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 Post subject: Assassin 374
PostPosted: Mon Apr 15, 2019 7:27 am 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 811
Location: Sydney, Australia
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a374.JPG
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NOTE: disjoint 16(4) cage r12c9 + r2c67

Assassin 374
Finally worked out a 'simple' way to solve this....on the third solve! If it didn't get a score of 1.35 I wouldn't have kept trying. Drove me a bit crazy. Loved it! Haven't checked the SS solving path yet in case I've made a mistake. JSudoku has to use a couple of fish. Happy Easter! Always good killer sudoku memories for this time of year for me. Way back when I first started killers on this long weekend.

code:
3x3::k:2048:2048:8193:4354:4354:4354:3587:3587:4100:3077:9222:8193:4615:4615:4100:4100:3587:4100:3077:9222:8193:8193:4615:4104:4104:3587:2569:4106:9222:8193:4363:4363:4104:1292:1292:2569:4106:9222:8193:8193:3597:3597:5390:2831:2831:4106:9222:9222:9222:9222:3597:5390:5904:5904:4113:4626:4626:3091:3091:2580:5390:5904:3605:4113:4626:2838:1303:1303:2580:5390:3605:3605:4113:2838:2838:4632:4632:4632:3865:3865:3865:
solution:
Code:
+-------+-------+-------+
| 1 7 9 | 4 5 8 | 2 6 3 |
| 8 5 3 | 6 9 2 | 4 1 7 |
| 4 2 6 | 7 3 1 | 8 5 9 |
+-------+-------+-------+
| 5 6 4 | 9 8 7 | 3 2 1 |
| 9 8 1 | 2 6 3 | 5 7 4 |
| 2 3 7 | 1 4 5 | 9 8 6 |
+-------+-------+-------+
| 3 1 8 | 5 7 4 | 6 9 2 |
| 7 9 5 | 3 2 6 | 1 4 8 |
| 6 4 2 | 8 1 9 | 7 3 5 |
+-------+-------+-------+
Cheers
Ed


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 Post subject: Re: Assassin 374
PostPosted: Wed Apr 24, 2019 7:25 pm 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 811
Location: Sydney, Australia
Here's how I did it. Step 8 helped to get things moving, 11 was fun but 22 was the key area for this 'simple' solution with a lot of setting up work to make it possible. Thanks to Andrew for checking my logic and for lots of typos.
a374 WT:
Preliminaries courtesy of SudokuSolver
Cage 17(2) n5 - cells ={89}
Cage 5(2) n8 - cells only uses 1234
Cage 5(2) n6 - cells only uses 1234
Cage 8(2) n1 - cells do not use 489
Cage 12(2) n8 - cells do not use 126
Cage 12(2) n1 - cells do not use 126
Cage 10(2) n8 - cells do not use 5
Cage 10(2) n36 - cells do not use 5
Cage 11(2) n6 - cells do not use 1
Cage 23(3) n69 - cells ={689}
Cage 11(3) n7 - cells do not use 9
Cage 14(4) n3 - cells do not use 9
Cage 36(8) n145 - cells ={12345678}

note: no clean-up unless stated
1. 1 outie n69 -> r3c9 = 9 -> r4c9 = 1

2. 1 innie c1 -> r1c1 = 1, r1c2 = 7

3. 5(2)n6 = {23}: both locked for r4 and n6

4. 17(2)n5 = {89}: both locked for r4 and n5

5. 12(2)n1 = [93]/{48}(no 5)

6. 9 in c2 only in r78c2: 9 locked for n7 and no 9 in r7c3

7. 16(3)r7c1: {358} blocked by 12(2)n1
7a. = {268/367/457}
7b. = 3/4/8
7c. 12(2)n1 = 3/ both 4,8
7d. -> killer single 3 locked for c1 in r3789

Took a long time to see this one (not as long as the next key step though!)
8a. 16(3)r4c1: {457} blocked by r4c23 = [66] (Almost Locked Set ALS)
8b. = {259/268}(no 4,7)
8c. must have 2: locked for c1 and n4

