3
c) 10(4) cage at R3C5 = {1234}
d) 30(4) cage in N4 = {6789}
e) 14(4) cage at R8C2 = {1238/1247/1256/1346/2345}, no 9

Steps resulting from Prelims
1a. 11(4) cage in N1 = {1235}, locked for N1
1b. 10(4) cage at R3C5 = {1234}, CPE no 1,2,3,4 in R56C5
1c. 30(4) cage in N4 = {6789}, locked for N4

2. 45 rule on whole grid 1 innie R5C5 = 7
2a. 7 in N4 only in R4C23, locked for R4
2b. 7 in N6 only in R6C789, CPE no 7 in R7C7

3. 45 rule on N1 2 innies R12C3 = 1 outie R4C1 + 13
3a. Max R12C3 = 17 -> max R4C1 = 4
3b. Min R12C3 = 14, no 4
3c. 4 in N1 only in R123C1, locked for C1
3d. 4,5 in N4 only in R5C3 + R6C23, CPE no 4,5 in R6C4 and R7C3
3e. 5 in C1 only in R6789C1, CPE no 5 in R7C2

4. Naked quad {1234} in R4C1456, locked for R4
4a. 4 in R4 only in R4C456, locked for N5 and 10(4) cage at R3C5, no 4 in R3C5
4b. 5 in R4 only in R4C789, locked for N6

5. 45 rule on R1234 4 innies R4C2378 = 27 = {5679} (only remaining combination), locked for R4 -> R4C9 = 8
5a. R4C9 = 8 -> R123C9 = 11, no 9
5b. 8 in N4 only in R5C12, locked for R5

6. 45 rule on N7 2 innies R7C23 = 1 outie R9C4 + 11
6a. Max R7C23 = 17 -> max R9C4 = 6
6b. Min R7C23 = 12, no 1,2

7. 45 rule on R89 2 outies R7C19 = 8 = {17/26/35}, no 4,8,9

8. 45 rule on N9 1 outie R9C6 = 2 outies R7C78 + 1
8a. Min R7C78 = 3 -> min R9C6 = 4
8b. Max R7C78 = 8, no 8,9
8c. 8 in N9 only in R89C78, CPE no 8 in R9C6

9. 45 rule on N3 2 remaining outies R23C6 = 10 = {19/28/37/46}, no 5
9a. R23C6 = 10 -> R12C7 = 11 = {29/38/47/56}, no 1

10. 5 locked in 17(4) cage at R4C7 = {1259/2456}, no 3, 2 only in R5C89, locked for R5 and N6
10a. R4C78 = {569} -> no 6,9 in R5C89
10b. 3 in N6 only in R5C7 + R6C789, CPE no 3 in R6C6 and R7C7

11. 45 rule on C1 2 innies R56C1 = 1 outie R9C2 + 4
11a. Min R56C1 = 7 -> min R9C2 = 3

12. 45 rule on C9 2 innies R56C9 = 1 outie R9C8 + 3
12a. R56C9 cannot total 12 -> no 9 in R9C8

13. 28(4) cage at R1C3 = {4789/5689}
13a. R12C3 = R4C1 + 13 (step 3)
13b. Max R4C1 = 3 -> max R12C3 = 16 -> R12C3 cannot contain both of 8,9
13c. Hidden killer pair 8,9 in R12C3 and R23C4 for 28(4) cage -> R12C3 and R23C4 must each contain one of 8,9
13d. R23C4 must contain one of 4,5 and one of 8,9 -> no 6,7 in R23C4

14. Hidden killer quad 1,2,3,5 in R4C1, R6C1 and R789C1 for C1 -> R789C1 must contain two of 1,2,3,5
14a. 20(4) cage in N7 cannot contain more than two of 1,2,3,5 -> no 3,5 in R9C2

15. 20(4) cage at R5C3 = {1469/1568/2369/2459/2468/3458} (cannot be {1289} which clashes with R23C4)
15a. Killer pair 8,9 in R23C4 and R56C4, locked for C4
15b. Max R56C3 = 9 -> min R56C4 = 11, no 1

16. 7 in C4 only in R178C4
16a. 45 rule on C1234 4 innies R1478C4 = 15 = {1257/1347}, no 6, 1 locked for C4
16b. Killer pair 4,5 in R1478C4 and R23C4, locked for C4
16c. 5 in N5 only in R5C6 + R6C56, CPE no 5 in R7C6

17. R7C23 = R9C4 + 11 (step 6)
17a. Min R9C4 = 2 -> min R7C23 = 13, no 3
17b. Naked quad {6789} in R1247C3, locked for C3

18. 20(4) cage at R5C3 (step 15) = {1469/1568/2369/2459/2468/3458}
18a. 3 of {2369} must be in R5C3, 3 of {3458} must be in R5C4 -> no 3 in R6C34

19. 16(4) cage at R5C6 = {1249/1267/1348/1357/1456/2356} (cannot be {1258} because 2,8 only in R6C6, cannot be {2347} which clashes with R4C456, ALS block)
19a. 9 of {1249} must be in R5C6 (R5C67 cannot be [14] which clashes with R5C89, ALS block, R56C6 cannot be [12] which clashes with R4C456, ALS block) -> no 9 in R5C7 + R6C67
19b. 2 of {1267/2356} must be in R6C6, 6 of {1456} must be in R56C7 (R56C7 cannot be {14} which clashes with R5C89, ALS block), no 6 in R6C6

20. Hidden killer quad 1,2,3,5 in R789C1 and R8C23 + R9C3 for N7 -> R789C1 contains two of 1,2,3,5 (step 14) -> R8C23 + R9C3 must contain two of 1,2,3,5
20a. 14(4) cage at R8C2 = {1238/1256/1346/2345} (cannot be {1247} which only contains one of 1,2,3,5 in R8C23 + R9C3), no 7

21. 45 rule on N69 2 remaining innies R56C7 = 1 outie R9C6 + 1
21a. Min R9C6 = 4 -> min R56C7 = 5
21b. R56C7 cannot be {14} which clashes with R5C89 (ALS block) -> min R56C7 = 7 -> min R9C6 = 6

22. 45 rule on N8 2 innies R9C46 = 1 outie R6C5 + 2
22a. Min R9C46 = 8 -> min R6C5 = 6
22b. Max R9C46 = 11 -> no 6 in R9C4

23. Killer pair 2,3 in R1478C4 and R9C4, locked for C4

24. 6 in C4 only in R56C4, locked for N5
24a. Naked triple {689} in R5C124, locked for R5
24b. Naked triple {689} in R56C4 + R6C5, locked for N5
24c. R9C46 = R6C5 + 2 (step 22)
24d. Min R6C5 = 8 -> min R9C46 = 10, no 6 in R9C6

25. 5 in N5 only in R56C6, locked for C6
25a. 16(4) cage at R5C6 (step 19) must contain 5 = {1357/1456/2356}
25b. R56C7 = R9C6 + 1 (step 21)
25c. R9C6 = {79} -> R56C7 = 8,10
25d. 16(4) cage at R5C6 = {1357/1456} (cannot be {2356} because R56C7 must total 8 or 10 and 2,5 only in R56C6), no 2
25e. 6,7 only in R6C7 -> R6C7 = {67}
25f. 2 in N5 only in R4C456, locked for R4 and 10(4) cage in R3C5, no 2 in R3C5

26. 45 rule on N7 3(2+1) outies R6C12 + R9C4 = 10
26a. R9C4 = {23} -> R6C12 = 7,8 = {25/34/35}, no 1

27. 20(4) cage at R5C3 (step 15) must contain 6 = {1469/1568/2468} (cannot be {2369} which clashes with R6C12), no 3

28. 3 in R5 only in R5C67 -> 16(4) cage at R5C6 (step 25d) = {1357} (only remaining combination) -> R6C7 = 7, R5C7 = {13}, clean-up: no 4 in R12C7 (step 9a)

29. 45 rule on R6789 3 remaining innies R6C346 = 11 = {128/146} (cannot be {245} because 2,4 only in R6C3) -> R6C6 = 1, R6C34 = [28/46], R5C67 = [53], clean-up: no 9 in R23C6 (step 9), no 8 in R12C7 (step 9a)

30. Naked triple {234} in R4C456, locked for R4 and 10(4) cage at R3C5 -> R3C5 = 1, R4C1 = 1, R56C3 = [42], clean-up: no 7 in R7C9 (step 7)
30a. 20(4) cage at R5C3 (step 27) = {2468} (only remaining combination) -> R56C4 = [68], R6C5 = 9

31. R6C12 = {35} = 8 -> R9C4 = 2 (step 26)
31a. R9C46 = R6C5 + 2 (step 22), R6C5 = 9, R9C4 = 2 -> R9C6 = 9
31b. R8C9 = 9 (hidden single in N9)

32. Naked pair {46} in R6C89, locked for N6 and 18(4) cage at R6C8, no 4,6 in R7C78
32a. Naked pair {59} in R4C78, locked for R4
32b. R6C89 = {46} = 10 -> R7C78 = 8 = [17/53], no 2, no 1,5 in R7C8

33. R7C23 = R9C4 + 11 (step 6)
33a. R9C4 = 2 -> R7C23 = 13
33b. 9 in N7 only in R7C23 -> R7C23 = [49]

34. R5C2 = 9 (hidden single in C2), R5C1 = 8

35. 14(4) cage at R8C2 (step 20a) = {1238/1256}
35a. 6,8 only in R8C2 -> R8C2 = {68}

36. 21(4) cage at R1C1 = {1479} (only remaining combination), 7 locked for N1 and C1, clean-up: no 1 in R7C9 (step 7)

37. Naked pair {68} in R12C3, locked for C3 -> R4C23 = [67], R89C2 = [87]
37a. 7 in N9 only in R78C8, locked for C8

38. 7 in N3 only in 19(4) cage at R1C9 = {1378} (only remaining combination), 1,3 locked for C9 and N3 -> R5C89 = [12], clean-up: no 5,6 in R7C1 (step 7)

39. 5 in C9 only in R79C9, locked for N9 -> R7C7 = 1, R7C8 = 7 (step 32b)

40. R12C3 = {68} = 14 -> R23C4 = 14 = {59}, locked for C4 and N2 -> R7C4 = 3, R7C1 = 2, R7C9 = 6 (step 7), R7C56 = [58], R4C4 = 4, R1C4 = 7, R8C4 = 1, clean-up: no 2,3 in R23C6 (step 9)

41. Naked pair {46} in R23C6, locked for C6, N2 and 21(4) cage at R1C7, no 6 in R12C7, clean-up: no 5 in R12C7 (step 9a)

42. 14(4) cage at R8C2 (step 35) = {1238} (only remaining combination) -> R89C3 = [31]

43. Naked pair {29} in R12C7, locked for C7 and N3 -> R4C7 = 5, R8C7 = 4

and the rest is naked singles.


Top
 Profile  
Reply with quote  
PostPosted: Sun Jul 31, 2011 5:12 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Tetris Killer V2 by tarek (March 2009) here
Puzzle Diagram:
Image
Images with "udosuk style Killer Cages" by Børge:
Image     Image
Code: Select, Copy & Paste into solver:
3x3::k:6662:4627:5140:3585:3585:3585:4359:5640:6149:6662:4627:5140:5140:3585:4359:4359:5640:6149:6662:4627:4627:5140:3842:4359:5640:5640:6149:6662:4114:4114:3842:3842:3842:5642:5642:6149:4114:4114:6417:6417:21:4617:4617:5642:5642:4112:4112:6417:6417:5892:4617:4617:6411:6411:6158:4112:4112:5892:5892:5892:6411:6411:3084:6158:4367:4367:6915:6915:6915:4365:4365:3084:6158:6158:4367:4367:6915:4365:4365:3084:3084:
81-character code string
QIKE<<HMO^^^<^>^^^^^<^F^>^^^G<>^<M<^>^P<0I<^<G<^^N^^P<O^<>^<>^C^H<R<<H<^^<^<^>^>^
Solution:
+-------+-------+-------+
| 9 7 1 | 6 2 5 | 4 8 3 |
| 5 6 8 | 4 1 3 | 2 7 9 |
| 4 2 3 | 7 9 8 | 1 6 5 |
+-------+-------+-------+
| 8 5 6 | 1 3 2 | 9 4 7 |
| 2 3 4 | 9 7 6 | 5 1 8 |
| 1 9 7 | 5 8 4 | 3 2 6 |
+-------+-------+-------+
| 6 4 2 | 3 5 7 | 8 9 1 |
| 7 1 5 | 8 4 9 | 6 3 2 |
| 3 8 9 | 2 6 1 | 7 5 4 |
+-------+-------+-------+
Quote:
tarek: Here is a lighter version. SSS=1.22.

manu: This V2 seems really hard : I have used ... I might have missed something since this puzzle seems to be as difficult as many 1.5 I have solved (not able to rate exactly)

Andrew: I finished Tetris Killer v2 over a week ago, soon after Manu's walkthrough was posted, but waited until Richard had moved the interesting What is an Assassin? discussion to its own thread.
I'll rate Tetris Killer v2 at 1.25 to Hard 1.25 the way I solved it.

Walkthrough by manu:
This V2 seems really hard : I have used killer pairs and some cage blockers. I might have missed something since this puzzle seems to be as difficult as many 1.5 I have solved (not able to rate exactly)

Here is my walkthrough :


WALKTHOUGH TETRIS V2


1)Innie for the grid : r5c5=7

2)IO for n9 : r7c78 = 16+r9c6 → r7c78={89} and r9c6=1
→ split cage 8(2) at r6c89 : {17/26/35}

3)IO for n8 : r6c5=r9c4+6 → r9c4={23}, r6c5={89}


4)IO for c1 : r9c2=r56c1+5 → r9c2={89}, r56c1={12/13}
→ 1 locked for c1 and n4 at r56c1

5)Combination for cage 23(4) at n58 : 8{357/456} (r7 c456 cannot contain 1, 8, 9 and 2 from step3) and 9{257} ( r7c456 cannot contains 1,8,9,and 3 from step3)
→ 5 locked for n8 and r7

6)Outies for r89 : r7c19 total 7 : [61] or {34}


7)IO for n7 : total of r7c23=4+r9c4
a) r9c4<=3 → total of r7c23 <=7 : no 7 for r7c23
b) 7 locked in r7c456 for r7 and n8 : combination 8{456} removed for cage 23(4) (step 5)
c) 27(4)={4689} (cannot contain 5 7)
d) r4c9={23} → total of r7c23 = 6/7 : r7c23={24/16/34}


8)Combination for cage 16(4) at n47 : [19]{24} [37]{24} [27]{16} [18]{34} [27]{34}
→ r6c12 contains one of {17} → split cage 8(2) at r6 ={26/35}

9)Outies for r5 = r5c1289 totals 14 : no 9

10)IO for c9 : r56c9=r9c8+9, with r6c9={2356}
a) cage 12(4) at n9 : {1236/1245} → r9c8={23456}
b) r56c9 : combination {56} impossible since it would imply r9c8=2 and both combinations of cage 12(4) would be blocked
c) r9c8 >=2 → total r56c9 >= 11 → r5c9 >= 5 since r6c9 <= 6
d) r5c9 <>5 since total r56c9 >= 11, r6c9 <=6 and combination {56} impossible for r56c9
We deduce r5c9={68}
e) r5c9 <>6 since total r56c9 >= 11, r6c9 <=6 and combination {56} impossible for r56c9
We deduce r5c9=8, r6c9={356} and r9c8={245}
f) No 8 for cage 24(4) at c9 : {2679/3579/4569} → r9c8 <> 4 since {125} blocks all these combinations → r6c89=[53/26]
g) Killer pair {36} at cage 24(4) and r6c9 → no 3 6 for cage 12(4). Deduce cage 12(4) = {1245} - > r7c9={14} and r7c1= {36} (step 6)

11)From step 9, r5c1289={123}8, no 1 at r5c2, no 2 at r5c8 (naked pair {25} at r69c8, 2 and 5 locked for c8)
a) 2 locked for r5 and n4 at r5c12 → r6c1<>2
→ combination {16} removed for r7c23 (step 8)
→ 4 locked for r7 and n8 at r7c23 (step 8)
→ r7c9=1 (HS) , r7c1=6

12)Combinations for cage 24(4) at n7 : 6{37}8 or 6{27}9
→ Naked quad {1237} at r5689c1 → cage 26(4) = {4589}

13)IO for n3 : r4c9= 1 + r12c7 >= 4 : no 1 2 3 at r4c9

14)Naked triple {123} at r5c12+r6c1 : locked for n4

15)a) No 1,3 at r4c78 (no valid combination for cage 22(4) )
b) No 2 at r4c78 since combination {29}[38] for cage 22(4) would block split cage 8(2)
c) Deduce that r4c456= {123} (hidden triple) and r3c5=9

16)r6c5=8 (NS) r7c456={357}, r9c4=2, r7c23={24}, r89c1={37}, r9c2=8

17)Cage 17(4) at n78 = {159}2, r9c89=[54], r8c9=2, r9c3=9 r9c5=6 r6c89=[26] Naked pair {15} at r8c23, r8c5=4

18)Naked pair {37} at r89c1 → r6c1= 1 r6c2=9 r5c12=[23] r5c8=1

19)Last combinations : r4c78={49} r4c23={56} : r4c1=8 r4c9=7 r56c7=[53]

20)Hidden pair for r5 : r5c46={69}, and r5c6=6 (combinations for 18(4) cage) r5c4=9 r6c6= r5c3=4 and r6c34=[75] NS

21)Innies for n3 : r12c7={24} → r23c6={38}, r4c6=2, r23c4={47} r1c6=5, r1c4=6

22) Hidden killer pair {38} locked at r12c3 and r3c3. r12c3 totals 9, so contains one of {38} -> r3c3={38}

23)Naked pair {38} at r3c36 : locked for r3

24)Rest is singles


EDIT : Thanks to Andrew for having pointed out some typos and lack of explanations. There was also a mistake at step 23 (have forgotten an elimination)
Walkthrough by Andrew:
I finished Tetris Killer v2 over a week ago, soon after Manu's walkthrough was posted, but waited until Richard had moved the interesting What is an Assassin? discussion to its own thread.

I'll rate Tetris Killer v2 at 1.25 to Hard 1.25 the way I solved it, because of some of the combination eliminations and for the hidden killer triple in step 12a; Manu's walkthrough should probably be rated at 1.5.

Here is my walkthrough. I found things hard going in the middle until I spotted the simple step 20; the rest was easy.