9. 16(3)r7c1 = {367/457}(no 8)
9a. must have 7: 7 locked for n7

10. "45" on n23: 1 innie r3c4 = 1 outie r4c6
10a. r4c6 = (4567) -> r3c4 = (4567)

11. both the 32(7)r1c3 and 36(8) must have 2 which are only in n1 and n5: 2 locked in those two cages for n5 in one of r5c4 or r6c45 (caged x-wing)

12. 36(8)r2c2 must have 7 which is only in r6: 7 locked for r6

13. 7 in n6 only in r5: 7 locked for r5

14. 14(3)r5c5 = {356} only: all locked for n5
14a. no 5,6 in r3c4 (r3c4=r4c6)

15. 32(7)r1c3 and 36(8)r2c1 must both have 3 which are only in n1 and n4 -> no 3 in r3c1 (caged x-wing)

16. 12(2)n1 = {48} only: both locked for c1 and n1

17. 16(3)r4c1 = [5]{29} only: 9 locked for n4

18. r789c1 = {367} only, 3 & 6 locked for n7

19. 36(8)r2c2 must have 5 which is only in n1: locked for n1 and c2

20. "45" on n3: 1 outie r2c6 + 6 = 1 innie r3c7 = [17/28]

21. naked triple {478} in r3c147: all locked for r3

The key step. It involves 5 combos hence I took a long time to look at it.
22. 14(4)r1c7 = {1238/1247/1256/1346/2345}
22a. note: can't have two of 4,5,8 in r1c78 since the only combo with two of them, {2345} must have 2 or 3 in r1c7 to avoid {23} clashing with r4c8 = (23)
22b. "45" on r1: 4 innies r1c3789 = 20
22c. but {3458} as [3]{458} only, blocked by r1c78 can't have two of 4,5,8
22d. = {2369/2459/2468}
22e. must have 2, 2 locked for r1

23. 17(3)r1c4 = {359/368/458}
23a. ->18(3)r2c4: {189/378/567} all blocked
23b. and in 18(3): {468} as {48}[6] only blocked by r2c1 = (48)
23c. -> 18(3) = {279/369/459}(no 1,8)
23d. must have 9: 9 locked for r2 and n2

24. r1c3 = 9 (hidden single 9 in r1)
24a. -> r1c789 = 11 = {236/245}(no 8)
24b. must have 2: 2 locked for n3

25. 1 in n2 only in r23c6: 1 locked for c6
25a. no 9 in 10(2)n8

26. hidden single 9 in c6 -> r9c6 = 9

27. "45" on c6789: 1 remaining innie r1c6 - 2 = 1 outie r5c5
27a. but [53] blocked by r56c6 = {356}
27b. -> = [86] only
27c. -> r56c6 = {35} only: both locked for c6
27d. -> 10(2)n8 = {46} only: both locked for c6 and n8
cracked
27e. -> r4c6 = 7, r3c7 = 8, r3c6 = 1 (cage sum), r2c6 = 2, r23c1 = [84], r3c4 = 7

28. 11(2)n6 = {47} only: both locked for n6 and r5

29. 32(7)r1c3 must have both 7 & 9 -> = {1234679}(no 8)
29a. must have 4 -> r4c3 = 4, r4c2 = 6

30. r5c2 = 8 (hsingle r5)

31. 5(2)n8 = {23} only: both locked for n8 and r8
31a. -> 12(2)n8 = [57] only
31c. r9c45 = {18}: both locked for r9

32. 11(3)n7 = [542] only permutation

33. "45" on r9: 1 remaining innie r9c1 = 6

etc
Cheers
Ed


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 Post subject: Re: Assassin 374
PostPosted: Sat Apr 27, 2019 4:41 am 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1658
Location: Lethbridge, Alberta, Canada
This puzzle had some similarities to A373 in that I found myself with linked groups of cages with only 2 or 3 remaining combinations but it wasn't easy to find the way to unlock which group was correct.

Ed mentioned that he started on killers in an Easter long weekend. Was that in 2006 or earlier? I first came across killers on 1st April 2006 and they quickly became my favourite form of sudokus; Ruud's first Assassin was posted on 2nd June 2006 but I only came across them about a month later, I think Ed found them before I did.

Here is my walkthrough for Assassin 374:
Prelims

a) R1C12 = {17/26/35}, no 4,8,9
b) R23C1 = {39/48/57}, no 1,2,6
c) R34C9 = {19/28/37/46}, no 5
d) R4C45 = {89}
e) R4C78 = {14/23}
f) R5C89 = {29/38/47/56}, no 1
g) R7C45 = {39/48/57}, no 1,2,6
h) R78C6 = {19/28/37/46}, no 5
i) R8C45 = {14/23}
j) 23(3) cage at R6C8 = {689}
k) 11(3) cage at R8C3 = {128/137/146/236/245}, no 9
l) 14(4) cage at R1C7 = {1238/1247/1256/1346/2345}, no 9
m) 36(8) cage at R2C2 = {12345678}, no 9

Steps resulting from Prelims and Initial Placements.
1a. Naked pair {89} in R4C45, locked for R4 and N5, clean-up: no 1,2 in R3C9
1b. Naked triple {689} in 23(3) cage at R6C8, CPE no 6,8,9 in R5C8, clean-up: no 2,3,5 in R5C9
1c. 45 rule on C1 1 innie R1C1 = 1 -> R1C2 = 7, clean-up: no 5 in R23C1
1d. 45 rule on N69 1 innie R4C9 = 1 -> R3C9 = 9, clean-up: no 3 in R2C1, no 4 in R4C78
1e. Naked pair {23} in R4C78, locked for R4 and N6, clean-up: no 8 in R5C9
1f. 36(8) cage at R2C2 = {12345678}, 7 in R6C345, locked for R6
1g. 7 in N6 only in R5C789, locked for R5
1h. 23(3) cage at R6C8 = {689}, 9 locked for C8

2. 45 rule on N145 1 outie R3C4 = 1 innie R4C6, R4C6 = {4567} -> R3C4 = {4567}

3. 45 rule on N3 1 remaining innie R3C7 = 1 outie R2C6 + 6 -> R2C6 = {12}, R3C7 = {78}
3a. Min R3C7 + R4C6 = 11 -> max R3C6 = 5

4a. 32(7) cage at R1C3 must contain 1 in R5C34, locked for R5
4b. 36(8) cage at R2C2 must contain 1 in R6C2345, locked for R6
4c. 14(3) cage at R5C5 = {356} (only remaining combination), locked for N5, clean-up: no 5,6 in R3C4 (step 2)
4d. R5C89 = {47} (cannot be [56] which clashes with 14(3) cage, ALS block), locked for R5 and N6
4e. 5,6 in R4 only in R4C123, locked for N4
4f. 5 in N6 only in R56C7, locked for C7
4g. 32(7) cage must contain 3 in R1235C3, locked for C3

5a. 17(3) cage at R1C4 = {269/359/368/458}
5b. 18(3) cage at R2C4 = {279/369/378/459/468} (cannot be {189/567} which clash with 17(3) cage), no 1
5c. 1 in N2 only in R23C6, locked for C6, clean-up: no 9 in R78C6
5d. 45 rule on N2 3 innies R2C6 + R3C46 = 10 contains 1 = {127/145}, no 3
5e. 5 of {145} must be in R3C6 -> no 4 in R3C6
5f. 2 of {127} must be in R2C6 (cannot be [172] which clashes with R2C6 + R3C7 = [17], step 3), no 2 in R3C6
5g. 45 rule on N23 3 remaining innies R3C467 = 16 = [457/718], 7 locked for R3