Prelims

a) R1234C1 = {2789/3689/4589/4679/5678}, no 1
b) 14(4) cage in N2 = {1238/1247/1256/1346/2345}, no 9
c) 27(4) cage in N8 = {3789/4689/5679}, no 1,2, 9 locked for N8
d) 12(4) cage in N9 = {1236/1245}, no 7,8,9, 1,2 locked for N9

1. 45 rule on whole grid 1 innie R5C5 = 7

2. 45 rule on R89 2 outies R7C19 = 7 = {16/25/34}, no 7,8,9

3. 45 rule on R1234 4 outies R5C1289 = 14 = {1238/1256/1346/2345}, no 9
3a. Max R5C89 = 11 (from the combinations of R5C1289) -> min R4C78 = 11, no 1

4. 45 rule on N9 2 innies R7C78 = 1 outie R9C6 + 16 -> R9C6 = 1, R7C78 = 17 = {89}, locked for R7, N9 and 25(4) cage at R6C8
4a. R7C78 = 17 -> R6C89 = 8 = {17/26/35}, no 4
4b. 1 in N9 locked in R78C9, locked for C9, clean-up: no 7 in R6C8

5. 45 rule on N8 1 outie R6C5 = 1 remaining innie R9C4 + 6, R6C5 = {89}, R9C4 = {23}

6. 23(4) cage at R6C5 = {2579/3578} (cannot be {2489} because 8,9 only in R6C5, cannot be {2678/3479/3569} which clash with 27(4) cage in N8, cannot be {4568} which clash with R7C19), no 4,6, 5,7 locked in R7C456, locked for R7 and N8, clean-up: no 2 in R7C19 (step 2), no 3 in 27(4) cage in N8

7. 45 rule on C789 4 innies R1256C7 = 14 = {1238/1247/1256/1346/2345}, no 9
7a. 9 in N6 locked in R4C789, locked for R4

8. 45 rule on N3 1 outie R4C9 = 2 innies R12C7 + 1
8a. Min R12C7 = 3 -> min R4C9 = 4
8b. Max R4C9 = 9 -> max R12C7 = 8, no 8

9. 12(4) cage in N9 = {1236/1245}
9a. 6 of {1236} must be in R9C89 (R9C89 cannot be {23} which clashes with R9C4), no 6 in R78C9, clean-up: no 1 in R7C1 (step 2)
9b. 6 in R7 locked in R7C123, locked for N7

10. 45 rule on C1 1 outie R9C2 = 2 innies R56C1 + 5
10a. Min R56C1 = 3 -> min R9C2 = 8
10b. R9C2 = {89} -> R56C1 = 3,4 = {12/13}, 1 locked for C1 and N4
10c. 1 in R4 locked in R4C456, locked for N5 and 15(4) cage at R3C5

11. 45 rule on N7 2 innies R7C23 = 1 outie R9C4 + 4
11a. R9C4 = {23} -> R7C23 = 6,7 = {16/24/34}
11b. R7C23 = 6,7 -> R6C12 = 9,10
11c. Max R6C1 = 3 -> min R6C2 = 6
11d. 16(4) cage at R6C1 = {1249/1267/1348/2347}
11e. 7,8,9 only in R6C2 -> R6C2 = {789}

12. 17(4) cage at R8C2 = {1259/1358/2348/2357} (cannot be {1349} which clashes with R7C23, cannot be {1457} because R9C4 only contains 2,3)
12a. Hidden killer triple 1,2,3 in R7C23, 17(4) cage at R8C2 (contains two of 1,2,3, one within N7 and one at R9C4) and R789C1 for N7 -> R789C1 must contain one of 2,3
12b. Killer triple 1,2,3 in R56C1 and R789C1, locked for C1

13. 45 rule on N1 2 innies R12C3 = 1 outie R4C1 + 1
13a. Max R4C1 = 8 -> max R12C3 = 9, no 9

14. 45 rule on R123 2 outies R4C19 = 1 innie R3C5 + 6
14a. Min R4C19 = 9 -> min R3C5 = 3

15. 45 rule on C9 2 innies R56C9 = 1 outie R9C8 + 9
15a. Min R9C8 = 2 -> min R56C9 = 11, no 2,3 in R5C9, no 2 in R6C9, clean-up: no 6 in R6C8 (step 4a)

16. R5C1289 (step 3) = {1238/1256/1346/2345}
16a. 8 of {1238} must be in R5C9 -> no 8 in R5C28

17. 4 in R6 locked in R6C3467
17a. 45 rule on R6789 4 innies R6C3467 = 19 = {1459/1468/2458/2467/3457}
17b. Killer triple 7,8,9 in R6C2, R6C3467 and R6C5, locked for R6, clean-up: no 4 in R5C9 (step 15a), no 1 in R6C8 (step 4a)

18. Max R56C9 = 14 -> max R9C8 = 5 (step 15)
18a. R56C9 cannot total 12 -> no 3 in R9C8 (step 15)
18b. 12(4) cage in N9 = {1236/1245}
18c. 6 of {1236} must be in R9C9 -> no 3 in R9C9
[There’s a forcing chain possible here
R9C8 = 2 => R56C9 = 11 (step 15) = {38/56} -> 12(4) cage in N9 = {1245} (cannot be {1236} which clashes with R56C9)
R9C8 = {45} => 12(4) cage in N9 = {1245}
-> 12(4) cage in N9 = {1245}, locked for N9
but I’ll try to avoid using it to keep the rating down. Step 22 shows that it wasn’t needed]

19. 22(4) cage in N6 = {1489/1579/1678/3478} (cannot be {2389/2569/2578/3469/3568/4567} which clash with R6C89, cannot be {2479} because R5C9 only contains 5,6,8), no 2
19a. 5 of {1579} must be in R5C9 -> no 5 in R4C78 + R5C8
19b. 1 of {1678} must be in R5C8 -> no 6 in R5C8

20. 7,9 in C9 locked in R1234C9 = {2679/3579}, no 4,8

21. R5C9 = 8 (hidden single in C9)
21a. R5C1289 (step 3) = {1238} (only remaining combination) -> R5C128 = {123}, locked for R5
21b. Naked triple {123} in R5C12 + R6C1, locked for N4
21c. 2 in N6 locked in R6C78, locked for R6

22. 1,4 in C9 locked in R789C9, locked for N9
22a. 12(4) cage in N9 = {1245} (only remaining combination), locked for N9, clean-up: no 4 in R7C1 (step 2)
22b. R56C9 = R9C8 + 9 (step 15) -> R6C9 = R9C8 + 1, no 5 in R6C9, clean-up: no 3 in R6C8 (step 4a)

23. 22(4) cage in N6 (step 19) = {1489/1678/3478}
23a. R5C8 = {13} -> no 3 in R4C78

24. R4C456 = {123} (hidden triple in R4), locked for N5, R3C5 = 9 (cage sum), R6C5 = 8
24a. Naked pair {46} in R89C5, locked for C5 and N8
24b. Naked pair {89} in R8C46, locked for R8

25. R3C5 = 9 -> R4C19 = 15 (step 14) = [69/87]

26. R6C12 (step 11b) = 10 (cannot be 9 because R6C12 are both odd) -> R7C23 = 6 = {24}, locked for R7 and N7 -> R7C9 = 1, R7C1 = 6 (step 2), R4C1 = 8, R4C9 = 7 (step 25), R9C4 = 2 (step 11), R9C89 = [54], R8C9 = 2, R6C8 = 2, R6C9 = 6 (step 4a), R89C5 = [46]

27. R7C1 = 6, R89C1 both odd -> R9C2 must be even -> R9C2 = 8 -> R56C1 = 3 (step 10) = [21], R5C2 = 3, R5C8 = 1

28. Naked pair {49} in R4C78, locked for R4 and N6 -> R56C7 = [53], R89C7 = [67], R8C8 = 3

29. R6C12 = 10 (step 26) -> R6C2 = 9 (cage sum), R6C6 = 4, R6C34 = [75], R5C6 = 6 (cage sum), R5C34 = [49], R7C23 = [42], R8C46 = [89]

30. R1234C1 = {4589} (only remaining combination) -> R123C1 = {459}, locked for C1 and N1 -> R89C1= [73], R9C3 = 9

31. 45 rule on N1 2 remaining outies R23C4 = 11 = {47}, locked for C4 and N2 -> R7C4 = 3, R7C56 = [57], R4C4 = 1, R1C4 = 6

32. R1C4 = 6 -> 14(4) cage in N2 = {1256} (only remaining combination) -> R1C6 = 5, R12C5 = {12}, locked for C5 and N2 -> R4C56 = [32]

33. 45 rule on N3 2 remaining innies R12C7 = 6 = {24}, locked for C7 and N3 -> R4C78 = [94], R7C78 = [89], R3C7 = 1

34. R3C2 = 2 (hidden single in R3)

35. 45 rule on C12 2 remaining outies R34C3 = 1 innie R8C2 + 8
35a. R8C2 = {15} -> R34C3 = 9,13 = [36/85]
[Alternatively R23C4 = {47} = 11 -> R12C3 = 9 = {18}/[36]
Hidden killer pair 3,8 in R12C3 and R3C3 for C3 -> R3C3 = {38}]

36. Naked pair {38} in R3C36, locked for R3 -> R3C9 = 5, R3C1 = 4, R12C1 = [95], R12C9 = [39], R23C4 = [47], R3C8 = 6, R12C7 = [42], R12C5 = [21]

37. R23C4 = [47] = 11 -> R12C3 = 9 = [18] (cannot be {36} because 3,6 only in R2C3)

and the rest is naked singles.


Top
 Profile  
Reply with quote  
PostPosted: Sun Jul 31, 2011 5:29 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Assassin 146 by manu (March 2009) here
Puzzle Diagram:
Image
Images with "udosuk style Killer Cages" by Børge:
Image     Image
Code: Select, Copy & Paste into solver:
3x3:d:k:5120:5120:4866:4866:4866:4866:4870:4870:4870:5120:3338:3083:3083:3341:4622:4622:1296:4870:5120:2835:3338:3083:3341:4622:1296:4633:5402:4891:2835:2835:11550:11550:11550:4633:4633:5402:4891:6693:6693:11550:11550:11550:5930:5930:5402:4891:6693:6693:11550:11550:11550:5930:5930:6197:6454:6693:2360:4409:4409:4409:1596:5930:6197:6454:2360:5697:5697:5697:5697:5697:1596:6197:6454:6454:6454:5195:5195:5195:5195:6197:6197:
Solution:
+-------+-------+-------+
| 3 7 1 | 4 5 9 | 8 6 2 |
| 4 5 9 | 2 6 8 | 7 1 3 |
| 6 2 8 | 1 7 3 | 4 9 5 |
+-------+-------+-------+
| 2 3 6 | 7 4 5 | 1 8 9 |
| 8 5 4 | 3 9 1 | 6 2 7 |
| 9 1 7 | 8 2 6 | 5 3 4 |
+-------+-------+-------+
| 1 9 3 | 5 8 4 | 2 7 6 |
| 5 6 2 | 9 1 7 | 3 4 8 |
| 7 8 4 | 6 3 2 | 9 5 1 |
+-------+-------+-------+
Quote:
manu: I had much hesitations about the choice of the puzzle between two of them (the other one will be sent as an extra killer for JFF4 EDIT : Have talked about this with Andrew and have finally decided to post it for further Assassin).
SSolver rating is 3.50, but fall down to 1.19 after a single step not seen by the solver.
The solving path is narrow, but no doubt that you will be able to find the right way ;) : must not be added to Tarek unsolvables :brickwall:

Afmob: Rating: 1.25 - Hard 1.25.

Andrew:
manu wrote:
The solving path is narrow, but no doubt that you will be able to find the right way
Yes it is. My key moves were the mostly the same as Afmob's but sometimes for different reasons ...
I'll rate A146 at Hard 1.25.

Walkthrough by Afmob:
A146 Walkthrough:

1. D\/
a) Overlap of R19+C19 = R19C19 = 13(4) = 1{237/246/345} <> 8,9; CPE: R5C5 <> 1
b) ! Using R19C19 = 13(4): Innies D\/ + Overlap D\/ = R46C46+R5C5 + R5C5 = 44
-> R46C46+R46C5 = 35(5) = {56789} locked for N5 and R5C5 = 9
c) 13(2) <> 4
d) Naked quad (5678) locked in R2C2+R3C3+R4C4+R6C6 for D\
e) 6(2) = {24} locked for N9+D\
f) R19C19 = 13(4) = 13{27/45} since R1C1+R9C9 = {13} -> R1C9+R9C1 = {27/45}
g) Killer pair (24) locked in R19C19 + 5(2) for D/
h) 9(2) <> 5,7

2. N1247
a) Outies N124 = 16(1+1) = {79/88}
b) Innies N7 = 11(2) = [74/92] since (38) is a Killer pair of 9(2)
c) Outies N4 = 11(2) = [29/47]
d) Outies N124 = 16(2) = {79}; CPE: R2C2 <> 7

3. C789 !
a) ! Innies C789 = 19(3) = {379} locked for C7 because R2C7 = (79); 3 also locked for N9
b) R9C9 = 1, R1C1 = 3
c) ! Outies C9 = 19(2+1) <> 1 because R1C7 <> 9
d) Innies N3 = 21(3) <> 1,2,3
e) 1 locked in 5(2) @ N3 = {14} locked for N3+D/
f) 19(4) = 23{59/68} -> R2C9 = 3; 2 locked for R1

4. D\/+N7
a) R19C19 = 13(4) = {1237} -> R1C9 = 2, R9C1 = 7
b) 24(5) = {14568} -> R6C9 = 4; {568} locked for N9
c) R7C2 = 9, R7C8 = 7
d) Innie N7 = R8C3 = 2
e) R8C8 = 4, R2C8 = 1, R3C7 = 4, R3C2 = 2
f) 9(2) = {36} locked for N7+D/
g) 25(5) = {14578} -> 1 locked for C1

5. R123
a) 18(3) @ R3C8 = 9{18/36} -> 9 locked for C8
b) 19(4) @ N3 = {2368} -> 6,8 locked for R1+N3
c) R3C8 = 9, R2C7 = 7, R3C9 = 5
d) 20(4) = 34{58/67} because (17) only possible @ R1C2; 4 locked for N1
e) Hidden Single: R1C3 = 1 @ N1, R2C3 = 9 @ N1
f) 19(4) @ N2 = {1459} -> 4,5,9 locked for R1+N2
g) 13(2) @ N2 = {67} -> R2C5 = 6, R3C5 = 7
h) 13(2) @ N1 = {58} -> R3C3 = 8, R2C2 = 5
i) 12(3) = {129} -> R2C4 = 2, R3C4 = 1
j) 11(3) = 2{18/36/45}

6. R7
a) 17(3) = 8{36/45} -> 8 locked for R7+N8

7. Rest is singles.

Rating: 1.25 - Hard 1.25 with hardest move being step 1b.
Walkthrough by Andrew:
manu wrote:
The solving path is narrow, but no doubt that you will be able to find the right way
Yes it is. My key moves were the mostly the same as Afmob's but sometimes for different reasons, particularly for the 19(4) cage in N3.

I'll rate A146 at Hard 1.25 mainly for the first two moves but also because I still had to work fairly hard until I found steps 13 and 13b.

Here is my walkthrough

This is a Killer-X.

Prelims

a) 13(2) diagonal cage at R2C2 = {49/58/67}, no 1,2,3
b) R23C5 = {49/58/67}, no 1,2,3
c) 5(2) diagonal cage at R2C8 = {14/23}
d) 9(2) diagonal cage at R7C3 = {18/27/36/45}, no 9
e) 6(2) diagonal cage at R7C7 = {15/24}
f) 11(3) cage at R3C2 = {128/137/146/236/245}, no 9
g) R456C1 = {289/379/469/478/568}, no 1
h) R345C9 = {489/579/678}, no 1,2,3

I’d done three routine steps before I spotted step 1, which more inspirational solvers will have spotted immediately, so I had to start again. Using an Excel worksheet with coloured cages may have made it harder for me to see the outer ring.

1. 45 rule on outer ring 4 innies R19C19 = 13
[Note that R19C9 can ‘see’ each other because of the diagonals but no need to use this yet.]

2. 45 rule on both diagonals 3 remaining innies on each diagonal = 44. This is only possible when the crossover value is 9 -> R5C5 = 9, placed for both diagonals, clean-up: no 4 in R2C2 + R3C3 and R23C5
2a. R46C46 + R5C5 (twice) = 44 -> R46C46 = 26 = {5678}, locked for N5
2b. R4C4 + R6C6 = {58/67} (other combinations clash with R2C2 + R3C3 on D\), R4C6 + R6C4 = {58/67}
2c. Naked quad {5678} in R2C2 + R3C3 + R4C4+ R6C6, locked for D\, clean-up: no 1 in R7C7 + R8C8
2d. Naked pair {24} in R7C7 + R8C8, locked for D\ and N9
2e. Naked pair {13} in R1C1 + R9C9, CPE no 1,3 in R1C9 + R9C1
2f. R1C1 + R9C9 = {13} = 4 -> R1C9 + R9C1 = 9 (step 1) = {27/45}, no 6,8
2g. Killer pair 2,4 in R1C9 + R9C1 and R2C8 + R3C7, locked for D/, clean-up: no 5,7 in R7C3 + R8C2

3. 45 rule on N3 3 innies R2C7 + R3C89 = 21 = {489/579/678}, no 1,2,3

4. 45 rule on N4 2 outies R37C2 = 11 = [29]/{38/47/56}, no 1, no 2 in R7C2

5. 45 rule on C789 3 innies R289C7 = 19 = {379/469/478/568}, no 1

6. 45 rule on R789 2 innies R7C28 = 1 outie R6C9 + 12
6a. Min R7C28 = 13, no 1,3, clean-up: no 8 in R3C2 (step 4)
6b. Max R7C28 = 17 -> max R6C9 = 5
6c. 1 in N9 locked in R78C9 + R9C89 for 24(5) cage, no 1 in R6C9
6d. Min R7C28 = 14, no 4, clean-up: no 7 in R3C2 (step 4)

7. 45 rule on N7 2 innies R7C2 + R8C3 = 11 = {56}/[74/92] (cannot be [83] which clashes with R7C3 + R8C2) -> R7C2 = {5679}, R8C3 = {2456}, clean-up: no 3 in R3C2
7a. 11(3) cage at R3C2 = {128/146/236/245} (cannot be {137} because no 1,3,7 in R3C2), no 7

8. 45 rule on N1 3 innies R12C3 + R3C2 = 12 = {129/147/237/246/345} (cannot be {138} which clashes with R1C1, cannot be {156} which clashes with R2C2 + R3C3), no 8

9. 45 rule on R1 2 innies R1C12 = 1 outie R2C9 + 7
9a. Max R1C12 = 12 -> max R2C9 = 5
9b. Min R1C12 = 8 -> min R1C2 = 5

10. 45 rule on C9 2 innies R12C9 = 1 outie R9C8
10a. Min R12C9 = 3 -> min R9C8 = 3
10b. 1 in N9 locked in R789C9, locked for C9
10c. Min R12C9 = 5 -> min R9C8 = 5

11. 45 rule on N124 2(1+1) outies R2C7 + R7C2 = 16 = {79} (only remaining combination because no 8 in R7C2), CPE no 7 in R2C2, clean-up: no 5,6 in R3C2 (step 4), no 6 in R3C3, no 5,6 in R8C3 (step 7)
11a. Naked pair {24} in R8C38, locked for R8

12. R289C7 (step 5) = {379} (only remaining combination, cannot be {568} because R2C7 only contains 7,9), locked for C7, 3 locked in R89C7, locked for N9 -> R9C9 = 1, R1C1 = 3, clean-up: no 2 in R2C8
12a. R12C3 + R3C2 (step 8) = {129/147/246}, no 5

13. Hidden killer pair 2,3 in R12C9 and R6C9 for C9 -> R12C9 must contain at least one of 2,3
13a. 19(4) cage in N3 = {2359/2368} (cannot be {1279/1369/1378/2458/2467/3457} which clash with R2C8 + R3C7, cannot be {1459/1468/1567} which don’t contain one of 2,3), no 1,4,7, clean-up: no 2,5 in R9C1 (step 2f)
13b. 2 on D/ locked in R1C9 + R3C7, locked for N3
13c. 19(4) cage = {2359/2368} -> R12C9 = [23], R1C78 = [59/68/86], no 5 in R1C8

14. Naked pair {14} in R2C8 + R3C7, locked for N3 and D/ -> R9C1 = 7, placed for D/, R7C2 = 9, R3C2 = 2 (step 4), R8C3 = 2 (step 7), R8C8 = 4, R7C7 = 2, R2C8 = 1, R3C7 = 4, R2C7 = 7 (step 11), clean-up: no 6 in R3C5, no 8 in R7C3 + R8C2
14a. Naked pair {39} in R89C7, locked for N9
14b. Naked pair {36} in R7C3 + R8C2, locked for N7 and D/
14c. Naked pair {58} in R4C6 + R6C4, locked for N5
14d. Naked pair {67} in R4C4 + R6C6, locked for D\
14e. Naked pair {58} in R2C2 + R3C3, locked for N1

15. 1 in N7 locked in R78C1, locked for C1
15a. R1C3 = 1 (hidden single in N1), R2C3 = 9 (step 12a), R23C1 = [46], R1C2 = 7, clean-up: no 8 in R3C89 (step 3)
15b. R2C3 = 9 -> R23C4 = 3 = [21]
15c. Naked pair {59} in R3C89, locked for R3 and N3 -> R3C3 = 8, R2C2 = 5, R3C5 = 7, R2C5 = 6, R23C6 = [83], R4C6 = 5, R6C4 = 8

16. R456C1 = {289} (only remaining combination), locked for C1 and N4
16a. Naked pair {15} in R78C1, locked for N7 -> R9C23 = [84]

17. 11(3) cage at R3C2 (step 7a) = {236} (only remaining combination), R4C23 = {36}, locked for R4 and N4 -> R4C4 = 7, R6C6 = 6

18. 45 rule on R8 3 remaining innies R8C129 = 19 = {568} (only remaining combination) -> R78C1 = [15], R8C29 = [68], R7C3 = 3, R4C23 = [36]
18a. Naked pair {39} in R8C47, locked for R8 -> R8C56 = [17], R7C6 = 4

19. R345C9 = {579} (only remaining combination) = [597], R3C8 = 9, R4C78 = 9 = [18]

and the rest is naked singles.


Top
 Profile  
Reply with quote  
PostPosted: Wed Aug 03, 2011 12:41 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Just For Fun Killer 4 by manu (March 2009) here
Puzzle Diagram:
Image
Edit :Caution : r2c258 r5c258 r8c258 is not a 45(9) cage : digit can be repeated in this set of cells !
Thanks Ed for posting a new diagram after the link to the original one stopped working.
Images with "udosuk style Killer Cages" by Børge:
Image     Image
Code: Select, Copy & Paste into solver:
3x3::k:3840:3840:3330:3330:3332:3332:2310:3335:3335:3840:10:3083:4620:13:3332:2310:16:3335:3346:3083:3083:4620:4620:2327:2327:3609:3609:3346:3100:3100:1822:3871:3871:3871:5410:5410:3364:37:3100:1822:40:1833:3626:43:5410:3364:3364:5167:5167:5167:1833:3626:3626:1589:3126:3126:2104:2104:4410:4410:5692:5692:1589:4671:64:2881:2370:67:4410:5692:70:2375:4671:4671:2881:2370:2370:3149:3149:2375:2375:
Solution:
+-------+-------+-------+
| 2 4 7 | 6 3 8 | 5 1 9 |
| 9 6 8 | 5 1 2 | 4 7 3 |
| 5 1 3 | 9 4 7 | 2 8 6 |
+-------+-------+-------+
| 8 2 4 | 3 9 5 | 1 6 7 |
| 3 7 6 | 4 2 1 | 9 5 8 |
| 1 9 5 | 8 7 6 | 3 2 4 |
+-------+-------+-------+
| 4 8 1 | 7 5 3 | 6 9 2 |
| 6 3 2 | 1 8 9 | 7 4 5 |
| 7 5 9 | 2 6 4 | 8 3 1 |
+-------+-------+-------+
Quote:
manu: Hi, not able to provide a V2 for A146. I will have a look to the WTs posted for that puzzle. Waiting for Tarek's puzzle, here is another one. Not planned for a future Assassin because this one is a blank cells killer. BTW, I would need to know if such puzzles can be accepted for Assassins ? I have never seen this kind of puzzle in our Assassins archive ; what is the position of the others participants ? Blank cells can offer some spices to killer puzzles. I feel much difficulties to make blank cells killers because either they are too hard, either the solving path is too apparent from the cages pattern.
For this one, I have chosen to make few blank cells ; with regard to the solving path, this puzzle is very similar to classical killer puzzles. I had to use technicals moves to solve it (...) but it feel not to be so difficult....
SSscore : 1.65.

Afmob: Your cage pattern reminded me of this (Archive Note. Link to Ruud's former site; not now accessible. The link may have been to Centre Dot Killer, here). I think V1 Assassins should have no holes but otherwise you can do as you please on V2 or non-Assassin Killers as you can see in the Human Solvable series.
Rating: Hard 1.25 - Easy 1.5.

Andrew: I've got no problem with Assassins having blank cells provided they are in the right range of difficulty. Assassins have developed significantly since Ruud started them. Diagonally-linked cages and Killer-Xs started in variants and forum puzzles and are now accepted for Assassins.
I'll be interested to see what views other forum members have.
My solving path for JFFK4 started with it being another fun puzzle, then I got bogged down ... and then it became fun again when I found steps 25 and 26.
I'll rate my walkthrough for JFFK4 at 1.5.

Walkthrough by Afmob:
Your cage pattern reminded me of this (Archive Note. Link to Ruud's former site; not now accessible. The link may have been to Centre Dot Killer, here). I think V1 Assassins should have no holes but otherwise you can do as you please on V2 or non-Assassin Killers as you can see in the Human Solvable series.

JFF 4 Walkthrough:

1. R789
a) Innies N7 = 4(2) = {13} locked for N7
b) 8(2) = [17/35]
c) 12(2) @ R7 = {48} locked for R7+N7 because {57} blocked by R7C4 = (57)
d) 8 locked in 12(2) @ R9 = {48} locked for R9
e) Innies N8 = 19(3) = 8{47/56} because R7C4 = (57) and R9C6 = (48) -> 8 locked for N8; R8C5 = (468)
f) Innies N9 = 14(3) = {149/158/248} <> 3,6,7 because R9C7 = (48) and R7C9 = (125)
g) 7 locked in 22(3) @ N9 = {679} locked for N9
h) 7,9 locked in R9C123 @ R9 for N7
i) Hidden pair (79) locked in R8C67 for R8 -> R8C67 = {79}

2. R789+N6
a) Innies+Outies R7: 14 = R8C67 - R7C9: R8C67 = {79} -> R7C9 = 2
b) Cage sum: R6C9 = 4
c) Innies N6 = 6(2) = {15} locked for N6
d) 14(3) = {239} locked for N6
e) 15(3) = 5{19/28/37/46} because R4C7 = (15) and {168} blocked by R4C89 = (678) -> 5 locked for R4

3. R456
a) 20(3) = 5{69/78} because {389} blocked by R6C78 = (239) -> 5 locked for R6
b) 13(3): R5C1 <> 6,7 since R6C12 <> 4,5
c) 7(2) @ R6: R5C6 <> 2,3
d) Outies R6 = 13(3) = {139/256/346} <> 8 because R5C6 = (1456) and R5C7 = (239)
e) Outies R6 = 13(3): R5C1 <> 1 because R5C6 <> 3,9
f) Outies R6 = 13(3) = {139/256/346} -> R5C6 = (16)
g) 7(2) @ R6 = {16} locked for C6+N5
h) Hidden Killer pair (16) in R6C123 for R6
i) 12(3) <> 5 because {156} blocked by Killer pair (16) of R6C123 and (345) is a Killer triple of (345) of 13(3)

4. C789 !
a) Outies C9 = 18(4) must have two of (1234) -> R19C8 = (1234)
b) 9(3) = {135} -> 5 locked for C9
c) 13(3) <> 7 because R12C9 <> 2,4
d) ! 9(2) @ R1 <> {27} since it's blocked by R568C7 = (2379)
e) 7 locked in Innies N3 = 9(2) = {27} locked for N3
f) 9(2) @ R3 = {27} locked for R3

5. ! C789+R3
a) Innies+Outies R3: 8 = R2C34 - R3C1 -> R2C23 <> 1,2 because R3C1 >= 4
b) 12(3) = {138/147/156/345} <> 9
c) ! Grouped Killer pair (13) in 12(3) @ N1 + R7C3+R8C2 for C23 -> 12(3) @ N4 can only have one of (13) -> 12(3) @ N4 <> 8
d) ! Innies N4 = 20(3) = {389/569/578} <> 1,2,4 since (479) is a Killer triple of 12(3) @ N4
e) 13(2) = [49/58/67]
f) Innies N1 = 18(3) <> 1,2 because R3C1 = (456)
g) 2 locked in 15(3) @ N1 = 2{49/58/67} <> 1,3
h) Hidden Single: R6C1 = 1 @ C1, R5C1 = 3 @ C1 -> R6C2 = 9
i) R6C6 = 6, R5C6 = 1, R5C8 = 5, R4C7 = 1

6. C456
a) 7(2) = {34} -> R5C4 = 4, R4C4 = 3
b) 15(3) = {159} -> 5,9 locked for N5
c) 2 locked in 9(3) @ N8 = {126} locked for N8
d) 17(3) = {359} -> R8C6 = 9; 3,5 locked for R7
e) R4C6 = 5, R7C6 = 3, R7C5 = 5
f) 13(3) = 2{38/47} because R12C6 = (2478) and 1{48} blocked by R9C6 -> 2 locked for N2
g) R3C6 = 7
h) 13(3) = {238} -> R1C5 = 3; 8 locked for C6+N2
i) 18(3) = {459} -> R3C5 = 4; 5,9 locked for N2
j) R1C4 = 6 -> R1C3 = 7

7. Rest is singles.

Rating: Hard 1.25 - Easy 1.5. I used some cage blockers and a Grouped Killer Pair.
Walkthrough by Andrew:
manu wrote:
Not planned for a future Assassin because this one is a blank cells killer. BTW, I would need to know if such puzzles can be accepted for Assassins ?
I've got no problem with Assassins having blank cells provided they are in the right range of difficulty. Assassins have developed significantly since Ruud started them. Diagonally-linked cages and Killer-Xs started in variants and forum puzzles and are now accepted for Assassins.

I'll be interested to see what views other forum members have.


My solving path for JFFK4 started with it being another fun puzzle, then I got bogged down with nibbling away for a while, with some of this almost certainly not needed for the solving path, and then it became fun again when I found steps 25 and 26.

Afmob and I started in fairly similar ways but then our solving paths became very different. I'd spotted the outies in Afmob's step 4a but there were so many possible combinations that I didn't notice that they all contained two of 1,2,3,4. Afmob's step 5c is clever and, along with step 4d, the hardest.

I'll rate my walkthrough for JFFK4 at 1.5 because of step 11 and the whole of step 26. I'm not really sure how to rate step 26 but I feel it shouldn't be any higher than 1.5.

Here is my walkthrough. It would have been a lot shorter if I'd spotted step 26 earlier, which could have been done any time after step 15. Thanks Afmob for pointing out that my original step 11a was incorrect. I've re-worked parts of steps 11, 12 and 13 but resisted the temptation to move step 26 earlier; that would have made it a different walkthrough.

Prelims

a) R1C34 = {49/58/67}, no 1,2,3
b) R12C7 = {18/27/36/45}, no 9
c) R34C1 = {49/58/67}, no 1,2,3
d) R3C67 = {18/27/36/45}, no 9
e) R3C89 = {59/68}
f) R45C4 = {16/25/34}, no 7,8,9
g) R56C6 = {16/25/34}, no 7,8,9
h) R67C9 = {15/24}
i) R7C12 = {39/48/57}, no 1,2,6
j) R7C34 = {17/26/35}, no 4,8,9
k) R78C3 = {29/38/47/56}, no 1
l) R9C78 = {39/48/57}, no 1,2,6
m) R6C345 = {389/479/569/578}, no 1,2
n) 21(3) cage in N6 = {489/579/678}, no 1,2,3
o) 22(3) cage in N9 = {589/679}, 9 locked for N9, clean-up: no 3 in R9C6
p) 9(3) cage in N8 = {126/135/234}, no 7,8,9
q) 9(3) cage in N9 = {126/135/234}, no 7,8

1. 45 rule on N3 2 innies R2C8 + R3C7 = 9 = {18/27/36/45}, no 9
1a. 45 rule on N3 1 innie R2C8 = 1 outie R3C6

2. 45 rule on N4 3 innies R4C1 + R5C2 + R6C3 = 20 = {389/479/569/578}, no 1,2

3. 45 rule on N6 3 innies R4C7 + R5C8 + R6C9 = 10 = {127/136/145/235}, no 8,9

4. 45 rule on N7 2 innies R7C3 + R8C2 = 4 = {13}, locked for N7, clean-up: no 9 in R7C12, no 1,2,3,6 in R7C4, no 8 in R89C3
4a. R7C12 = {48} (only remaining combination, cannot be {57} which clashes with R7C4), locked for R7 and N7, clean-up: no 2 in R6C9, no 7 in R89C3
4b. 8 in R9 locked in R9C78 = {48}, locked for R9
4c. 7 in R9 locked in R9C12, locked for N7
4d. 9 in R9 locked in R9C123, locked for N7, clean-up: no 2 in R9C3

5. 45 rule on N8 3 innies R7C4 + R8C5 + R9C6 = 19 = {478/568} (cannot be {289/469} because R7C4 only contains 5,7, cannot be {379} because R9C6 only contains 4,8), no 1,2,3,9, 8 locked for N8
5a. R7C4 = {57} -> no 5,7 in R8C5
5b. 9 in N8 locked in 17(3) cage = 9{17/26/35}, no 4

6. 45 rule on N9 3 innies R7C9 + R8C8 + R9C7 = 14 = {158/248} (cannot be {167/257/356} because R9C7 only contains 4,8, cannot be {347} because 3,7 only in R8C8), no 3,6,7, 8 locked for N9, clean-up: no 5 in 22(3) cage (prelim o)
6a. 2 of {248} must be in R7C9 -> no 2 in R8C8
6b. Naked triple {679} in 22(3) cage, locked for N9

7. 45 rule on R3 2 outies R2C34 = 1 innie R3C1 + 8
7a. Min R3C1 = 4 -> min R2C34 = 12, no 1,2

8. R8C67 = {79} (hidden pair in R8)
8a. 6 in N9 locked in R7C78, locked for R7
8b. 45 rule on R7 2 outies R8C67 = 1 innie R7C9 + 14 -> R7C9 = 2, R6C9 = 4, clean-up: no 3 in R5C6
8c. Naked triple {135} in 9(3) cage, locked for N9
8d. 5 in R7 locked in R7C456, locked for N8

9. R6C9 = 4 -> R4C7 + R5C8 (step 3) = {15}, locked for N6, clean-up: no 9 in 21(3) cage (prelim n)
9a. Naked triple {678} in 21(3) cage, locked for N6

10. R6C345 = {569/578} (cannot be {389} which clashes with 14(3) cage in N6), no 3, 5 locked for R6, clean-up: no 2 in R5C6
10a. Hidden killer pair 7,8 in R6C12 and R6C345 for R6, R6C345 must contain both or neither of 7,8, R6C12 cannot contain both of 7,8 -> R6C345 = {578}, locked for R6

11. R12C7 = {18/45} (cannot be {27/36} which clash with 2,3,6,7 in R5678C7), no 2,3,6,7
[I think this is an ALS block]
11a. Naked quad {1458} in R1249C7, locked for C7, clean-up: no 1,4,5,8 in R2C8 (step 1), no 1,4,5,8 in R3C6
11b. 9 in C9 locked in R123C9, locked for N3, clean-up: no 5 in R3C9

12. Killer pair 5,8 in R12C7 and R3C89, locked for N3
12a. 13(3) cage in N3 = {139/346} (cannot be {247} because 2,4 only in R1C8), no 2,7
12b. 4 of {346} must be in R1C8 -> no 6 in R1C8
12c. 5 in C9 locked in R89C9, locked for N9

13. Hidden pair {27} in R2C8 + R3C7, clean-up: R3C6 = {27}
13a. Naked pair {27} in R3C67, locked for R3, clean-up: no 6 in R4C1
13b. R7C7 = 6 (hidden single in C7)
13c. 3 in C7 locked in R45C7, locked for N6
13d. 7 in C9 locked in R45C9, locked for N6

14. 13(3) cage in N4 = {139/238/256/346} (cannot be {148/157/247} because 4,5,7,8 only in R5C1), no 7
14a. 4,5 of {256/346} must be in R5C1 -> no 6 in R5C1
14b. 1 of {139} must be in R6C12 (R6C12 cannot be {39} which clashes with R6C78), no 1 in R5C1
14c. 8 of {238} must be in R6C12 (R6C12 cannot be {23} which clashes with R6C78), no 8 in R5C1

15. 45 rule on R6 3 outies R5C167 = 13 = {139/256/346}
15a. 1,6 only in R5C6 -> R5C6 = {16}, clean-up: no 2,3 in R6C6
15b. 5 of {256} must be in R5C1 -> no 2 in R5C1
15c. Naked pair {16} in R56C6, locked for C6 and N5

16. R4C567 = {159/258/357} (cannot be {249/348} because R4C7 only contains 1,5), no 4, 5 locked for R4, clean-up: no 8 in R3C1, no 2 in R5C4

17. 12(3) cage in N4 = {129/138/147/156/246} (cannot be {237/345} which clash with 13(3) cage)
17a. 8 of {138} must be in R45C3 (R45C3 cannot be {13} which clashes with R7C3), no 8 in R4C2

18. 12(3) cage in N1 = {138/147/156/345}, no 9, clean-up: no 3 in R2C4 (step 7)
18a. 8 of {138} must be in R23C3 (R23C3 cannot be [31] which clashes with R7C3), no 8 in R3C2
18b. 45 rule on N1 3 innies R1C3 + R2C2 + R3C1 = 18 = {189/279/369/459/567} (cannot be {378} because R3C1 only contains 4,5,6,9, cannot be {468} which clashes with 12(3) cage)
18c. 1 in {189} must be in R2C2 -> no 8 in R2C2
18d. 15(3) cage in N1 = {168/249/258/267/348/456} (cannot be {159/357} which clash with 12(3) cage)
18e. 3 of {348} must be in R12C1 (R12C1 cannot be {48} which clashes with R7C1), no 3 in R1C2

19. 45 rule on N2 3 innies R1C4 + R2C5 + R3C6 = 14 = {167/239/248/257/347} (cannot be {149/158/356} because R3C6 only contains 2,7)
19a. 1,3 of {167/239} must be in R2C5 -> no 6,9 in R2C5
19b. 13(3) cage in N2 = {139/157/238/256/346} (cannot be {148} which clashes with R9C6, cannot be {247} which clashes with R1C4 + R2C5 + R3C6)
19c. 1,6 of {139/157/256/346} must be in R1C5 -> no 4,5,7,9 in R1C5
19d. 18(3) cage in N2 = {189/369/459/468} (cannot be {378} which clashes with R1C4 + R2C5 + R3C6, cannot be {567} which clashes with R3C89), no 7

20. 45 rule on C1 4 outies R1679C2 = 26 = {2789/3689/4589/4679/5678}, no 1

21. 2,5 in R8 locked in R8C1349
21a. 45 rule on R9 4 outies R8C1349 = 14 = {1256/2345}
21b. 4 of {2345} must be in R8C4 -> no 3 in R8C4

22. 17(3) cage in N8 (step 5b) = {179/359}
22a. 1 of {179} must be in R7C5, 9 of {359} must be in R8C6 -> no 7,9 in R7C5

23. 13(3) cage in N4 (step 14) = {139/256/346}
23a. 1 of {139} must be in R6C1 -> no 9 in R6C1
23b. R4C1 + R5C2 + R6C3 (step 2) = {389/479/578} (cannot be {569} which clashes with 13(3) cage), no 6
23c. 12(3) cage in N4 (step 17) = {129/138/147/246} (cannot be {156} which clashes with 13(3) cage), no 5

24. 45 rule on R4 3 outies R5C349 = 1 innie R4C1 + 10, R4C1 = {4789} -> R5C349 = 14,17,18,19
24a. R5C349 cannot be {149} because R5C9 only contains 6,7,8, cannot be {158/167} which clash with R5C6 and R5C8 respectively, cannot be {179/189} because R5C4 only contains 3,4,5 -> no 1 in R5C3

25. 45 rule on N5 3 innies R5C5 + R6C45 = 1 outie R4C7 + 16
25a. R4C7 = {15} -> R5C5 + R6C45 = 17,21 = {278/458/579} (cannot be {359/489} because 3,4,9 only in R5C5)
25b. 2,4,9 only in R5C5 -> R5C5 = {249}

26. 5 in R4 locked in R4C567, 5 in R6 locked in R6C345
26a. 45 rule on N5 2 outies R4C7 + R6C3 = 1 innie R5C5 + 4
26b. R4C7 + R6C3 cannot be [55] because no 6 in R5C5 -> 5 locked in R4C56 + R6C45, locked for N5, clean-up: no 2 in R4C4

27. Naked pair {34} in R45C4, locked for C4 and N5, clean-up: no 9 in R1C3, no 7 in R4C56 (step 16), no 3 in R9C5 (prelim p)
27a. Naked triple {126} in 9(3) cage, locked for N8, clean-up: no 7 in 17(3) cage in N8 (step 22) -> R8C6 = 9, R8C7 = 7, R7C8 = 9, R3C67 = [72], R2C8 = 7, R6C8 = 2, clean-up: no 6 in R1C3
27b. Naked pair {35} in R7C56, locked for R7 -> R7C34 = [17], R8C2 = 3
27c. R6C5 = 7 (hidden single in C5)

28. R4C1 + R5C2 + R6C3 (step 23b) = {578} (only remaining combination, cannot be {479} because R6C3 only contains 5,8), locked for N4, clean-up: no 4,9 in R3C1
28a. Naked triple {678} in R4C189, locked for R4, clean-up: no 2 in R4C56 (step 16)
28b. R4C56 = [95], R4C7 = 1, R5C5 = 2, R5C8 = 5, R6C34 = [58], R7C56 = [53], clean-up: no 8 in R12C7, no 9 in R3C9, no 6 in R89C3
28c. R89C3 = [29]

29. Naked pair {45} in R12C7, locked for C7 and N3 -> R9C67 = [48], R8C58 = [84]
29a. Naked pair {68} in R3C89, locked for R3 and N3 -> R3C1 = 5, R89C1 = [67], R4C1 = 8, R4C89 = [67], R5C9 = 8, R3C89 = [86], R5C2 = 7, R7C12 = [48], R9C2 = 5, R8C4 = 1, R8C9 = 5, R9C45 = [26], R3C4 = 9, clean-up: no 4 in R1C3

30. R1C3 = 7 (hidden single in R1), R1C4 = 6

31. 13(3) cage in N4 (step 12) = {139} (only remaining combination) -> R6C2 = 9

32. R12C6 = {28} -> R1C5 = 3 (step 19b)

and the rest is naked singles.


Top
 Profile  
Reply with quote  
PostPosted: Wed Aug 03, 2011 2:24 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Assassin 147 by tarek (March 2009) here
Puzzle Diagram:
Image
Images with "udosuk style Killer Cages" by Børge:
Image     Image
Code: Select, Copy & Paste into solver:
3x3::k:4865:4865:2306:2306:6915:6915:6915:2308:2308:4865:5125:5125:5125:3334:6915:6151:6151:2308:1032:5125:3337:3337:3334:1802:6151:6151:6155:1032:5125:3337:8204:8204:1802:1802:6155:6155:5133:4366:4366:8204:8204:8204:2063:2063:6155:5133:5133:4624:4624:8204:8204:4881:7698:1555:5133:4372:4372:4624:1301:4881:4881:7698:1555:4374:4372:4372:5655:1301:7698:7698:7698:4120:4374:4374:5655:5655:5655:2329:2329:4120:4120:
81-character code
J<9<R<<9<^K<<D^O<^4^D<^7^^O^^^W<^<>^KH<^^<8<^^<I<^^JU6^H<^5>^^^H^^M^>>^G^<>^<9<>^
Solution:
+-------+-------+-------+
| 6 8 4 | 5 3 9 | 7 2 1 |
| 5 2 9 | 1 7 8 | 3 4 6 |
| 1 3 7 | 4 6 2 | 9 8 5 |
+-------+-------+-------+
| 3 5 2 | 6 8 4 | 1 7 9 |
| 4 9 8 | 7 5 1 | 2 6 3 |
| 7 1 6 | 9 2 3 | 8 5 4 |
+-------+-------+-------+
| 8 7 1 | 3 4 6 | 5 9 2 |
| 9 4 5 | 2 1 7 | 6 3 8 |
| 2 6 3 | 8 9 5 | 4 1 7 |
+-------+-------+-------+
Quote:
tarek: Here is my 1st ASSASSIN, completely computer generated but verified also using independent software.
SSS=1.13.