6. R78C6 = {28/37/46}, R8C45 = {14/23} -> combined cage R78C6 + R8C45 = {28}{14}/{37}{14}/{46}{23}, 4 locked for N8, clean-up: no 8 in R7C45
6a. R78C6 = {28/46} (cannot be {37} which clashes with R7C45), no 3,7
6b. Killer pair 2,4 in R78C6 and R8C24, locked for N8
6c. 18(3) cage at R9C4 = {189/369/567} (cannot be {378} which clashes with R7C45)
6d. 15(3) cage at R9C7 = {249/258/267/348/357/456} (cannot be {159/168} which clash with 18(3) cage), no 1
6e. 45 rule on C789 3 outies R234C6 = 10 = [217/154]
6f. Killer pair 2,4 in R234C6 and R78C6, locked for C6

7. 21(4) cage at R5C7 must contain 5 = {1569/2568/3459/3567} (cannot be {1578} which clashes with R3C7)

8. 45 rule on C6789 2 innies R19C6 = 1 outie R5C5 + 11
8a. Min R5C5 = 3 -> min R19C6 = 14, no 3 in R19C6
8b. 3 in C6 only in R56C6, locked for N5
8c. Min R5C5 = 5 -> min R19C6 = 16, no 5,6 in R19C6

9. 32(7) cage at R1C3 and 36(8) cage at R2C2 must both contain 3, locked for N14 (caged X-Wing), clean-up: no 9 in R2C1
9a. Naked pair {48} in R23C1, locked for C1 and N1
9b. Naked pair {29} in R56C1, locked for C1 and N4, R4C1 = 5 (cage sum)
9c. Naked triple {367} in 16(3) cage at R7C1, locked for N7
9d. 36(8) cage = {12345678}, 8 locked for N4
9e. 32(7) cage R1C3 = {1234679} (only remaining combination), no 5, 9 locked for C3
9f. 5 in N1 only in R23C2, locked for C2
9g. 4 in R6 only in R6C2345, locked for 36(8) cage -> R4C2 = 6

10. Killer pair 4,8 in R3C1 and R3C467 (step 5g), locked for R3
[That’s how I saw it although, after going through Ed’s walkthrough I can see that it’s actually naked triple {478} in R3C147.]
10a. 18(3) cage at R2C4 (step 5b) = {279/369/378/459} (cannot be {468} = {48}6 which clashes with R2C1)
10b. 2 of {279} must be in R3C5 -> no 2 in R2C45
10c. 17(3) cage at R1C4 (step 5a) = {269/368/458} (cannot be {359} which clashes with 18(3) cage)

11a. 18(3) cage at R7C2 = {189/459}, no 2
11b. 5 on {459} must be in R7C3 -> no 4 in R7C3
11c. 45 rule on R9 1 innie R9C1 = 1 outie R8C3 + 1 -> R8C3 = {25}, R9C1 = {36}
11d. 18(3) cage at R9C4 (step 6c) = {189/567} (cannot be {369} which clashes with R9C1), no 3
11e. Hidden killer pair 7,9 in 18(3) cage and 15(3) cage at R9C7 (step 6d) for R9, 18(3) cage contains one of 7,9 -> 15(3) cage must contain one of 7,9 = {249/267/357} (cannot be {258/348/456}, no 8
11f. 9 of {249} must be in R9C7 -> no 4 in R9C7
11g. 14(3) cage at R7C9 = {158/167/248/356} (cannot be {257/347} which clash with 15(3) cage at R9C7)
11h. 45 rule on N9 3 innies R7C78 + R8C7 = 16 = {169/349/367} (cannot be {178} because 21(4) cage at R5C7 (step 7) doesn’t contain both of 1,7, cannot be {268} which clashes with 14(3) cage), no 2,8
11i. 8 in N9 only in 14(3) cage = {158/248}, no 3,6,7
11j. 1 of {158} must be in R8C8 -> no 5 in R8C8
11k. 23(3) cage at R6C8 = {689}, 8 locked for R6 and N6
11l. R5C2 = 8 (hidden single in N4)