Afmob: Thanks for the new Assassin! The solving path was pretty straightforward, I think.
Rating: Hard 1.0.

Andrew: Thanks Tarek for your first Assassin.
I found this more challenging than I'd expected. I'll accept that it's straightforward if one finds both of Afmob's key steps easily but it took me a long time to find the second one, in fact I left this puzzle to try other ones and only came back to it this week.
I'll rate A147 the way I solved it at Easy 1.25 to 1.25.

Walkthrough by Afmob:
Thanks for the new Assassin! The solving path was pretty straightforward, I think.

A147 Walkthrough:

1. R456
a) Innies N5 = 13(2) = [49] -> R4C6 = 4, R6C4 = 9
b) 17(2) = {89} locked for R5+N4
c) Innies+Outies R6789: -1 = R5C1 - R6C56 -> R5C1 <> 1 and R6C56 <> 8 since R5C1 <= 7
d) 8 locked in R4C45 @ N5 for R4
e) Innies+Outies R1234: -11 = R5C9 - R4C45 -> 12 <= R4C45 = 8{5/6/7} -> R5C9 = (234)
f) 9 locked in 24(4) @ R4 for 24(4) = 9{258/267/348/357/456} <> 1 because R5C9 = (234); R3C9+R4C89 <> 2,3,4

2. R123
a) Innies N3 = 12(2) = [48/57/75]
b) 27(4) = 9{378/468/567} -> 9 locked for N2
c) 13(2) <> 4
d) 27(4) = 79{38/56} because {4689} blocked by Killer pair (68) of 13(2); CPE: R1C4 <> 7
e) Killer pair (68) locked in 27(4) + 13(2) for N2
f) 4 locked in R123C4 @ N2 for C4
g) Innies N3 = 12(2) = {57} locked for N3

3. C789 !
a) Outies C9 = 10(3) <> 8,9; R19C8 <> 5,6,7 since R4C8 >= 5
b) Hidden Single: R4C9 = 9 @ N6
c) ! 24(4) <> 4 because [5694] blocked by Killer pair (45) of 6(2)
d) Hidden Single: R5C1 = 4 @ R5
e) 8 locked in 16(3) @ C9 for N9 -> 16(3) = 8{17/26/35} <> 4; R89C9 <> 1,2,3 since R9C8 = (123)

4. R456
a) Innies R6789 = 5(2) = {23} locked for R6+N5
b) 2 locked in R5C789 @ R5 for N6
c) R4C7 = 1, R3C6 = 2, R4C1 = 3, R3C1 = 1
d) 20(4) = 14{69/78} since (89) only possible @ R7C1 -> R6C2 = 1; R7C1 = (89)
e) 18(3) = 9{27/36} -> R7C3 = (23)
f) Naked pair (67) locked in R6C13 for R6+N4
g) 13(3) = 2{38/47/56} <> 9 because R4C3 = (25) -> R4C3 = 2

5. C123
a) Innies N7 = 11(2) = [83] -> R7C1 = 8, R9C3 = 3
b) Cage sum: R6C1 = 7
c) R6C3 = 6 -> R7C4 = 3
d) 17(3) = {269} locked for N7 since R89C1 = (2569)
e) 5 locked in 19(3) @ C1 = {568} for N1 -> R1C2 = 8; 6 locked for C1+N1
f) 9(2) = {45} -> R1C3 = 4, R1C4 = 5
g) R3C3 = 7, R3C9 = 5

6. N69
a) 24(4) = {3579} -> R4C8 = 7, R5C9 = 3
b) R6C9 = 4 -> R7C9 = 2
c) 9(2) = {45} -> R9C6 = 5, R9C7 = 4
d) 19(3) = {568} -> R7C6 = 6, R7C7 = 5, R6C7 = 8

7. Rest is singles.

Rating: Hard 1.0. I used Killer pairs.
Walkthrough by Andrew:
Thanks Tarek for your first Assassin.

I found this more challenging than I'd expected. I'll accept that it's straightforward if one finds both of Afmob's key steps easily but it took me a long time to find the second one, in fact I left this puzzle to try other ones and only came back to it this week.

I'll rate A147 the way I solved it at Easy 1.25 to 1.25 because of steps 10a, 14 and 20; I've included steps 10a and 20 at this level because they each extend into two nonets and into two rows or columns. Also it has a narrow solving path until one has found both key steps.

Here is my walkthough for A147.

Prelims

a) R1C34 = {18/27/36/45}, no 9
b) R23C5 = {49/58/67}, no 1,2,3
c) R34C1 = {13}, locked for C1
d) R5C23 = {89}, locked for R5 and N4
e) R5C78 = {17/26/35}, no 4
f) R67C9 = {15/24}
g) R78C5 = {14/23}
h) R9C67 = {18/27/36/45}, no 9
i) 19(3) cage in N1 = {289/379/469/478/568}, no 1
j) 9(3) cage in N3 = {126/135/234}, no 7,8,9
k) 7(3) cage at R3C6 = {124}
l) 19(3) cage at R6C7 = {289/379/469/478/568}, no 1
m) 27(4) cage at R1C5 = {3789/4689/5679}, no 1,2

1. 45 rule on N5 2 innies R4C6 + R6C4 = 13 -> R4C6 = 4, R6C4 = 9, clean-up: no 5 in R9C7
1a. R3C6 + R4C7 = {12}, CPE no 1,2 in R3C7
1b. X-Wing for 1 in R34C1 and R4C6 + R6C4, locked for R34
1c. R6C4 = 9 -> R6C3 + R7C4 = 9 = [18]/{27/36/45}, no 1 in R7C4

2. 45 rule on N3 2 innies R1C7 + R3C9 = 12 = {39/48/57}, no 2,6

3. 45 rule on N7 2 innies R7C1 + R9C3 = 11 = {29/47/56}/[83], no 1,8 in R9C3

4. 45 rule on R1 3 outies R2C169 = 19 = {289/379/469/478/568}, no 1
4a. 2,3 of {289/379} must be in R2C9, no 2 in R2C1, no 3 in R2C6

5. 45 rule on R9 3 outies R8C149 = 19 = {289/379/469/478/568}, no 1

6. 45 rule on C9 3 outies R149C8 = 10 = {127/136/145/235}, no 8,9

7. R4C9 = 9 (hidden single in R4), clean-up: no 3 in R1C7 (step 2)

8. 8 in R4 locked in R4C45, locked for N5
8a. 45 rule on R1234 2 innies R4C45 = 1 outie R5C9 + 11
8b. Max R4C45 = 15 -> max R5C9 = 4
8c. Min R5C9 = 1 -> min R4C45 = 12, no 2,3 in R4C45
8d. Min R4C45 = {58} = 13, min R5C9 = 2

9. 24(4) cage at R3C9 = {2589/2679/3489/3579/4569}
9a. Max R345C9 = 21 -> min R4C8 = 3
9b. Max R4C89 + R5C9 = 20 and contains 4 -> min R3C9 = 5, clean-up: no 8,9 in R1C7 (step 2)
9c. Min R14C8 = 4 -> max R9C8 = 6 (step 6)

10. 27(4) cage at R1C5 = {3789/4689/5679}, 9 locked for N2, clean-up: no 4 in R23C5
10a. 27(4) cage at R1C5 = {3789/5679} (cannot be {4689} which clashes with R23C5), no 4, CPE no 7 in R1C4, clean-up: no 2 in R1C3, no 8 in R3C9 (step 2)
10b. 5 of {5679} must be in R1C7 (R1C56 + R2C6) cannot be {569} which clashes with R23C5), no 5 in R1C56 + R2C6
10c. Killer pair 6,8 in R1C56 + R2C6 and R23C5, locked for N2, clean-up: no 1,3 in R1C3
10d. 4 in N2 locked in R123C4, locked for C4, clean-up: no 5 in R6C3 (step 1c)
[I could also lock 7 for N2 using interactions between the 13(2) and 27(4) cages but that’s a higher rated step so I won’t use it.]

11. Naked pair {57} in R1C7 + R3C9, locked for N3
11a. 9(3) cage in N3 = {126/234}, 2 locked for N3
11b. 24(4) cage at R3C9 (step 9) = {2679/3579/4569}
11c. R5C9 = {234} -> no 3 in R4C8
11d. 3 in R4 locked in R4C123, locked for N4, clean-up: no 6 in R7C4 (step 1c)
11e. Min R14C8 = 6 -> max R9C8 = 4 (step 6)
11f. Min R49C8 = 6 -> max R1C8 = 4 (step 6)

12. 8 in C9 locked in R89C9, locked for N9, clean-up: no 1 in R9C6
12a. 16(3) cage in N9 = 8{17/26/35}, no 4
12b. R9C8 = {123} -> no 1,2,3 in R89C9

13. R8C149 (step 5) = {289/379/478/568} (cannot be {469} because 4,9 only in R8C1)
13a. 4,9 of {289/379/478} must be in R8C1 -> no 2,7 in R8C1

14. Hidden killer triple 1,2,3 in R4C1, R4C23 and R4C7 for R4 -> R4C23 must contain one of 2,3 -> R4C23 must contain one of 5,6,7
[The final part of this could also be obtained from hidden killer triple 5,6,7 in R4C23, R4C45 and R4C8 for R4]

15. 20(4) at R5C1 = {1469/1478/1568/2459/2468/2567} (cannot be {1289} because 8,9 only in R6C1)
15a. 8,9 of {1469/1478/2459/2468} must be in R7C1 -> no 4 in R7C1, clean-up: no 7 in R9C3 (step 3)
15b. 2 of {2567} must be in R5C1 + R6C12 (R5C1 + R6C12 cannot be {567} which clashes with R4C23), 8,9 of {2459/2468} must be in R7C1 -> no 2 in R7C1, clean-up: no 9 in R9C3 (step 3)
15c. Killer triple 1,2,3 in R4C1, R4C23 and R5C1 + R6C12, locked for N4, clean-up: no 7,8 in R7C4 (step 1c)

16. 13(3) cage at R3C3 = {238/247/256/346}, no 9

17. 45 rule on R123 4 remaining outies R4C1237 = 1 innie R3C9 + 6
17a. R3C9 = {57} -> R4C1237 = 11,13 = {1235/1237}, no 6

18. 20(4) at R5C1 (step 15) = {1469/1478/1568/2459/2468/2567}
18a. 6 of {2567} must be in R5C1 + R6C12 (R5C1 + R6C12 cannot be {257} which clashes with R4C23), 8,9 of {1469/1478/2459/2468} must be in R6C1 -> no 6 in R7C1, no 5 in R9C3 (step 3)

19. 13(3) cage at R3C3 (step 16) = {238/247/256/346}
19a. 6,8 of {238/256/346} must be in R3C3 -> no 3,5 in R3C3

20. 24(4) cage at R3C9 (step 11b) = {2679/3579} (cannot be {4569} which clashes with R67C9), no 4, clean-up: no 7 in R4C45 (steps 8 and 8a)
[I missed that clash earlier; {4569} could have been eliminated in step 9.]
20a. R5C1 = 4 (hidden single in R5), clean-up: no 5 in R7C3 (step 1c)
20b. 6 in N4 locked in R6C123, locked for R6
[After fixing R5C1, Afmob found 45 rule on R6789 2 innies R6C56 = 5 = {23}, locked for R6 and N5, which makes the later stages quicker.]

21. R78C5 = {14} (cannot be {23} which clashes with R7C4), locked for C5 and N8

22. 20(4) at R5C1 (step 15) = {1469/1478/2459/2468}
22a. 8,9 only in R7C1 -> R7C1 = {89}, clean-up: no 4,6 in R9C3 (step 3)
22b. 1 of {1478} must be in R6C2 -> no 7 in R6C2

23. 22(4) cage at R8C4 = {2389/2569/2578/3568}
23a. 9 of {2389} must be in R9C5, 2,3 of other combinations must be in R9C3 -> no 2,3 in R9C5

24. 9 in C5 locked in R19C5
24a. 45 rule on C5 5 innies R14569C5 = 27 = {23589/23679}
24b. 2 locked in R56C5, locked for N5
24c. 6 of {23679} must be in R4C5 -> no 6 in R159C5

25. Killer triple 1,2,3 in R4C7, R5C78 and R5C9, locked for N6, clean-up: no 4,5 in R7C9

26. 3 in R6 locked in R6C56, locked for N5
26a. Hidden killer pair 1,2 in R6C12 and R6C56 for R6, R6C12 contains one of 1,2 -> R6C56 must contain one of 1,2 and also 3 (step 26) -> R6C5 = {23}, R6C6 = {13}
26b. 7 in N5 locked in R5C456, locked for R5, clean-up: no 1 in R5C78

27. R4C7 = 1 (hidden single in N6), R3C6 = 2, R4C1 = 3, R3C1 = 1, clean-up: no 7 in R1C3, no 8 in R9C6, no 7 in R9C7
27a. 2 in N6 locked in R5C789, locked for R5
27b. R6C5 = 2 (hidden single in C5), R6C6 = 3 (hidden single in R6), R6C2 = 1 (hidden single in R6), clean-up: no 6 in R9C7
27c. R1C5 = 3 (hidden single in C5), R9C5 = 9 (hidden single in C5), clean-up: no 6 in R1C3
27d. Killer pair 5,7 in R23C5 and R5C5, locked for C5

28. R1C5 = 3 -> 27(4) cage at R1C5 (step 10a) = {3789}, no 5,6 -> R1C7 = 7, R3C9 = 5, R6C9 = 4, R7C9 = 2, R5C9 = 3, R12C9 = [16], R1C8 = 2 (step 11a), R7C4 = 3, R6C3 = 6 (step 1c), clean-up: no 8 in R1C3, no 8 in R2C5, no 7 in R3C5, no 5,6 in R5C7, no 5 in R5C8
28a. R5C78 = [26], R4C8 = 7, clean-up: no 7 in R9C6

29. Naked pair {89} in R12C6, locked for C6 and N2, clean-up: no 5 in R2C5
29a. R23C5 = [76], R45C5 = [85], R4C4 = 6, R3C4 = 4, R1C34 = [45], R2C4 = 1, R5C46 = [71]
29b. Naked pair {28} in R89C4, locked for 22(4) cage at R8C4 -> R9C3 = 3, R9C7 = 4, R9C6 = 5, R9C8 = 1, R7C1 = 8 (step 3), R6C1 = 7 (step 22)

30. R3C4 = 4 -> R34C3 = 9 = [72], R4C2 = 5, R2C1 = 5, R2C8 = 4 (hidden singles in R2)
30a. R2C1 = 5 -> R1C12 = 14 = [68], R12C6 = [98], R89C1 = [92], R89C4 = [28], R89C9 = [87], R9C2 = 6, R5C23 = [98], R23C2 = [23], R2C3 = 9, R2C7 = 3

31. 5 in R6 locked in R6C78, CPE no 5 in R8C7
31a. R8C67 = [76], R7C6 = 6, R67C7 = 13 = [85]

and the rest is naked singles.


Top
 Profile  
Reply with quote  
PostPosted: Wed Aug 03, 2011 3:11 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Assassin 148 by Afmob (March 2009) here
Puzzle Diagram:
Image
Images with "udosuk style Killer Cages" by Børge:
Image     Image
Code: Select, Copy & Paste into solver:
3x3::k:5635:5635:4353:5128:1814:1814:1814:3352:3865:5635:4353:4353:4353:5128:4114:3865:3865:3352:5635:5893:5893:5128:2314:4114:4114:3093:3093:5893:3852:3852:5127:2314:2063:2063:4881:4881:5893:3600:3852:3852:5127:4877:4877:4881:3846:3600:3600:3342:3342:1803:5127:4877:4877:3846:788:788:4371:4371:1803:3593:3846:3846:3588:3354:3611:3611:4371:3593:6402:6402:6402:3588:3611:3354:5399:5399:5399:3593:6402:3588:3588:
Solution:
+-------+-------+-------+
| 8 7 9 | 3 4 2 | 1 5 6 |
| 6 4 3 | 1 9 5 | 7 2 8 |
| 1 2 5 | 8 6 7 | 4 9 3 |
+-------+-------+-------+
| 7 8 1 | 5 3 6 | 2 4 9 |
| 9 3 2 | 4 7 1 | 8 6 5 |
| 5 6 4 | 9 2 8 | 3 7 1 |
+-------+-------+-------+
| 2 1 8 | 7 5 9 | 6 3 4 |
| 4 5 6 | 2 1 3 | 9 8 7 |
| 3 9 7 | 6 8 4 | 5 1 2 |
+-------+-------+-------+
Quote:
Afmob: Despite the hurry, I took my time to create this Killer because I wanted to make one like I did in the beginning: Generate a random sudoku and transform it into a Killer. The good thing about this approach is that the solution path is a bit broader since you don't focus on an unusual cage pattern but on getting the uniqueness right.
SS Score: 1.33. Estimated rating: Easy 1.25 - 1.25.

manu: Thanks Afmob for a new Assassin.
I had to work hard ... to solve this puzzle. I have seen an interesting particularity of the cage pattern (see PS remark), but I could not use it effectively...

Ed: This solution is "a Para" - got so caught up in ...! Presumably, there is a simpler solution. Very enjoyable puzzle. Thanks Afmob!
This walkthrough has a number of crucial steps that, on their own, I would put in the 1.25 rating range ... I'll make this solution an Easy 1.50 rating.

Afmob: Great ... find in your step 10, Ed!

Andrew: Another Assassin where I'd got stuck and came back to it later, then finding the breakthrough as I've commented under step 16.
My solving path was much more like Afmob's one than the other two ...
I'll rate A148 at Easy 1.25 to 1.25 since, although longer, it's about the same difficulty level as Afmob's walkthrough; that is, of course, ignoring the fact that I got stuck. ;)

Walkthrough by manu:
Thanks Afmob for a new Assassin.
I had to work hard with combinations to solve this puzzle. I have seen an interesting particularity of the cage pattern (see PS remark), but I could not use it effectively...

Edit : Ed has pointed out some steps that should been clarified. Thanks Ed ! I have also added a final remark. Interesting puzzle that can be viewed using different ways


Walkthrough Assassin 148

1)cage 3(2) at r7 : {12} locked for r7 and n7

2)Innies for n78 : r7c5+r8c6=8 → r7c5=(356), r8c6=(532). Using cage 7(2), r6c5=(124)

3)Innies for n3 : r1c7+r3c7=5 → r13c7=[14/23/41]

4)a) Innies for r789 : r7c5+r7c7+r7c8=14. Combinations : r7c578={347/356}
b) Cells r7c78 contain at least one of {346} and at least one of {345} (because from step a) cells r7c578 contain two of {346} and two of {345}) : combinations
{1346/2345} for cage 14(4) are blocked → 14(4)=12{38/47/56}
c) cage 15(4) = {1347/1356/2346} from step a)

5)Cells r789c9 of cage 14(4) see all cells of cage 15(4)
a) 14(4) <>{1238} because all combinations of cage 15(4) contain two of {1238}
→ 14(4) =12{47/56}
b) Cage 14(4) contains two of {246} → cells r789c9 contain at least one of {246}
→ 15(4) <> {2346}, so 15(4) = 13{47/56}
c) Both cages 14(4) and 15(4) contain 1 → r9c8=1 and 1 is locked at r56c9 for c9 and n6.
d) 2 is locked for c9 and n9 at r789c9.

6)Outies for n6789 : we deduce a hcage 9(3) at r6c5+r5c6+r4c6.
a) Innies for n23 : r2c4+r3c5=7 → no 7,8,9 for r2c4 and r3c5, no 1,2 for r4c5.
b) Outies for n1 : r2c4+r4c1+r5c1=17. r2c4<=6 → r4c1+r5c1 >= 11 : no 1.
c) from steps a and b, digit 1 is locked for r4 at r4c23+r4c6 → r5c4<>1 (it sees all 1 of r4)
d) We deduce that 1 is locked for n5 at hcage 9(3) : {126/135}
→ r6c5<>4 (no combination with digit 4), r7c5=(56), r8c6=(32) (step 2)

7)a)Using steps 6)d) and 4)a), deduce that r7c578={356}, all locked for r7, and 3 is locked for
n9 at r7c78
b) cage 15(4) at n69 : {1356} (because it must contain two of {356}), with 3 locked at r7c78
→ cage 14(4) at n9 = {1247} (remind from step 5 that r789c9 see all cells of cage 15(4), so combinations of cage
14(4) cannot have two of {1356} : no {1256}) , with 2,4 an 7 locked for c9.

8)Innies for n7 : r7c3+r9c3=15 → r79c3=[78/87/96] (remind : 6 locked for r7)
a) 8 is locked for r7 at r7c34+r7c6. Using r7c3+r9c3=15 and cage 21(3), we deduce that
cells r9c45 cannot contain digit 8 unless r9c3 is 7 (↔ r7c3=8). We deduce that r9c3<>6 : no valid combination for cage 21(3).
b) r79c3={78} (locked for n7), cage 13(2) at n7 is {49}, cage 14(3) = {356}
c) 9 is locked for r7 and n8 at r7c46. We deduce there is no 9 in cage 21(3) → 21(3)={678} all locked for r9 with 6 locked at r9c45 for n8.
d) NS : r7c5=5 → r6c5=2, r8c6=3 (step 2)
e) Naked pair : r7c78={36} locked for r7,n9 and the rest of the cage 15(4)→ r56c9={15}
locked for c9 and n6.
f) HS for n7 : r9c1=3, naked pair {56} at r8c23 locked for r8 and n7.
g) HS for n9 : r9c7=5, r8c78={89} locked for r8 and n9
h) NS : r8c1=4, r9c2=9
i) Naked pair {24} at r9c69

9) a) hcage 9(3) at n5 : r45c6={16} (all locked for c6 and n5)
b) Naked pair {24} at r19c6 : 2,4 locked for c6 → r7c6=(789) (could been deduced using
killer pair {89} at r7c34+r7c6 and r7c23<>{89}, which proves r7c6=(89) )

10) No valid combination for cage 17(3) at n78 with digit 4 at r7c4 since r8c4<>5,6
→ r9c6=4 (HS for n8)

11) a) NS : r9c9=2. → r78c9=[47] → r8c45=[21] (all NS)
b) Cage combination for 17(3) : r7c34={78} locked for r7 → (NS) r7c6=9
c) NS : r1c6=2 → (NS) r1c57=[41]
d) r3c7=4 (step 3) and r23c6={57} (cage combination)

12) Cage 9(2) at c5 : [63] → (step 6)a) r2c4=1

13) Step 6)b → r4c1+r5c1=16 : r45c1={79} (locked for c1) → r3c23= {25} (locked for r3)
→ cage 12(2) at n3 : {39} locked for r3 and n3.

14) Singles and simple cage combinations





Remark 1) : cells r56789c9 and r7c78 see each over, so the total is at least 28. If we add these cells to r9c8, one must find 14+15=29, which proves (min-max argument) r8c1=1, and r56789c9 + r7c78 ={1234567}. But I did not find this interesting move really fruitful for the rest, so I did not use it.

Remark 2) : Step 8a) (and 8c) ) can also be deduced more clearly using IOE : see steps 7 and 10 of Ed's WT
Walkthrough by Ed:
This solution is "a Para" - got so caught up in fun combo work (very different to manu's) that forgot to do many "45s"! Presumably, there is a simpler solution. Very enjoyable puzzle. Thanks Afmob!

This walkthrough has a number of crucial steps that, on their own, I would put in the 1.25 rating range. See steps 6, 7, 9 & 10. Perhaps step 10 should be in the 1.5 range. With this many crucial steps [edit: used to be 5 crucial steps], I'll make this solution an Easy 1.50 rating. [edit: Afmob found a flaw in the original step 10. The new step 10 is definitely a 1.50 rating]. I also like to rate "messy" cage patterns a bit higher. [edit: Afmob has pointed out, that it has rotational and diagonal symmetry. I was thinking of the crossing-over and diagonal cages. Personally, I find plain cage patterns a bit boring now - so "messy" is not a complaint from me!]. It takes 16 steps before it's cracked (new step 10 helped a lot!).


Assassin 148 Walkthrough
NOTE: this walkthrough is an optimised solution so some obvious eliminations are left out since they are not essential to the early solution. However, I still want to show most of the clean-up while going through. Please let me know of any corrections or clarifications. [Thanks Andrew for some typos and clarifications. Always appreciated.]

Prelims
i. 20(3)n2: no 1,2
ii. 7(3)n2 = {124}
iii. 13(2)n3: no 1,2,3
iv. 9(2)n2: no 9
v. 12(2)n3: no 1,2,6
vi. 20(3)n5: no 1,2
vii. 8(2)n5: no 4,8,9
viii. 19(3)n6: no 1
ix. 13(2)n4: no 1,2,3
x. 7(2)n5: no 7,8,9
xi. 3(2)n7 = {12}
xii. 14(4)n9: no 9
xiii. 13(2)n7: no 1,2,3
xiv. 21(3)n7: no 1,2,3

1. 3(2)n7 = {12}: both locked for r7 & n7
1a. no 5,6 in r6c5

2. "45" n7: 2 innies r79c3 = 15 = {69/78}

3. "45" n78: 2 innies r7c5 + r8c6 = 8 = [62]/{35}(no 4 in r7c5, no 789) = [2/3..]
3a. r8c6 = (235)
3b. no 3 in r6c5

4. "45" n9: 3 outies r56c9 + r8c6 = 9
4a. min. r8c6 = 2 -> max. r56c9 = 7 (no 7,8,9)
4b. max. r8c6 = 5 -> min. r56c9 = 4 (important for next step)

5. 15(4)n6 cannot have both {12} in r56c9 since must be min. 4 (step 4b) -> 12{39/48/57} all impossible
5a. = {1347/1356/2346}(no 8,9)
5b. = two of 1/2/3 (important for next step)

6. 14(4)n9, except for r9c8, sees all of the 15(4)n6-> the 14(4) can have at most two of 1/2/3 -> {1238} blocked. If that is not clear, I had to think of it like this. If every cell in the 14(4) "sees" the 15(4)n6 then it could only have one of 1/2/3 for the same house it shares since the 15(4) must have two of 1/2/3. This would make it a killer triple (123). However, in this puzzle, r9c8 hides from r56c9 -> a second 1/2/3 can hide here. But there is nowhere for a third 1/2/3 to hide.
6a. In summary, 14(4)n9 = {1247/1256/1346/2345}(no 8)
6b. = two of 1/2/3 -> r9c8 = (123) (NOTE: manu's PS comment at the end of his walkthrough is much better still!)

7. Hidden killer pair (89) in r7 -> r7c6 = (89). ie. r7c34 cannot be both 8 & 9 since it is in a 17(3) cage -> the only other place for (89) in r7 is r7c6
7a. r7c6 = (89) -> 14(3)n8 = {149/158/248}(no 3,6,7) ({239} blocked by h8(2)n8 step 3)
7b. no 8,9 in r8c5 nor r9c6 since the 14(3) can only have one of 8/9

8. "45" n789: 3 innies r7c578 = 14 = {347/356}
8a. 3 locked for r7

9. Hidden Killer triple (123) in n8 -> r8c4 = (123). ie. since 14(3)n8 = one of 1/2/3 (step 7a) & h8(2)n8 = one of 1/2/3 (step 3). The only other place for 1/2/3 in n8 is r8c4
9a. 17(3)n7 = {179/269/278/359/368}(no 4)

10. "45" n8: 1 outie r7c3 + 6 = 2 innies r9c45 (adding in the h8(2) in n8)
10a. r7c3 = (6789). For each of these, when the candidate is in r7c3, the only place for that digit in n8 is in the innies r9c45 -> the IOD (6) is locked in r9c45 (IOE)
10b. 6 locked in r9c45 for r9 & n8
10c. no 1 in r6c5

11. 21(3)n7 = {678}: 7 & 8 locked for r9
11a. no 5,6,7 in r8c1

12. h15(2)n7 = {78}: both locked for n7 & c3
12a. no 5,6 in r6c4

13. h8(2)n8 = {35}: both locked for n8

14. 17(3)n7 = {179/278}: 7 locked for r7

15. h14(3)r7c578 = {356}: 5 & 6 locked for r7 & 6 locked for n9 and 15(4)n6
15a. r7c9 = 4 (hsingle r7)

16. "45" n9: 3 outies = 9 -> r56c9 = 4/6 = {13/15}(no 2)
16a. 1 locked for c9 & n6
16b. 15(4) must have 1 = {1356}
16c. no 3 or 5 in r89c9: CPE on 3 & 5 in 15(4)

It's cracked now. Trying to get to singles ASAP from here. Excuse the lack of cleanup.

17. 14(4)n9 = [4]{127} -> r9c8 = 1, r89c9 = [72]

18. r9c6 = 4
18a. no 9 in r8c1
18b. r8c1 = 4, r9c2 = 9

19. naked triple {124} in r168c5: all locked for c5

20. 9(2)n2 = {36}: both locked for c5

21. r67c5 = [25]
21a. r8c56 = [13]
21b. r7c6 = 9 (cage sum)

22. r8c4 = 2

23. r9c4 = 6 (hsingle n8)

24. r9c7 = 5, r9c1 = 3

25. 2 remaining outies n9 r56c9 = 6 = {15}: 5 locked for c9 & n6

26. "45" n69: 2 remaining outies r45c6 = 7 = {16}: both locked for c6 & n5

27. r1c567 = [421]

28. 1 remaining innie n3 r3c7 = 4
28a. r23c6 = 12 = {57}: both locked for c6 & n2

29. r6c6 = 8

30. r2c4 = 1 (hsingle n2)
30a. r34c5 = [63]

31. 12(2)n3 = {39}: both locked for n3 & r3

32. naked pair {68} in r12c9: both locked for c9 & n3
32a. r4c9 = 9

33. "45" n1: 2 remaining outies r45c1 = 16 = [79]
33a. r3c23 = 7 (cage sum) = {25}: both locked for n1 & r3

34. naked pair {68} in r12c1: both locked for c1 & n1
34a. r3c1 = 1
34b. r1c2 = 7 (cage sum)

35. r7c12 = [21]
35a. r6c1 = 5 -> r56c2 = 9 = {36}: both locked for c2 & n4

36. 8(2)n5 = [62] (last permutation)
36a. r45c8 = 10 = [46]

37. r1c8 = 5 -> r2c9 = 8

Rest is singles.
Walkthrough by Afmob:
Great IOE find in your step 10, Ed! I used two Hidden Killer pairs (one was already mentioned by manu) to crack it.

A148 Walkthrough:

1. R789 !
a) 3(2) = {12} locked for R7+N7
b) Innies N7 = 15(2) = {69/78}
c) Innies N78 = 8(2) = [35/53/62]
d) Innies R789 = 14(3) = 3{47/56} -> 3 locked for R7
e) Outies N9 = 9(2+1): R56C9 <> 7,8,9 since R8C6 >= 2; R56C9 >= 4 since R8C6 <= 5
f) ! 15(4) = 3{147/156/246} because R56C9 >= 4, so it can't be {12} -> CPE: R789C9 <> 3
g) 25(4): R8C78+R9C7 <> 1,2 since R8C6 <= 5
h) 1,2 locked in 14(4) @ N9 = 12{38/47/56}

2. N89 !
a) 14(4): R9C8 = (12) because R789C9 = 12{...} blocked by Killer pair (12) of 15(4)
b) 14(4) = 12{47/56}
c) ! Hidden Killer pair (89) in R7C6 for R7 since 17(3) can only have one of (89) -> R7C6 = (89)
d) 14(3) = {149/158/248} <> 3,6,7 because R7C6 = (89) and {239} blocked by Killer pair (23) of Innies N78

3. C456 !
a) ! Hidden Killer pair (12) in Outies N14 = 14(3) + R8C4 for C4 since Outies N14 can only have one of (12)
-> R8C4 = (12)
b) 3 locked in Innies N78 @ N8 = 8(2) = {35} locked for N8
c) 14(3) = 4{19/28} -> 4 locked for N8
d) 21(3) = {678} locked for R9

4. R789
a) 8,9 locked in 25(4) @ N9 = {3589} -> 8 locked for R8
b) 13(2) = {49} locked for N7
c) Innies N7 = 15(2) = {78} locked for C7+N8
d) Hidden Single: R8C9 = 7 @ R8
e) 14(4) = {1247} -> R7C9 = 4; 1,2 locked for R9
f) 14(3) @ N8 = 4{19/28} -> R8C5 = (12), R9C6 = 4
g) 15(4) = {1356} -> 1 locked for C9+N6
h) R9C9 = 2, R9C8 = 1
i) 7(2) = [25/43]

5. C456
a) Naked triple (124) locked in R168C5 for C5
b) 9(2) = {36} locked for C5
c) R8C5 = 5 -> R7C5 = 2, R8C5 = 1 -> R7C6 = 9
d) Outies N69 = 10(3) = {136} -> R8C6 = 3; 1,6 locked for C6+N5
e) R1C5 = 4, R1C6 = 2, R1C7 = 1

6. R123
a) Innie N3 = R3C7 = 4
b) 16(3) = {457} -> 5,7 locked for C6+N2
c) 12(2) = {39} locked for R3+N3 since {57} blocked by R3C6 = (57)
d) Hidden Single: R2C4 = 1 @ N2
e) Outies N1 = 16(2) = {79} locked for C1+N4+23(4)
f) R3C5 = 6, R4C5 = 3, R6C6 = 8
g) 23(4) = {2579} because R45C1 = {79} -> 2,5 locked for R3+N1

7. R456
a) 20(3) = {578} -> R5C5 = 7, R4C4 = 5
b) R5C1 = 9, R4C1 = 7
c) 8(2) = {26} -> R4C6 = 6, R4C7 = 2
d) 19(3) = {469} because R4C89 <> 5,6 -> R4C9 = 9, R4C8 = 4, R5C8 = 6
e) 13(2) = {49} -> R6C3 = 4, R6C4 = 9

8. N13
a) R3C4 = 8, R3C1 = 1, R8C1 = 4
b) 22(4) = {1678} -> R1C2 = 7; 6,8 locked for C1+N1
c) 13(2) = {58} locked for N3

9. Rest is singles.
Walkthrough by Andrew:
Another Assassin where I'd got stuck and came back to it later, then finding the breakthrough as I've commented under step 16.

The key to this puzzle is clearly the interaction between the 15(4) cage at R5C9 and the 14(4) cage in N9, which I took some time to find. The first remark after manu's walkthrough is a neat piece of logic, which would give the first placement immediately by using a technically harder step.

The IOE in Ed's step 10 is neat! I've suggest by PM that it ought to be included as another IOE example in the Killer Techniques topic because it's simpler than the two already posted by Ed and Afmob.

My solving path was much more like Afmob's one than the other two although my later stages could probably a lot shorter if I'd remembered to use step 11 again after I'd fixed R2C4.

I'll rate A148 at Easy 1.25 to 1.25 since, although longer, it's about the same difficulty level as Afmob's walkthrough; that is, of course, ignoring the fact that I got stuck. ;)

Here is my walkthrough. Thanks Ed for your comments, particularly on step 18 where I've added a clarification and noted that I'd missed a combo elimination.

Prelims

a) 13(2) cage in N3 = {49/58/67}, no 1,2,3
b) R34C5 = {18/27/36/45}, no 9
c) R3C89 = {39/48/57}, no 1,2,6
d) R4C67 = {17/26/35}, no 4,8,9
e) R6C34 = {49/58/67}, no 1,2,3
f) R67C5 = {16/25/34}, no 7,8,9
g) R7C12 = {12}, locked for R7 and N7, clean-up: no 5,6 in R6C5
h) 13(2) cage in N7 = {49/58/67}, no 3
i) 20(3) cage in N2 = {389/479/569/578}, no 1,2
j) R1C567 = {124}, locked for R1, clean-up: no 9 in R2C9
k) 20(3) cage in N5 = {389/479/569/578}, no 1,2
l) 19(3) cage in N6 = {289/379/469/478/568}, no 1
m) R9C345 = {489/579/678}, no 1,2,3
n) 14(4) cage in N9 = {1238/1247/1256/1346/2345}, no 9

1. 45 rule on N3 2 innies R13C7 = 5 = [14/23/41]

2. 45 rule on N7 2 innies R79C3 = 15 = {69/78}, no 3,4,5
2a. 13(2) cage in N7 = {49/58} (cannot be {67} which clashes with R79C3), no 6,7
2b. Killer pair 8,9 in R79C3 and 13(2) cage, locked for N7

3. 45 rule on N23 2 innies R2C4 + R3C5 = 7 = {16/25/34}, no 7,8,9, clean-up: no 1,2 in R4C5
3a. Killer triple 1,2,4 in R1C56 and R2C4 + R3C5, locked for N2

4. 45 rule on N78 2 innies R7C5 + R8C6 = 8 = [35/53/62], clean-up: no 3 in R6C5

5. 45 rule on R789 3 innies R7C578 = 14 = {347/356}, no 8,9, 3 locked for R7

6. 45 rule on N9 2 innies R7C78 = 1 outie R8C6 + 6
6a. Min R8C6 = 2 -> min R7C78 = 8 -> max R56C9 = 7, no 7,8,9

7. 45 rule on R89 2 outies R7C69 = 1 innie R8C4 + 11
7a. Max R7C69 = 17 -> max R8C4 = 6

8. 45 rule on C6789 1 innie R6C6 = 2 outies R18C5 + 3
8a. Min R18C5 = 3 -> min R6C6 = 6
8b. Max R18C5 = 6, no 6,7,8,9 in R8C5

9. 45 rule on C1234 2 outies R29C5 = 1 innie R4C4 + 12
9a. Max R29C5 = 17 -> max R4C4 = 5
9b. Min R4C4 = 3 -> min R29C5 = 15, no 3,4,5

10. 20(3) cage in N5 = {389/479/569/578}
10a. R4C4 = {345} -> no 3,4,5 in R5C5

11. 45 rule on N1 2 innies R3C23 = 1 outie R2C4 + 6
11a. Max R2C4 = 6 -> max R3C23 = 12, min R45C1 = 11, no 1

12. 45 rule on N69 3 outies R458C6 = 10 = {127/136/145/235}, no 8,9

13. Hidden killer pair 1,2 in R13C7 and 15(3) cage for N3 -> 15(3) cage must contain one of 1,2
13a. 15(3) cage in N3 = {159/168/258/267} (cannot be {249/348} which clash with R13C7, cannot be {357/456} which don’t contain 1 or 2), no 3,4

14. 15(4) cage at R5C9 = {1347/1356/2346} (cannot be {1257} which clashes with combinations of R7C578), CPE no 3 in R89C9

15. 9 in N9 locked in 25(4) cage at R8C6 = {2689/3589/3679/4579} (cannot be {1789} because R8C6 only contains 2,3,5), no 1
15a. 2 of {2689} must be in R8C6 -> no 2 in R8C78 + R9C7

16. 1,2 in N9 locked in 14(4) cage
16a. Hidden killer pair 1,2 in R56C9 and R89C9 for C9 -> R89C9 cannot contain both of 1,2 -> R9C8 = {12}
16b. Killer pair 1,2 in R56C9 and R89C9, locked for C9
16c. 14(4) cage = {1247/1256}, no 8
[I got stuck a couple of steps later until I found step 16a so I’ve done a small rework. With hindsight, I could have done step 21 next.]

17. 8,9 in N9 locked in 25(4) cage at R8C6 (step 15) = {2689/3589}, no 4,7

18. 17(3) cage at R7C3 = {179/269/278/368/467} (cannot be {359} which clashes with R13C4 because 20(3) cage at R1C4 must contain one of 3,5 in R13C4, cannot be {458} which clashes with R13C4 + R4C4), no 5
18a. 4 of {467} must be in R7C4 (R7C34 cannot be {67} which clashes with R7C578), no 4 in R8C4
[Ed pointed that that 17(3) cage cannot be {368} which clashes with R7C5 + R8C6. This would eliminate 3 from R8C4.]