12. 15(3) cage at R9C7 (step 11e) = {249/267/357}
12a. Consider combinations for 14(3) cage at R7C9 (step 11i) = {158/248}
14(3) cage = {158} => R8C8 = 1, naked pair {58} in R78C9, locked for C9, R6C9 = 6, R67C8 = [89] => 15(3) cage = {267}
or 14(3) cage = {248}, 2 locked for N9 -> 15(3) cage = {357}
-> 15(3) cage = {267/357}, no 4,9, 7 locked for R9 and N9
[Cracked. The rest is fairly straightforward.]
12b. Naked pair {89} in R19C6, locked for C6, clean-up: no 2 in R78C6
12c. Naked pair {46} in R78C6, locked for C6 and N8, clean-up: no 1 in R8C45
12d. Naked pair {35} in R56C6, 5 locked for C6 and N5 -> R5C5 = 6
12e. Naked pair {23} in R8C45, locked for R8 and N8, clean-up: no 9 in R7C45
12f. Naked pair {57} in R7C45, locked for R7 and N8
12g. R234C6 = [217], R3C7 = 8, R23C1 = [84], R3C4 = 7, R4C3 = 4, R7C45 = [57]
12h. R8C3 = 5 -> R9C24 = 6 = [42]
12i. Naked triple {369} in R123C3, 3 locked for C3 and N1

13a. 15(3) cage at R7C9 = {357} (only remaining combination), 3 locked for R9 and N9
13b. R7C9 = 2 (hidden single in N9) -> R8C89 = 12 = {48}, locked for R8, 4 locked for N9
13c. 4 in C7 only in R12C7, locked for N3
13d. Naked quad {1569} in 21(4) cage at R5C7, locked for C7

14. 18(3) cage at R2C4 (step 5b) = {369/459}, 9 locked for R2 and N2

15a. R2C8 = 1 (hidden single in N3)
15b. 7 in R2 only in R2C79 -> 16(4) disjoint cage at R1C9 = {2347} -> R1C9 = 3
15c. R1C6 = 8 -> R1C45 = 9 = [45]

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough for A374 at Easy 1.5; I used one short forcing chain to crack it.
If I'd spotted Ed's alternative ending for my walkthrough, in the next post, I'd have rated it at 1.25.


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 Post subject: Re: Assassin 374
PostPosted: Tue Apr 30, 2019 10:44 pm 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 811
Location: Sydney, Australia
Really good WT Andrew! Found a different way to go after your step 11 (see below). Your step 12 is in the same area I used in my first solves of this puzzle (no WT). SudokuSolver worked in the same area I did for the final breakthrough but simpler (no WT). I was already on old hand at killers when you started at Ruud's forum so I must have started in 2005. 14 years flies!

Alt ending for Andrew's WT:
end of Andrew's step 11 here
Code:
.-------------------------------.-------------------------------.-------------------------------.
| 1         7         2369      | 2345689   2345689   89        | 23468     234568    234568    |
| 48        235       2369      | 3456789   3456789   12        | 1234678   12345678  2345678   |
| 48        235       236       | 47        2356      15        | 78        12356     9         |
:-------------------------------+-------------------------------+-------------------------------:
| 5         6         47        | 89        89        47        | 23        23        1         |
| 29        8         13        | 12        56        356       | 569       47        47        |
| 29        134       147       | 1247      1247      356       | 569       689       68        |
:-------------------------------+-------------------------------+-------------------------------:
| 367       149       158       | 3579      3579      2468      | 134679    69        2458      |
| 367       149       25        | 1234      1234      2468      | 134679    1248      2458      |
| 36        124       12458     | 156789    156789    789       | 23679     234567    234567    |
'-------------------------------.-------------------------------.-------------------------------'
12. 8 in c7 only n3: 8 locked for n3

13. 14(4)r1c7: {1238} as [8]{123} only, blocked by r4c8
13a. = {1247/1256/1346/2345}(no 8)

14. 17(3)r1c4: can't have both 8 and 9 -> no 8,9 in r1c45

15. r1c36 = [98] (hsingles r1)
15a. r9c6 = 9 (hsingle c6)

cracked
Cheers
Ed

Many thanks for posting that alternative and much better ending for my walkthrough.
I really ought to have spotted the step 12, in which case I may well have seen step 13; I'd seen step 14 but didn't include it in my walkthrough as it didn't add anything when I saw it.

Andrew


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