19. 45 rule on R89 4 outies R7C3469 = 28 = {4789/5689}
19a. Hidden killer pair 8,9 in R7C34 and R7C6 for R7, R7C34 cannot contain both of 8,9 -> R7C6 = {89}, R7C34 must contain one of 8,9
19b. 17(3) cage at R7C3 (step 18) = {179/269/278/368} (cannot be {467} which doesn’t contain 8 or 9), no 4
19c. 1,2,3 only in R8C4 -> R8C4 = {123}
19d. 4,5 of R7C3469 only in R7C9 -> R7C9 = {45}

20. 14(4) cage in N9 (step 16c) = {1247/1256}
20a. R7C9 = {45} -> no 4,5 in R89C9

21. 15(4) cage at R5C9 (step 14) = {1347/1356} (cannot be {2346} which clashes with 14(4) cage in N9 which must have 4 or 6 in C9), no 2, 1 locked in R56C9, locked for C9 and N6, clean-up: no 7 in R4C6
21a. R9C8 = 1 (hidden single in N9)

22. 14(3) cage in N8 = {149/158/248} (cannot be {167/257/347/356} because R7C6 only contains 8,9, cannot be {239} which clashes with R7C5 + R8C6), no 3,6,7
22a. R7C6 = {89} -> no 8,9 in R9C6
22b. 1 of {158} must be in R8C5 -> no 5 in R8C5

23. Naked triple {124} in R168C5, locked for C5, clean-up: no 5,7,8 in R34C5, no 2,3,5,6 in R2C4 (step 3)
23a. Naked pair {36} in R34C5, locked for C5, clean-up: no 1,4 in R6C5
23b. R67C5 = [25], R7C9 = 4, R8C6 = 3 (step 4), clean-up: no 9 in R1C8, no 8 in R3C8, no 5,6 in R4C7, no 7 in R7C78 (step 5)
23c. Naked pair {36} in R7C78, locked for R7, N9 and 15(4) cage at R5C9, clean-up: no 9 in R9C3 (step 2)
23d. Naked pair {15} in R56C9, locked for C9 and N6, clean-up: no 8 in R1C8, no 7 in R3C8
23e. Naked pair {27} in R89C9, locked for C9, clean-up: no 6 in R1C8, no 5 in R3C8

24. R1C6 = 2 (hidden single in N2), R9C6 = 4, R8C5 = 1, R7C6 = 9 (step 22), R1C5 = 4, R2C4 = 1, R1C7 = 1, R3C7 = 4 (step 1), R8C4 = 2, R89C9 = [72], clean-up: no 8 in R3C9, no 9 in R8C1, no 6 in R9C3 (step 2)

25. Naked pair {39} in R3C89, locked for R3 and N3 -> R34C5 = [63], clean-up: no 5 in R4C6
25a. Naked pair {68} in R12C9, locked for C9 and N3 -> R4C9 = 9, R3C89 = [93]
25b. 2 in N3 locked in R2C78, locked for R2

26. R9C1 = 3, R9C4 = 6 (hidden singles in R9), clean-up: no 7 in R6C3
26a. R9C2 = 9 (hidden single in N7), R8C1 = 4
26b. Naked pair {56} in R8C23, locked for R8 -> R8C78 = [98], R9C7 = 5
26c. Naked pair {78} in R79C3, locked for C3, clean-up: no 5 in R6C4

27. R1C4 = 3 (hidden single in C4), R2C5 + R3C4 = 17 = [98], R7C34 = [87], R9C35 = [78], R5C5 = 7, R4C4 + R6C6 = 13 = [58], clean-up: no 5,6 in R6C3
27a. Naked pair {49} in R6C34, locked for R6

28. Naked pair {27} in R24C7, locked for C7
28a. Naked pair {36} in R67C7, locked for C7 -> R5C7 = 8

29. 4 in C8 locked in R45C8
29a. R4C9 = 9 -> R45C8 = 10 = {46}, locked for C8 and N6 -> R6C78 = [37], R1C8 = 5, R2C9 = 8, R1C9 = 6, R1C3 = 9, R2C78 = [72], R23C6 = [57], R2C1 = 6, R6C34 = [49], R2C23 = [43], R5C4 = 4, R45C8 = [46], R5C6 = 1, R4C67 = [62], R4C3 = 1, R6C12 = [56], R5C123 = [932], R4C2 = 8 (cage sum), R3C1 = 1 (cage sum)

and the rest is naked singles.


Top
 Profile  
Reply with quote  
PostPosted: Wed Aug 03, 2011 3:26 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Just For Fun Killer 5 by manu (March 2009) here
Puzzle Diagram:
Image
PS : I apologize for the bad picture quality, but I can't do a better one since I have a new computer (?)
Images with "udosuk style Killer Cages" by Børge:
Image     Image
Code: Select, Copy & Paste into solver:
3x3::k:2560:1281:1538:1538:1028:2821:2821:2823:4360:1281:2560:11:1028:13:3598:15:4360:2823:4370:19:3092:21:3598:23:4360:25:1818:4370:1564:29:3092:31:2336:33:3106:1818:1564:37:1318:39:2336:41:3106:43:1580:2861:1318:47:2336:49:2866:51:1580:4149:2861:55:3384:57:2874:59:2866:61:4149:2879:3384:65:2874:67:2884:69:1606:2887:3384:2879:3146:3146:2884:2125:2125:2887:1606:
Solution:
+-------+-------+-------+
| 6 2 1 | 5 3 7 | 4 9 8 |
| 3 4 7 | 1 9 8 | 5 6 2 |
| 8 9 5 | 4 6 2 | 3 7 1 |
+-------+-------+-------+
| 9 5 8 | 7 1 3 | 2 4 6 |
| 1 7 2 | 6 4 9 | 8 3 5 |
| 4 3 6 | 2 8 5 | 9 1 7 |
+-------+-------+-------+
| 7 1 3 | 8 2 4 | 6 5 9 |
| 5 8 4 | 9 7 6 | 1 2 3 |
| 2 6 9 | 3 5 1 | 7 8 4 |
+-------+-------+-------+
Quote:
manu: I won't post a V2 for the next assassin (would be happy if someone do it); here is a puzzle to keep you busy.
There are more blank cells than the previous JFFK, and 45 Rule becomes difficult to use here. Anyway, there is still a logical path and I whish you to have pleasure with solving it. Blank cells killers I have tried to make before are often tedious (too much combos), but this one is quite straightforward (seems to be easier than a 1.4 puzzle)
This is not a X-killer
SSolver : 1.41.

Afmob: I agree with manu that JFF5 isn't that hard though some moves might be hard to spot. But the cage design hints where you have to take a closer look so that lowers the difficulty a bit.
Rating: 1.25.

Andrew: Thanks manu for another fun puzzle in this series.
Afmob wrote:
... though some moves might be hard to spot.
Yes some were hard to spot. I got stuck for a while until I found step 10.
I'll rate JFFK5 at Easy 1.5.

Walkthrough by Afmob:
I agree with manu that JFF5 isn't that hard though some moves might be hard to spot. But the cage design hints where you have to take a closer look so that lowers the difficulty a bit.

JFF 5 Walkthrough:

1. R123 !
a) 4(2) = {13} locked for N2
b) 17(2) = {89} locked for C1
c) ! Innies+Outies R1: 2 = R2C1249 - R1C9 -> R1C9 = (89); R2C1249 = 10/11 = 123{4/5} -> 1,2,3 locked for R2
d) 6(2): R1C3 <> 5
e) Naked quad (1234) locked in R1C23+R2C12 for N1
f) 3 locked in R3C789 @ R3 for N3
g) Both 11(2) <> 8
h) Hidden Single: R1C9 = 8 @ R1
i) Outies R1 = 10(4) = {1234} locked for R2
j) 10(2) = [64/73]
k) ! Innies+Outies R1: 1 = R2C29 - R1C25: R2C9 <> 4 because R2C2 = (34) and R1C25 can't be 6 (R1C25 <> 5; R1C5 <> 2,4)

2. R123
a) R2C9 = 2 -> R1C8 = 9
b) 17(3) = 8[54/63]
c) 5(2): R1C2 <> 3
d) Hidden Single: R1C5 = 3 @ R1
e) R2C4 = 1

3. C789
a) 16(2) = {79} locked for C9
b) Both 6(2): R68C8 <> 4
c) 11(2) @ R8C9: R9C8 <> 2,3,4
d) Outies C9 = 11(3) = {128} -> R9C8 = 8; {12} locked for C8
e) Cage sum: R8C9 = 3
f) Hidden Single: R3C9 = 1 @ R3 -> R4C9 = 6

4. R789+C1 !
a) 11(2) @ R6C1 <> 2,3
b) Killer pair (67) locked in R1C1 + 11(2) @ R6C1 for C1
c) 11(2) @ R8C1 = [29/47/56]
d) 12(2) <> 4
e) ! 4 locked in Innies R9 = 17(4) = 45{17/26} because 1,3 only possible @ R9C1 ({1349} unplaceable) -> 5 locked R9
f) 11(2) @ R8C1 <> 2
g) Killer pair (45) locked in 11(2) @ R6C1+R8C1 for C1
h) R2C1 = 3 -> R1C2 = 2, R2C2 = 4 -> R1C1 = 6, R1C3 = 1 -> R1C4 = 5
i) 11(2) @ R6C1 = {47} locked for C1
j) R8C1 = 5 -> R9C2 = 6

5. R789
a) 8(2) = {17} locked for R9
b) R9C1 = 2
c) 13(3) = {238} because {247} blocked by R7C1 = (47) -> R8C2 = 8, R7C3 = 3
d) R5C1 = 1, R6C2 = 3 -> R5C3 = 2

6. N25
a) 9(3): R4C6+R6C4 <> 4,5,6 since R5C5 >= 4
b) R6C4 = 2, R6C8 = 1 -> R5C9 = 5, R9C9 = 4, R9C5 = 5 -> R8C6 = 6
c) 11(2) @ R6C6 = [47/56/92]
d) 14(2) = {68} -> R2C6 = 8, R3C5 = 6

7. Rest is singles.

Rating: 1.25. I used IOD.
Walkthrough by Andrew:
Thanks manu for another fun puzzle in this series.
Afmob wrote:
... though some moves might be hard to spot.
Yes some were hard to spot. I got stuck for a while until I found step 10.

I'll rate JFFK5 at Easy 1.5 the way I solved it because I used a very short forcing chain. Technically that's higher rated than innie-outie differences although at a human solving level I don't think it's any harder than Afmob's step 1k.

Here is my walkthrough

Prelims

a) R1C1 + R2C2 = {19/28/37/46}, no 5
b) R1C2 + R2C1 = {14/23}
c) R1C34 = {15/24}
d) R1C67 = {29/38/47/56}, no 1
e) R1C5 + R2C4 = {13}, locked for N2, clean-up: no 5 in R1C3, no 8 in R1C7
f) R1C8 + R2C9 = {29/38/47/56}, no 1
g) R2C6 + R3C5 = {59/68}
h) R3C3 + R4C4 = {39/48/57}, no 1,2,6
i) R34C9 = {16/25/34}, no 7,8,9
j) R4C2 + R5C1 = {15/24}
k) R4C8 + R5C7 = {39/48/57}, no 1,2,6
l) R5C3 + R6C2 = {14/23}
m) R5C9 + R6C8 = {15/24}
n) R67C1 = {29/38/47/56}, no 1
o) R6C6 + R7C7 = {29/38/47/56}, no 1
p) R7C5 + R8C4 = {29/38/47/56}, no 1
q) R8C1 + R9C2 = {29/38/47/56}, no 1
r) R8C6 + R9C5 = {29/38/47/56}, no 1
s) R8C8 + R9C9 = {15/24}
t) R8C9 + R9C8 = {29/38/47/56}, no 1
u) R9C34 = {39/48/57}, no 1,2,6
v) R9C67 = {17/26/35}, no 4,8,9
w) R34C1 = {89}, locked for C1, clean-up: no 1,2 in R2C2, no 2,3 in R67C1, no 2,3 in R9C2
x) R67C9 = {79}, locked for C9, clean-up: no 2,4 in R1C8, no 2,4 in R9C8
y) 9(3) cage in N5 = {126/135/234}, no 7,8,9

A new record number of Prelims! That's because there's also a record number of 2-cell cages.

1. R5C3 + R6C2 = {23} (cannot be {14} which clashes with R4C2 + R5C1), locked for N4, clean-up: no 4 in R4C2 + R5C1
1a. Naked pair {15} in R4C2 + R5C1, locked for N4, clean-up: no 6 in R7C1

2. Killer quad 1,2,3,4 in R1C1 + R2C2, R1C2 + R2C1 and R1C3, locked for N1, clean-up: no 8,9 in R4C4

3. 45 rule on R12 6(1+5) innies R1C9 + R2C35678 = 43
3a. Max R2C35678 = 35 -> R1C9 = 8, R2C35678 = 35 = {56789}, locked for R2, clean-up: no 1,2,3,4 in R1C1, no 3 in R1C7, no 3,5 in R1C8, no 3 in R9C8
3b. R1C9 = 8 -> R2C8 + R3C7 = 9 = [54/63/72]
[With hindsight 45 rule on R1 4 outies R2C1249 = 1 innie R1C9 + 2 -> R1C9 = 8, R2C1249 = 10 = {1234}, locked for R2 is technically slightly easier than steps 3 and 3a.]

4. Killer pair 6,7 in R1C1 and R67C1, locked for C1, clean-up: no 4,5 in R9C2
4a. Killer pair 3,4 in R1C2 + R2C1 and R2C2, locked for N1, clean-up: no 2 in R1C4

5. 3 in R1 locked in R1C25
R1C2 = 3 => R2C1 = 2 => no 1 in R2C1
R1C5 = 3 => R2C4 = 1 => no 1 in R2C1
-> no 1 in R2C1, clean-up: no 4 in R1C2
5a. 1 in N1 locked in R1C23, locked for R1 -> R1C5 = 3, R2C4 = 1, clean-up: no 2 in R2C1, no 8 in R8C4, no 8 in R8C6
5b. Naked pair {12} in R1C23, locked for R1, clean-up: no 9 in R1C67
5c. 2 in C1 locked in R89C1, locked for N7

6. R1C8 = 9 (hidden single in R1), R2C9 = 2, clean-up: no 7 in R2C8 (step 3b), no 5 in R34C9, no 3 in R5C7, no 4 in R6C8, no 4 in R8C8

7. 1,7 in N3 locked in R12C7 + R3C89
7a. 45 rule on N3 4 innies R12C7 + R3C89 = 17 = {1367/1457}
7b. 6,7 of {1367} must be in R12C7, no 6 in R3C89, clean-up: no 1 in R4C9

8. 45 rule on C9 3 outies R689C8 = 2 innies R12C9 + 1
8a. R12C9 = [82] = 10 -> R689C8 = 11 = {128} (only remaining combination) -> R9C8 = 8, R8C9 = 3, R68C8 = {12}, locked for C8, clean-up: no 4 in R34C9, no 4 in R5C7, no 1 in R5C9, no 3,8 in R6C6, no 8 in R7C5, no 4 in R9C34, no 5 in R9C6, no 1 in R9C9
8b. R34C9 = [16]

9. R9C67 = {17/26} (cannot be [35] which clashes with R9C34), no 3,5
9a. Killer triple 6,7,9 in R9C2, R9C34 and R9C67, locked for R9, clean-up: no 2,4,5 in R8C6

10. 4 in R9 locked in R9C159
10a. 45 rule on R9 4 remaining innies R9C1259 = 17 = {1457/2456} (cannot be {1349} because 1,3,9 only in R9C12), no 3,9, clean-up: no 2 in R8C1
10b. R9C34 = {39} (hidden pair in R9)

11. Killer pair 4,5 in R67C1 and R8C1, locked for C1 -> R5C1 = 1, R4C2 = 5, R2C1 = 3, R1C2 = 2, R1C3 = 1, R1C4 = 5, R2C2 = 4, R1C1 = 6, R6C2 = 3, R5C3 = 2, R9C1 = 2, clean-up: no 9 in R2C6 + R3C5, no 7 in R3C3, no 7 in R5C7, no 5 in R7C1, no 6 in R7C5, no 9 in R8C6, no 6 in R9C67
11a. Naked pair {68} in R2C6 + R3C5, locked for N2
[While checking my walkthrough I spotted there is now
X-Wing for 7 in R1C67 and R9C67, locked for C67
but it’s so near the end I didn’t re-work my steps.]

12. R8C1 = 5 (hidden single in C1), R9C2 = 6

13. R9C1 = 2 -> R7C3 + R8C2 = 11 = [38/47]
13a. R7C2 = 1 (hidden single in C2)
13b. 9 in N7 locked in R89C3, locked for C3, clean-up: no 3 in R4C4
13c. R2C5 = 9 (hidden single in R2), clean-up: no 2 in R8C4

14. R3C5 = 6 (hidden single in R3), R2C6 = 8
14a. Naked pair {45} in R59C5, locked for C5, clean-up: no 6,7 in R8C4

15. 9(3) cage in N5 = {234} (only remaining combination, cannot be {126} because R5C5 only contains 4,5, cannot be {135} because R6C4 only contains,2,4,6), no 1,5,6 -> R5C5 = 4

and the rest is naked singles.


Top
 Profile  
Reply with quote  
PostPosted: Wed Aug 03, 2011 3:45 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Assassin 149 by manu (April 2009) here
Puzzle Diagram:
Image
Note that cells r46c5 form a cage 14(2).
Edit : thanks Ed for that nice picture !
Images with "udosuk style Killer Cages" by Børge:
Image     Image
Code: Select, Copy & Paste into solver:
3x3::k:1536:1536:6914:6914:5636:5637:5637:2055:2055:5129:5129:6914:5636:5636:5636:5637:2320:2320:5129:1299:8212:6914:5636:5637:8212:3353:2320:1299:5660:4125:8212:3615:8212:4385:4130:3353:3876:5660:4125:4125:8212:4385:4385:4130:4908:3876:5660:4125:8212:3615:8212:4385:4130:4908:3876:3639:2360:5689:5689:5689:3132:3901:4908:3639:2360:1857:1857:5689:2884:2884:3132:3901:2360:4425:4425:4425:5689:3917:3917:3917:3132:
Solution:
+-------+-------+-------+
| 4 2 9 | 8 1 6 | 7 5 3 |
| 8 5 6 | 9 3 7 | 4 2 1 |
| 7 3 1 | 4 2 5 | 9 8 6 |
+-------+-------+-------+
| 2 6 8 | 7 9 4 | 1 3 5 |
| 5 9 3 | 1 6 8 | 2 4 7 |
| 1 7 4 | 3 5 2 | 6 9 8 |
+-------+-------+-------+
| 9 8 5 | 2 7 1 | 3 6 4 |
| 6 1 2 | 5 4 3 | 8 7 9 |
| 3 4 7 | 6 8 9 | 5 1 2 |
+-------+-------+-------+
Quote:
manu: This is a quite hard Assassin : I have had to use many little steps and the whole cage pattern before cracking it.
I have no V2, but I think this one will resist enough to keep you busy ...
SS (V3.3.0) Score : 1.71.

Afmob: That was different! :lol:
My original walkthrough was twice as long and I had some trouble getting into the puzzle and finding some place to start. But after that there were ... which made the solving really enjoyable. Thanks for this fun killer, manu!
Rating: 1.25 - (Hard) 1.25.

Ed: I missed Afmob's neat step 1f. so took a slightly longer route to do the beginning. Did his step 2 ....differently. I'll give this puzzle a 1.5 rating since, as manu says, you have to consider the big picture of the puzzle (NOT a hint).
Really great puzzle. Thanks very much manu!

manu: Thanks for these very different but elegant walkthroughs, Afmob and Ed ! I have followed another (slightly different) approach, so other WTs are yet possible ;)
Reading Afmob's and Ed's, I have finally wanted to re-try to make a V2 with the same cage pattern, and got the following. (See next archive entry)

Andrew: A149 was the third successive Assassin that I went back to after being stuck at the time.
Even then I missed Afmob's first two ! steps, the third one follows from the second one. I also missed the key step 15 in Ed's walkthrough which I'm more annoyed that I missed.
On the basis that I'd rate both Afmob's and Ed's walkthroughs as Hard 1.25, I'll rate my walkthrough at 1.5 to Hard 1.5.

Walkthrough by Afmob:
That was different! :lol:

My original walkthrough was twice as long and I had some trouble getting into the puzzle and finding some place to start. But after that there were so many Killer subsets (especially hidden ones) I've found which made the solving really enjoyable. Thanks for this fun killer, manu!

A149 Walkthrough:

1. R789 !
a) Innies C12 = 8(3) = 1{25/34} -> 1 locked for N7
b) Innies C89 = 10(3) <> 8,9
c) Innies+Outies C89: 2 = R7C7 - R9C8 -> R7C7 <> 1,2
d) 1 locked in R7C456 @ R7 for N8
e) 7(2) <> 6
f) ! Innies+Outies C12: 1 = R7C3 - R9C2: R7C3 <> 6 and R9C2 <> 5 since (56) is a Killer pair of 14(2)
g) Hidden Quad (6789) in R7C12+R8C1+R9C3 for N7 -> R7C12+R8C1+R9C3 = (6789)
h) 14(2) = {68} locked for N7
i) 9(3) = 3{15/24} -> 3 locked for N7
j) Innies R789 = 13(2) = [76/94]

2. C789 !
a) Innies N3 = 28(4) = 89{47/56}
b) Hidden Killer pair (89) in R789C7 for N9 since 15(2) can only have of (89)
c) Innies N3 = 28(4): R3C8 = (89) since R123C7 can only have of (89) because of R789C7
d) 13(2) = [85/94]
e) 19(3) = {469/478/568} <> 2,3 because R7C9 = (46)
f) Killer pair (45) locked in R4C9 + 19(3) for C9
g) 8(2): R1C8 <> 3
h) 9(3): R2C8 <> 3 since 4,5 only possible there
i) 3 locked in R123C9 @ N3 for C9
j) ! Innies+Outies C89: 2 = R7C7 - R9C8: R7C7 <> 8,9 and R9C8 <> 6,7 since (68,79) are Killer pairs of 15(2)

3. C789 !
a) 12(3) = {147/156/237/246} because R9C9 <> 3,4,5
b) ! Killer pair (67) locked in 15(2) + 12(3) for N9
c) R7C9 = 4, R4C9 = 5 -> R3C8 = 8
d) Outies N6 = R5C6 = 8
e) Hidden Single: R6C9 = 8 @ N6 -> R5C9 = 7, R8C9 = 9 @ C9 -> R7C8 = 6
f) R7C2 = 8, R8C1 = 6
g) 11(2) = {38} -> R8C6 = 3, R8C7 = 8
h) 12(3) = {237} -> R9C9 = 2, R8C8 = 7, R7C7 = 3
i) 15(3) = {159} -> R9C6 = 9; 1,5 locked for R9
j) R9C2 = 4, R9C3 = 7 -> R9C4 = 6

4. N457
a) 9(3) = {135} -> R9C1 = 3, R7C3 = 5, R8C2 = 1
b) 5(2) = {23} -> R4C1 = 2, R3C2 = 3
c) 15(3) = {159} -> R7C1 = 9; 1,5 locked for C1+N4
d) Hidden Single: R4C3 = 8 @ N4
e) 16(4) = {1348} because R56C3 = (3469) -> R5C4 = 1; 4 locked for C3
f) 14(2) = {59} -> R4C5 = 9, R6C5 = 5
g) 32(7) = {1234679} -> R3C3 = 1, R3C7 = 9

5. R1
a) R1C1 = 4 -> R1C2 = 2
b) 8(2) = {35} -> R1C8 = 5, R1C9 = 3

6. Rest is singles.

Rating: 1.25 - (Hard) 1.25. I used lots of Killers pairs (Naked, Hidden or in combination with IOD).
Walkthrough by Ed:
I missed Afmob's neat step 1f. so took a slightly longer route to do the beginning. Did his step 2 ....differently. I'll give this puzzle a 1.5 rating since, as manu says, you have to consider the big picture of the puzzle (NOT a hint). Yet without many little eliminations, just lots of implied stuff. It's cracked from step 15. Really great puzzle. Thanks very much manu!

Please let me know of any corrections or clarifications. [Thanks Andrew!]

Walkthrough for Assassin 149

Prelims
i. 6(2)n1 = {15/24}
ii. 27(4)n1: no 1,2
iii. 8(2)n3: no 4,8,9
iv. 20(3)n1: no 1,2
v. 9(3)n3: no 7,8,9
vi. 5(2)n1 = {14/23}
vii. 13(2)n3: no 1,2,3
viii. 22(3)n4: no 1,2,3,4
ix. 14(2)r46c5 = {59/68}
x. 19(3)n6: no 1
xi. 14(2)n7 = {59/68}
xii. 9(3)n7: no 7,8,9
xiii. 15(2)n9 = {69/78}
xiv. 7(2)n7: no 7,8,9
xv. 11(2)n8: no 1

1. 22(3)n4 = 9{58/67}
1a. 9 locked for n4 & c2
1b. no 5 r8c1

2. "45" c12: 3 innies r8c2 + r9c12 = 8 = 1{25/34}(no 6..8)
2a. 1 locked for n7
2b. no 6 in r8c4

3. Hidden killer triple (789) in n7 since 14(2) = one of 8/9
3a. r7c1 & r9c3 = (789)

4. 15(3)n4 must have (789) in r7c1 and cannot have two of 7/8/9 because of the cage sum
4a. -> no 7 or 8 in r56c1

5. Hidden killer pair (78) in n4 since 22(3)n4 = one of 7/8 (step 1)
5a. -> 16(4)n4 must have 7/8 -> {1249/1456/2356} blocked

6. hidden killer triple (789) in n1. Like this. Since r456c3 = one of 7/8 (step 5a) and r9c3 = (789) -> r123c3 must have one of 7/8/9 for c3
6a. -> 20(3)n1 must have two of (789) for n1 = {389/479/578}(no 6)

7. 6 in n1 only in c3: 6 locked for c3

8. 6 in n7 only in 14(2) = {68}: 8 locked for n7

9. "45" n789: 2 innies r7c19 = 13 = [76/94]
9a. r7c9 = (46)

10. 19(3)n6 must have 4/6 in r7c9 = {469/478/568}(no 2,3) = one of 8/9 (important in a few steps)

11. "45" c89: 3 innies r8c9 + r9c89 = 10 = {127/136/145/235}(no 8,9)

12. Hidden killer pair (89) in c89 -> 13(2)n3 and 16(3)n6 must have 8/9 for c89. Like this.
12a. 15(2)n9 = one of 8/9; 19(3)n6 = one of 8/9 (step 10); 16(3)n6 can have at most one of 8/9 because of the cage sum
12b. -> 13(2)n3 must have 8/9 for c89 = {49/58}(no 6,7)
12c. and 16(3)n6 must have 8/9 for c89 -> {367/457} blocked

13. Killer pair (89) in 16(3)n6 (step 12c) & 19(3)n6 (step 10): both locked for n6
13a. no (45) in r3c8

14. Killer pair (89) in 16(3)n6 (step 12c) & r3c8: both locked for c8
14a. no 6 or 7 in r8c9

15. h13(2)r7c19: [76] blocked by r7c8
15a. -> r7c19 = [94]
15b. r9c3 = 7
15c. r4c9 = 5
15d. no 3 in r1c8

Now just trying to get to singles so won't worry too much about cage cleanup.
16. r3c8 = 8 (cage sum)

17. "45" n6: 1 remaining outie r5c6 = 8
17a. 14(2)n5 = [95](last permutation)

18. r6c9 = 8 (hsingle n6)
18a. r5c9 = 7 (cage sum)

19. r8c9 = 9
19a. r7c8 = 6 (cage sum)

20. r7c2 = 8 -> r8c1 = 6

21. 16(3)n6 = {349}(last combination): 3 & 4 locked for n6 & c8

22. 12(3)n9 = {237}(last combination): all locked for n9

23. r8c67 = [38](last permutation)

24. 7(2)n7 = {25}(last combination): both locked for r8
24a. r8c8 = 7

25. "45" c89: 1 outie r7c7 - 2 = r9c8 = [31]
25a. r9c79 = [52]
25b. r9c6 = 9 (cage sum)

26. "45" n7: 2 remaining outies r89c4 = 11 = [56]
26a. r9c2 = 4 (cage sum)

27. 22(3)n4 = {679} (last combination): 7 locked for c2

28. r2c1 = 8 (hsingle c1)
28a. r2c2 + r3c1 = 12 = [57]

29. 6(2)n1 = [42] (last permutaion)
29a. r56c1 = 6 = [51]
29b. 5(2)n1 = [32]

30. r4c3 = 8 (hsingle n4)
30a. r56c3 = {34} = 7 -> r5c4 = 1(cage sum)

31. r1c89 = [53] (cage sum)

32. 32(7)n1 = {1234679} -> r3c37 = {19}: both locked for r3

32. r12c3 = {69}: both locked for n3 & 27(4) = 15 -> r13c4 = 12 = [84]

33. r3c37 = [19]

34. "45" n3: 2 remaining outies r13c6 = 11 = [65]

Rest is singles
Walkthrough by Andrew:
A149 was the third successive Assassin that I went back to after being stuck at the time.

Even then I missed Afmob's first two ! steps, the third one follows from the second one. I also missed the key step 15 in Ed's walkthrough which I'm more annoyed that I missed.

On the basis that I'd rate both Afmob's and Ed's walkthroughs as Hard 1.25, I'll rate my walkthrough at 1.5 to Hard 1.5.

Here is my walkthrough for A149.

Prelims

a) R1C12 = {15/24}
b) R1C89 = {17/26/35}, no 4,8,9
c) R3C2 + R4C1 = {14/23}
d) R3C8 + R4C9 = {49/58/67}, no 1,2,3
e) R46C5 = {59/68}
f) R7C2 + R8C1 = {59/68}
g) R7C8 + R8C9 = {69/78}
h) R8C34 = {16/25/34}, no 7,8,9
i) R8C67 = {29/38/47/56}, no 1
j) 20(3) cage in N1 = {389/479/569/578}, no 1,2
k) 9(3) cage in N3 = {126/135/234}, no 7,8,9
l) R456C2 = {589/679}, 9 locked for C2 and N4, clean-up: no 5 in R8C1
m) R567C9 = {289/379/469/478/568}, no 1
n) 9(3) cage in N7 = {126/135/234}, no 7,8,9
o) 27(4) cage at R1C3 = {3789/4689/5679}, no 1,2

1. 45 rule on N3 4 innies R12C7 + R3C78 = 28 = {4789/5689}, no 1,2,3

2. 45 rule on R789 2 innies R7C19 = 13 = {49/58/67}, no 1,2,3

3. 45 rule on C12 1 outie R7C3 = 1 innie R9C2 + 1, no 1 in R7C3, no 6,7,8 in R9C2

4. 45 rule on C89 1 outie R7C7 = 1 innie R9C8 + 2, no 1,2 in R7C7, no 8,9 in R9C8
4a. 1 in R7 locked in R7C456, locked for N8, clean-up: no 6 in R8C3

5. 45 rule on N9 2 outies R89C6 = 1 innie R7C9 + 8
5a. Min R7C9 = 4 -> min R89C6 = 12, no 2, clean-up: no 9 in R8C7

6. 45 rule on C12 3 innies R8C2 + R9C12 = 8 = {125/134}, no 6, 1 locked for N7, clean-up: no 6 in R8C4

7. 45 rule on C89 3 innies R8C8 + R9C89 = 10 = {127/136/145/235}, no 8,9
[My “killer brain” had been asleep; I really ought to have spotted steps 6 and 7 earlier even though they are less obvious than the innies-outies in steps 3 and 4.]

8. Combined cage R4567C2 = 27,28,30 = {5679/5689/6789}, 6 locked for C2
[Step 11 shows that this step wasn’t needed but I saw it first so I’ll leave it in.]

9. Hidden killer triple 7,8,9 in R7C1, R7C2 + R8C1 and R9C3 for N7 -> R7C1 = {789}, R9C3 = {789}, clean-up: no 7,8,9 in R7C9 (step 2)
9a. Max R7C9 = 6 -> min R56C9 = 13, no 2,3

10. R567C1 = {159/168/249/258/267/348/357} (cannot be {456} because R7C1 only contains 7,8,9)
10a. R7C1 = {789} -> no 7,8 in R56C1

11. Double hidden killer triple 7,8,9 in 20(3) cage in N1, R456C2, R7C1 and R7C2 + R8C1 for C12 -> 20(3) cage in N1 must contain two of 7,8,9 = {389/479/578}, no 6
11a. 6 in N1 locked in R123C3, locked for C3, clean-up: no 5 in R9C2 (step 3)
11b. 6 locked in R123C3, CPE no 6 in R3C4

12. 6 in N7 locked in R7C2 + R8C1 = {68}, locked for N7, clean-up: no 5 in R7C9 (step 2)
12a. Killer pair 6,8 in R456C2 and R7C2, locked for C2

13. 9(3) cage in N7 = {135/234}, 3 locked for N7, clean-up: no 4 in R7C3 (step 3), no 4 in R8C4
13a. R8C2 + R9C12 (step 6) = {125/134}
13b. 2 of {125} must be in R9C2 (R8C2 + R9C1 cannot be {25} which clashes with combinations of 9(3) cage), no 2 in R8C2 + R9C1

14. 45 rule on N4 3 outies R3C2 + R5C4 + R7C1 = 13
14a. Min R7C1 + R3C2 = 8 -> max R5C4 = 5

15. Double hidden killer pair 8,9 in R3C8 + R4C9, R456C8, R56C9 and R7C8 + R8C9 for C89 -> R56C9 and R7C8 + R8C9 can each only contain one of 8,9 -> R3C8 + R4C9 and R456C8 must each contain one of 8,9
15a. R3C8 + R4C9 = {49/58}, no 6,7
15b. Killer pair 8,9 in R456C8 and R56C9, locked for N6, clean-up: no 4,5 in R3C2
15c. Killer pair 4,5 in R4C9 and R567C9, locked for C9, clean-up: no 3 in R1C8
15d. Hidden killer pair 8,9 in R56C9 and R8C9 for C9 -> R8C9 = {89}, clean-up: no 8,9 in R7C8

16. 9(3) cage in N3 = {126/135/234}
16a. 4,5 of {135/234} must be in R2C8 -> no 3 in R2C8
16b. 3 in N3 locked in R123C9, locked for C9

17. 45 rule on N6 3 outies R3C8 + R5C6 + R7C9 = 20
17a. Max R3C8 + R7C9 = 15 -> min R5C6 = 5
17b. Min R3C8 + R7C9 = 12 -> max R5C6 = 8

18. R7C8 + R8C9 = R7C2 + R8C1 + 1 -> R8C9 cannot be 1 more than R8C1
18a. R8C19 = [68/69] (cannot be [89]) -> R8C1 = 6, R7C2 = 8, clean-up: no 5 in R456C2, no 5 in R8C67, no 6 in R9C8 (step 4)
[With hindsight step 23 could have been done after step 17; then there would only be one difficult move in my walkthrough.]

19. Naked triple {679} in R456C2, locked for C2 and N4
19a. 8 in N4 locked in R456C3, locked for C3
19b. 16(4) cage at R4C3 = {1258/1348}, CPE no 1 in R5C1

20. 8 in N1 locked in 20(3) cage = {389/578}, no 4
20a. R2C2 = {35} -> no 3,5 in R23C1

21. Combined cage R8C3467 = 18 = {2349/2358/2457}, 2 locked for R8

22. R9C234 = {179/269/278/467} (cannot be {359/368} because R9C2 only contains 1,2,4, cannot be {458} because R9C3 only contains 7,9), no 3,5
22a. R9C2 = {124} -> no 2,4 in R9C4

23. R567C9 = {469/478/568}
23a. {568} => R7C9 = 6 => R7C8 = 7 => R8C9 = 8 clashes with {568}
23b. -> R567C9 = {469/478}, no 5, 4 locked for C9 -> R4C9 = 5, R3C8 = 8, clean-up: no 9 in R6C5
23c. 9 in N3 locked in R123C7, locked for C7
[Ed’s step 15 was a much simpler way to get this result.
R7C19 (step 2) = 13 = [94] (cannot be [76] which clashes with R7C8).
This could have been done after step 15.]

24. R2C1 = 8 (hidden single in C1)

25. R8C9 = 9 (hidden single in N9), R7C8 = 6, R7C9 = 4, R56C9 = {78} (step 23), locked for C9 and N6, R7C1 = 9 (step 2), R9C3 = 7, R3C1 = 7, R2C2 = 5 (step 11), clean-up: no 1 in R1C12, no 1 in R1C8, no 2 in R1C9, no 7 in R8C6, no 2 in R8C7
25a. R7C1 = 9 -> R56C1 = 6 = [51] (cannot be {24} which clashes with R1C1), clean-up: no 4 in R3C2

26. Naked pair {24} in R1C12, locked for R1 and N1, clean-up: no 6 in R1C9, no 3 in R4C1
26a. 3 in N4 locked in R456C3, locked for C3 and 16(4) cage at R4C3

27. R3C23 = [31] (hidden singles in N1), R4C1 = 2, R1C12 = [42], R9C1 = 3

28. Naked pair {69} in R12C3, locked for 27(4) cage at R1C3
28a. R12C3 = {69} = 15 -> R13C4 = 12 = [75/84]

29. 12(3) cage in N9 = {237} (only remaining combination) -> R9C9 = 2, R7C7 + R8C8 = {37}, locked for N9 -> R8C7 = 8, R8C6 = 3, R8C8 = 7, R7C7 = 3, R1C8 = 5, R1C9 = 3, R23C9 = [16], R2C8 = 2 (step 16), clean-up: no 4 in R8C3
28a. Naked pair {25} in R8C34, locked for R8 -> R8C5 = 4, R89C2 = [14], R7C3 = 5 (step 13), R8C34 = [25], R9C4 = 6 (step 22)
28b. R9C78 = [51] -> R9C6 = 9 (cage sum), R9C5 = 8, clean-up: no 6 in R46C5
28c. R46C5 = [95], R3C45 = [42], R3C6 = 5, R3C7 = 9, R12C7 = [74], R1C4 = 8, R1C6 = 6 (cage sum)

29. R5C4 = 1 (hidden single in N5)

and the rest is naked singles.


Top
 Profile  
Reply with quote  
PostPosted: Wed Aug 03, 2011 4:20 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Assassin 149 V2 by manu (April 2009) here
Puzzle Diagram:
Image
Note that cells r46c5 form a cage 10(2).
PS : not yet solved the bad quality of the picture (??) Edit : thanks Ed !
Images with "udosuk style Killer Cages" by Børge:
Image     Image
Code: Select, Copy & Paste into solver:
3x3::k:2816:2816:5378:5378:5636:5381:5381:3591:3591:2569:2569:5378:5636:5636:5636:5381:3600:3600:2569:2579:9236:5378:5636:5381:9236:2329:3600:2579:2588:6941:9236:2591:9236:4385:5410:2329:4388:2588:6941:6941:9236:4385:4385:5410:3372:4388:2588:6941:9236:2591:9236:4385:5410:3372:4388:2103:5432:5689:5689:5689:2876:2365:3372:2103:5432:2113:2113:5689:2884:2884:2876:2365:5432:3913:3913:3913:5689:4429:4429:4429:2876:
Solution:
+-------+-------+-------+
| 9 2 4 | 3 7 5 | 1 6 8 |
| 3 6 5 | 4 8 1 | 9 2 7 |
| 1 8 7 | 9 2 6 | 4 3 5 |
+-------+-------+-------+
| 2 5 3 | 1 4 9 | 7 8 6 |
| 6 4 8 | 7 5 3 | 2 9 1 |
| 7 1 9 | 8 6 2 | 5 4 3 |
+-------+-------+-------+
| 4 3 6 | 2 1 7 | 8 5 9 |
| 5 7 2 | 6 9 8 | 3 1 4 |
| 8 9 1 | 5 3 4 | 6 7 2 |
+-------+-------+-------+
Quote:
manu: Thanks for these very different but elegant walkthroughs, Afmob and Ed ! I have followed another (slightly different) approach, so other WTs are yet possible ;)

Reading Afmob's and Ed's, I have finally wanted to re-try to make a V2 with the same cage pattern, and got the following. It might to be felt not much more difficult than V1 ; my solving path for V2 is shorter but however implies harder moves (a forcing chain, an ALS and killer subsets) which could explain the higher SSrating. See by yourself...
SS Score : 2.16.

Afmob: It took me some time to find the important steps (...), so I decided to rate this Killer "hard 1.5" but I think the moves are probably in the 1.5 territory.

manu: Here is how I have solved V2 :

Andrew (in 2010): A149 V2 was the next puzzle that I went back to in my backlog. I see from that I'd found the original A149 hard and hadn't tried V2 until a few days ago.
My solving path is different from both Afmob's and manu's walkthroughs. I was struggling until ...
I'll agree with Afmob's rating of Hard 1.5 for A149 V2.

Walkthrough by Afmob:
It took me some time to find the important steps (especially those Hidden Killer pairs), so I decided to rate this Killer "hard 1.5" but I think the moves are probably in the 1.5 territory.

A149 V2 Walkthrough:

1. R789
a) Innies C12 = 24(3) = {789} locked for N7
b) Innies R789 = 13(2) = [49/58/67]
c) 8(2) @ R7C2 <> 1
d) Hidden Killer triple (123) in R89C3 for N7 since 8(2) can only have one of (23)
-> R89C3 = (123)
e) Innies R9 = 13(3): R9C58 <> 6,7,8,9 since R9C1 >= 7
f) 15(3) must have one of (456) -> R9C4 = (456)
g) 13(3): R56C9 <> 6,7,8,9 since R7C9 >= 7
h) Innies C89 = 10(3) <> 8,9

2. R789
a) 17(3) @ R9 <> 7{19/28} because they are blocked by R9C12 = (789) -> 17(3) <> 1
b) 4 locked in R7C13 @ N7 for R7
c) 9(2): R8C9 <> 5
d) Innies+Outies C89: 1 = R7C7 - R9C8 -> R7C7 <> 1,2; R9C8 <> 3
e) 11(3): R8C8+R9C9 <> 5 since R7C7 <> 2,4
f) Innies C89 = 10(3): R9C8 <> 4 because R8C8+R9C9 <> 5
g) Innies+Outies C89: 1 = R7C7 - R9C8: R7C7 <> 5
h) 17(3) @ R9: R9C67 <> 5 since R9C8 <> 3,4,8,9

3. N89 !
a) ! Hidden Killer pair (89) in R89C6 for N8 since 22(5) cannot have more than one of (89)
b) Innies+Outies N9: 3 = R89C6 - R7C9: R89C6 <= 12 = {28/29/38/39/48} <> 5,6,7
c) 11(2): R8C7 <> 4,5,6
d) 5 locked in R79C8 @ N9 for C8

4. C789
a) 21(3) = 8{49/67} -> 8 locked for C8+N6
b) 14(2) = [68/95]
c) Killer pair (69) locked in R1C8 + 21(3) for C8
d) Innies+Outies C89: 1 = R7C7 - R9C8: R7C7 <> 7
e) 9(2) @ R3C8 <> 1; R4C9 <> 3,4
f) Innies+Outies N6: 6 = R5C6+R7C9 - R4C9 -> R5C6 <> 6 (IOU @ C9)
g) Outies N6 = 15(1+1+1): R5C6 <> 7,8,9 since R3C8+R7C9 >= 9

5. C789 !
a) 17(3) = {269/359/458/467} since R9C8 = (257)
b) 17(3): R9C67 <> 2,7 because R9C8 = (257)
c) ! Outies C89 = 18(2+1) = 3+{69} / 4+{68} / 8+{46} / 9+{36} -> 6 locked for C7+N9
d) 17(4) = {1259/1349/1457/2357}
e) Killer pair (79) locked in 17(4) + 21(3) for N6
f) 9(2) @ N3: R3C8 <> 2
g) 14(3) = {149/167/239/248/257} since 5{18/36} blocked by Killer pairs (56,58) of 14(2)
and {347} blocked by R3C8 = (347)
h) Hidden Killer pair (12) in R123C7 for N3 since 14(3) must have exactly one of (12) -> R123C7 must have exactly one of (12)
i) Innies N9 = 25(4): R8C7 <> 2 since R9C8 <> 6,8,9

6. C789 !
a) ! Hidden Killer pair (12) in R456C7 for C7 since R123C7 can only have one of (12)
b) Killer pair (12) locked in R456C7 + 13(3) for N6
c) ! Consider placement of R4C9 -> 21(3) <> 6
- i) R4C9 = 5 -> R1C9 = 8 -> R1C8 = 6
- ii) R4C9 = 6
d) Hidden Single: R4C9 = 6 @ N6 -> R3C8 = 3, R1C8 = 6 @ N3 -> R1C9 = 8
e) 21(3) = {489} locked for C8+N6
f) 13(3) = 1{39/57} -> 1 locked for C9+N6
g) 9(2) @ N9 <> 1,3
h) Hidden Single: R8C8 = 1 @ N9, R9C3 = 1 @ N7
i) 14(3) = {257} locked for N3; 5 also locked for C9
j) 13(3) = {139} -> R7C9 = 9; 3 locked for C9+N6

7. C789
a) 17(4) = {2357} since R456C7 = (257) -> R5C6 = 3; 7 locked for C7
c) 11(2) = {38} -> R8C6 = 8, R8C7 = 3
d) R8C3 = 2 -> R8C4 = 6, R8C1 = 5 -> R7C2 = 3

8. C123
a) 15(3) = {159} -> R9C2 = 9, R9C4 = 5
b) R8C2 = 7, R9C1 = 8 -> R7C3 = 6, R7C1 = 4
c) Hidden Single: R3C2 = 8 @ C2 -> R4C1 = 2
d) 17(3) = {467} -> 6,7 locked for C1+N4
e) 27(4) = {3789} -> R5C4 = 7; 3,9 locked for C3
f) 36(7) = {1245789} -> R3C3 = 7
g) 21(4) = {3459} -> R1C4 = 3, R3C4 = 9
h) R3C1 = 1, R3C7 = 4

9. Rest is singles.

Rating: Hard 1.5. I used Hidden Killer pairs and a small forcing chain.
Walkthrough by manu:
Here is how I have solved V2 :

Assassin V2 Walkthrough


1)Innies for c12 : r8c2+r9c1+r9c2 =24 → naked triple {789} locked for n7
a) combinations of cage 8(2) at n7 : {26/35} → no 1 and contains one of (56) (important for step 3) )
b) Combinations of cage 21(3) at n7 : {489/579/678} → r7c3=(456)

2)Innies for r789 : r7c1+r7c9=13 : combinations for the hidden cage 13(2) at r7 : [49/58/67] and r7c1=(456)

3)Killer triple {456} locked for n7 at cage 8(2) and cells r7c13 → r8c3,r9c3=(123)
with 1 locked at r89c3 for n7 and c3

4)Innies and outies for n4 : r5c4+r7c1=9+r4c1
a) r5c4<>9 since r4c1 sees r7c1
b) cage 27(4) at n4 must contain digit 9 → 9 locked for n4 and c3 at r456c3
c) Max r5c4+r7c1=8+6=14 → Max r4c1=14-9=5 : r4c1=(1234) r3c2=(6789)

5)Innies for r9 : r9c1+r9c5+r9c9=13
a) Only one combination for r9c159 with digit 9 : {139}. We deduce the following implication : r9c1=9 → r9c59={13} → r9c3=2 (important for step 6)

The following is the key-step : it will enable to find directly all combinations of
n147

6)Digit 9 is locked for n1 at cage 11(2) or cell r3c2. Forcing chain :
(i) If 9 is locked at cage 11(2), 11(2)={29} so 2 is locked for c3 and n7 at r89c3
(ii) If r3c2=9, r9c1=9 (HS for n7) → r9c3=2 from step 5)a)
a) → 2 is locked for c3 and n7 at r89c3
b) Hidden pair {12} at r89c3 locked for c3 and n7.
c) cage 8(2) at n7 : {35} (last combination)
d) Naked pair : r7c13={46} locked for r7

7)Cell r7c2=(35) blocks combination {235} for cage 10(2) at n4.
a) 1 is locked at cage 10(2) for n4 and c2
b) r4c1<>1, r3c2<>9 → (step 6) 9 is locked for for n1 at cage 11(2). 11(2)={29} locked for n1 and r1
c) Combination of cage 14(2) at n3 : {68} locked for n3 and r1.


8)a) ALS : r1389c2=(26789). We deduce that cage 10(3) at n4 cannot be {127}. Remaining combinations 1{36/45} : no 2
b) Hidden single for c2 : r1c2=2 → r1c1=9
c) Killer pair {35} at cage 10(3) (at n4) and r7c2 , 35 locked for c2
d) Combinations of cage 10(2) at n1 : 1{36/45} with r2c2=(46) (cannot be 135) →
r23c1=(135)
e) Naked triple {135} at r238c1 locked for c1

The puzzle is cracked now ; the rest is quite easy.

9)a) Combinations of cage 17(3) at n4 : {278/467}
b) Cell r9c1=(78) blocks combination {278}→ 17(3) ={467} all locked for c1
c) r4c1=2, r3c2=8
d) r9c1=8, r89c2={79}

10) a) 8 and 9 are locked at cells r456c3 for n4
b) Combinations of cage 27(4) : {3789/4689} : no 5
c) 5 is locked for n4 at cage 10(3) : {145} locked for c2 an n4
d) Naked singles : r2c2=6 r7c2=3
e) Naked pair : r56c1={67}
f) Cage combination : r7c1=4, r23c1={13} locked for n1 and c1, r8c1=5, 27(4) = {3789} with r5c4=7
g) Hidden single for c3 : r7c3=6. Cage combination : r8c2=7, r8c34= [26].
R9c2=9, r9c34=[15]

11) a) Step 2 → r7c9=9. R56c9={13} locked for c9 and n6
b) Step 5 → r9c59=[32]
c) Combinations : cage11(2) at n8 =[83], cage 9(2) at n9 =[54], cage 11(3) at
n9=[812]

12) Combination of cage 20(3) at n6 : {489} ( because {678} is blocked by cell r1c8=(68) ) locked for n6 and c8 → 14(3) at n3=[68], r9c78=[67], r9c6=4 (cage combination).

13) Hidden single for c9 : r4c9=6 → r3c8=3

14) Cage combination : 17(4) at n6 : {2357} with r5c6=3

15) a) Cage combination : no 3 for cage 36(7) at n1 → combination {1245789}
b) Hidden single for n5 : r6c5=6 → r4c5=4
c) Digit 7 at cage 36(7) must be at r3c3 : r3c3=7

16) Naked pair : r12c3={45} → (cage combination) r13c4=[39]

17) Innies for n5 : r1c6 + r3c6= 11 → r13c6=[56]

18) The rest is singles
Walkthrough by Andrew (in 2010):
A149 V2 was the next puzzle that I went back to in my backlog. I see from that I'd found the original A149 hard and hadn't tried V2 until a few days ago.

My solving path is different from both Afmob's and manu's walkthroughs. I was struggling until I found step 24 which used a "clone" although only after the two cells had been simplified. Even though it was a puzzle by manu, the cage pattern didn't look as if it would lead to a "clone" so I hadn't been looking for one.

Rating Comment. I'll agree with Afmob's rating of Hard 1.5 for A149 V2. I think my hardest steps have the same difficulty level as the hardest steps in Afmob's and manu's walkthroughs.

Here is my walkthrough for A149 V2.

Prelims

a) R1C12 = {29/38/47/56}, no 1
b) R1C89 = {59/68}
c) R3C2 + R4C1 = {19/28/37/46}, no 5
d) R3C8 + R4C9 = {18/27/36/45}, no 9
e) R46C5 = {19/28/37/46}, no 5
f) R7C2 + R8C1 = {17/26/35}, no 4,8,9
g) R7C8 + R8C9 = {18/27/36/45}, no 9
h) R8C34 = {17/26/35}, no 4,8,9
i) R8C67 = {29/38/47/56}, no 1
j) 10(3) cage in N1 = {127/136/145/235}, no 8,9
k) 10(3) cage in N4 = {127/136/145/235}, no 8,9
l) 21(3) cage in N6 = {489/579/678}, no 1,2,3
m) 21(3) cage in N7 = {489/579/678}, no 1,2,3
n) 11(3) cage in N9 = {128/137/146/236/245}, no 9
o) 27(4) cage at R4C3 = {3789/4689/5679}, no 1,2

1. R1C12 = {29/38/47} (cannot be {56} which clashes with R1C89), no 5,6

2. 45 rule on R789 2 innies R7C19 = 13 = {49/58/67}, no 1,2,3

3. 45 rule on C12 1 innie R9C2 = 1 outie R7C3 + 3, R7C3 = {456}, R9C2 = {789}
3a. 21(3) cage in N7 = {489/579/678}
3b. R7C3 = {456} -> no 4,5,6 in R8C2 + R9C1
3c. Naked triple {789} in R8C2 + R9C12, locked for N7, clean-up: no 1 in R7C2 + R8C1, no 4,5,6 in R7C9 (step 2), no 1 in R8C4
[See comment after step 21.]
3d. 1 in N7 only in R89C3, locked for C3
3e. 1 in R1 only in R1C4567, CPE no 1 in R3C6

4. Killer triple 4,5,6 in R7C1, R7C3 and R7C2 + R8C1, locked for N7, clean-up: no 2,3 in R8C4
4a. 4 in N7 only in R7C13, locked for R7, clean-up: no 5 in R8C9

5. 45 rule on C89 1 outie R7C7 = 1 innie R9C8 + 1, no 1 in R7C7, no 3,8,9 in R9C8

6. 15(3) cage at R9C2 = {159/168/249/258/267/348/357} (cannot be {456} because R9C2 only contains 7,8,9)
6a. 4,5,6 only in R9C4 -> R9C4 = {456}

7. 45 rule in R9 3 innies R9C159 = 13 = {139/148/157/238/247} (cannot be {256/346} because R9C1 only contains 7,8,9), no 6
7a. R9C1 = {789} -> no 7,8,9 in R9C59

8. Hidden killer triple 7,8,9 in R9C1, R9C2 and 17(3) cage at R9C6 for R9 -> 17(3) cage at R9C6 must contain one of 7,8,9
8a. 17(3) cage at R9C6 = {269/359/368/458/467} (cannot be {179/278} which contain two of 7,8,9), no 1, clean-up: no 2 in R7C7 (step 5)
[Alternatively 17(3) cage at R9C6 cannot be {179/278} which clash with R9C12, ALS block.]

9. 10(3) cage in N1 and 10(3) cage at R4C2 cannot both be {235} (R456C2 = {235} would clash with R2C2 = {235}) -> at least one of these 10(3) cages must contain 1, CPE no 1 in R3C2, clean-up: no 9 in R4C1
[With hindsight I could have got the elimination in step 9 from simpler steps, either by simplifying the 17(3) cage at R5C1 or by using step 10, but I’ve kept step 9 as an interesting step.]
9a. 1 in N1 only in 10(3) cage = {127/136/145}
9b. 45 rule on N1 4 innies R12C3 + R3C23 = 24 = {2589/2679/3678/4569/4578} (cannot be {3489/3579} which clash with R1C12)
[I originally used a hidden killer triple in N1, 4 innies must contain one of 2,3,4, but found that wasn’t necessary.]

10. 45 rule on N4 3(1+1+1) outies R3C2 + R5C4 + R7C1 = 19
10a. Max R7C1 = 6 -> min R3C2 + R5C4 = 13, no 2,3 in R3C2, no 3 in R5C4, clean-up: no 7,8 in R4C1

11. 45 rule on N4 2(1+1) outies R5C4 + R7C1 = 1 innie R4C1 + 9, IOU no 9 in R5C4
11a. 9 in 27(4) cage at R4C3 only in R456C3, locked for C3 and N4
11b. Max R5C4 + R7C1 = 14 -> no 6 in R4C1, clean-up: no 4 in R3C2

12. 17(3) cage at R5C1 = {368/458/467} (cannot be {278} because R7C1 only contains 4,5,6), no 1,2
12a. Min R7C9 = 7 -> max R56C9 = 6, no 6,7,8,9 in R56C9

13. 45 rule on N6 2(1+1) outies R5C6 + R7C9 = 1 innie R4C9 + 6, IOU no 6 in R5C6
13a. Min R5C6 + R7C9 = 8 -> min R4C9 = 2, clean-up: no 8 in R3C8
13b. Max R4C9 = 8 -> max R5C6 + R7C9 = 14 -> max R5C6 = 7

14. R12C3 + R3C23 (step 9b) = {2589/2679/3678/4578} (cannot be {4569} which clashes with R7C3)
14a. 10(3) cage in N1 (step 9a) = {136/145} (cannot be {127} which clashes with R12C3 + R3C23), no 2,7

15. Hidden killer triple 7,8,9 in R1C1, 17(3) cage at R5C1 and R9C1 for C1, 17(3) cage at R5C1 contains one of 7,8, R9C1 = {789} -> R1C1 = {789}, clean-up: no 7,8,9 in R1C2

16. 11(3) cage in N9 = {128/137/146/236/245}
16a. 5 of {245} must be in R7C7 -> no 5 in R8C8 + R9C9
16b. 8 of {128} must be in R7C7 -> no 8 in R8C8

17. 2 in C1 only in R48C1 -> no 7 in 10(3) cage at R4C2
17a. R4C1 = 2 => R3C2 = 8 => naked triple {789} in R389C2, locked for C2
R8C1 = 2 => R7C2 = 6 => naked quad {6789} in R3C789C2, locked for C2
[I got the idea for this step having just completed Human Solvable 7.]
17b. -> 10(3) cage at R4C2 = {136/145/235}
17c. Hidden killer pair 1,2 in R4C1 and 10(3) cage at R4C2 for N4 -> R4C1 = {12}, clean-up: R3C2 = {89}
17d. 7 in C2 only in R89C2, locked for N7

18. R5C4 + R7C1 = R4C1 + 9 (step 11)
18a. Max R4C1 = 2 -> max R5C4 + R7C1 = 11, max R5C4 = 7

19. R9C159 (step 7) = {139/148/238}, no 5
19a. 15(3) cage at R9C2 (step 6) = {159/258/267/357} (cannot be {168/249/348} which clash with R9C159), no 4

20. 45 rule on N47 3 outies R589C4 = 1 innie R4C1 + 16
20a. R4C1 = {12} -> R589C4 = 17,18 = {467/567}, 6,7 locked for C4

21. R7C7 + R8C8 + R9C9 = 11, R7C7 = R9C8 + 1 (step 5) -> R8C8 + R9C89 = 10 = {127/136/145/235}
21a. 5,6 of {136/145} must be in R9C8 -> no 6 in R8C8, no 4 in R9C8, clean-up: no 5 in R7C7 (step 5)
[It was only when I looked at my posted A149 walkthrough, after I’d finished this puzzle without looking at that earlier walkthrough, that I realised that step 21 was actually 45 rule on C89 3 innies R8C8 + R9C89 = 10. The same applies for step 3c which is more directly 45 rule on C12 3 innies R8C2 + R9C12 = 24. :oops: I also missed these innies when I solved A149.]

22. 17(3) cage at R9C6 (step 8a) = {269/359/458/467} (cannot be {368} which clashes with R9C159)
22a. 5 of {359/458} must be in R9C8 -> no 5 in R9C67

23. 1 in N8 only in 22(5) cage = {12379/12469/12478/13459/13468} (cannot be {12568/13567} which clash with R9C4)
23a. Killer triple 5,6,7 in 22(5) cage, R8C4 and R9C4, locked for N8, clean-up: no 4,5,6 in R8C7

24. R3C2 + R89C2 = {89} + {789}, R89C2 + R9C1 = {789} + {89} -> R3C2 = R9C1
[That had been there since step 17c but I’ve only just spotted how to use it.]
24a. R4C1 + R3C2 = [19/28] -> R49C1 = [19/28] = 10
24b. 45 rule on C1 4 remaining innies R1238C1 = 18 = {1359/2367/2457} (cannot be {1269/1278} which clash with R4C1, cannot be {1368/1458/2349} which clash with R49C1, cannot be {1467/3456} which clash with 17(3) cage at R5C1, cannot be {2358} which clashes with combinations for 10(3) cage in N1), no 8, clean-up: no 3 in R1C2
24c. 2 of {2367} must be in R8C1 -> no 6 in R8C1, clean-up: no 2 in R7C2
24d. R23C1 = {13/15/36/45} -> R2C2 = {146}

25. 6 in N7 only in R7C123, locked for R7, clean-up: no 3 in R8C9
[While checking I found that I’d missed a couple of clean-ups for R9C8 and later missed a placement for R9C8 after fixing R7C7. I’ve left them out rather than re-working later steps.]

26. 11(3) cage in N9 = {128/137}, no 4, 1 locked for N9, clean-up: no 8 in R7C8 + R8C9
26a. R7C8 + R8C9 = [36/54] (cannot be {27} which clashes with 11(3) cage), no 2,7

27. Naked quad {3456} in R7C1238, locked for R7
27a. 11(3) cage in N9 (step 26) = {128/137}
27b. R7C7 = {78} -> no 7 in R8C8
27c. 1,2 in R7 only in R7C456, locked for N8, clean-up: no 9 in R8C7

28. R9C159 (step 19) = {139/148/238}
28a. 1,2 only in R9C9 -> R9C9 = {12}

29. 13(3) cage at R5C9 = {139/148/157/238/247} (cannot be {256/346} because R7C9 only contains 7,8,9), no 6
29a. Killer pair 1,2 in R56C9 and R9C9, locked for C9, clean-up: no 7 in R3C8

30. 9 in N9 only in R7C9 + R9C7
30a. 45 rule on N9 4 innies R7C9 + R8C7 + R9C78 = 25 = {2689/3679/4579} (cannot be {3589} which clashes with R7C8)
30b. 45 rule on N9 2 innies R7C9 + R8C7 = 1 outie R9C6 + 8
30c. R9C6 = {3489} -> R7C9 + R8C7 = 11,12,16,17 = [92/93/97/98] (cannot be [83] which clashes with the 11(3) cage) -> R7C9 = 9, R7C1 = 4 (step 2), clean-up: no 5 in R1C8
[I originally did this step using interactions between the combinations for R7C9 + R8C7 + R9C78 and the permutations for R9C78 in 17(3) cage at R9C6. Then I realised that using the second 45 rule on N9 was much simpler.]

31. R7C9 = 9 -> R56C9 (step 29) = {13}, locked for C9 and N6 -> R9C9 = 2, clean-up: no 6 in R3C8, no 9 in R8C6
31a. R8C8 = 1 (hidden single in N9), R7C7 = 8 (step 26), clean-up: no 8 in R4C9, no 7 in R8C4, no 3 in R8C6
31b. R9C3 = 1 (hidden single in N7)

32. 21(3) cage in N7 = {579/678} -> R8C2 = 7, R8C7 = 3, R8C6 = 8, R7C8 = 5, R8C3 = 2, R8C1 = 5, R8C4 = 6, R8C9 = 4, R8C5 = 9, R7C3 = 6, R9C1 = 8, R7C2 = 3, R9C24 = [95], R3C2 = 8, R4C1 = 2, clean-up: no 1 in R4C5, no 1,8 in R6C5

33. R7C1 = 4 -> R56C1 = 13 = {67} (only remaining combination), locked for C1 and N4 -> R1C1 = 9, R1C2 = 2, clean-up: no 5 in R1C9
33a. Naked triple {145} in R456C2, locked for C2 and N4 -> R2C2 = 6
33b. Naked triple {389} in R456C3, locked for C3, R5C4 = 7 (cage sum), R56C1 = [67], clean-up: no 3 in R46C5
33c. Naked triple {457} in R123C3, CPE no 4 in R3C4

34. R9C78 = {67} = 13 -> R9C6 = 4, R9C5 = 3

35. Naked pair {68} in R1C89, locked for R1 and N3
35a. Naked pair {57} in R23C9, locked for C9 and N3 -> R4C9 = 6, R3C8 = 3, R23C1 = [31], R1C89 = [68], R9C78 = [67], clean-up: no 4 in R6C5

36. Naked triple {489} in R456C8, locked for C8 and N6 -> R2C8 = 2

37. Naked pair {25} in R56C7, locked for C7 and 17(4) cage at R4C7 -> R4C7 = 7, R5C6 = 3 (cage sum), R56C9 = [13]
37a. R4C3 = 3 (hidden single in N4)

38. 36(7) cage at R3C3 = {1245789} -> R3C3 = 7, R23C9 = [75]

39. R6C5 = 6 (hidden single in N5), R4C5 = 4, R3C5 = 2, R3C4 = 9, R3C6 = 6, R3C7 = 4, R12C7 = [19], R1C6 = 5 (cage sum)

and the rest is naked singles.


Top
 Profile  
Reply with quote  
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 54 posts ]  Go to page Previous  1, 2, 3, 4, 5, 6  Next

All times are UTC


Who is online

Users browsing this forum: No registered users and 46 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