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 Post subject: Assassin 374
PostPosted: Mon Apr 15, 2019 7:27 am 
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Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 798
Location: Sydney, Australia
Attachment:
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
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 798
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.
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 c9 in r23789

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)n1c7 = {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 r1c67 can't have two of 4,5,8
22d. = {2369/2459/2468}
22e. must have 2, 2 locked for r1

21. 17(3)r1c4 = {359/368/458}
21a. ->18(3)r2c4: {189/378/567} all blocked
21b. and in 18(3): {468} as {48}[6] only blocked by r2c1 = (48)
21c. -> 18(3) = {279/369/459}(no 1,8)
21d. must have 9: 9 locked for r2 and n2

22. r1c3 = 9 (hidden single 9 in r1)
22a. -> r1c789 = 11 = {236/245}(no 8)
22b. must have 2: 2 locked for n3

23. 1 in n2 only in r23c6: 1 locked for c6
23a. no 9 in 10(2)n6

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

25. "45" on c6789: 1 remaining innie r1c6 - 2 = 1 outie r5c5
25a. but [53] blocked by r56c6 = {356}
25b. -> = [86] only
25c. -> r56c6 = {35} only: both locked for c6
25d. -> 10(2)n8 = {46} only: both locked for c6 and n8
cracked
25e. -> r4c6 = 7, r3c7 = 8, r3c6 = 1 (cage sum), r2c6 = 2, r23c1 = [84], r3c4 = 7

26. 11(2)n6 = {47} only: both locked for n6 and r5

27. 32(7)r1c3 must have both 7 & 9 -> = {1234679}(no 8)
27a. must have 4 -> r4c3 = 4, r4c2 = 6

28. r5c2 = 8 (hsingle r5)

29. 5(2)n8 = {23} only: both locked for n8 and r8
29a. -> 12(2)n8 = [57] only
29c. r9c45 = {18}: both locked for r9

30. 11(3)n7 = [542] only permutation

31. "45" on r9: 1 remaining innie r9c1 = 6

etc
Cheers
Ed


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 Post subject: Re: Assassin 374
PostPosted: Thu Apr 25, 2019 4:32 am 
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Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1637
Location: Lethbridge, Alberta, Canada
I first came across Killers on 1st April 2006; Ruud's first Assassin was posted on 2nd June 2006 but I only came across them several weeks later.

Just finished. Haven't had time to check my walkthrough or compare it with Ed's, which is probably an optimised one. It's getting late; I'll try to find time tomorrow.
Here's 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

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

5. 17(3) cage at R1C4 = {269/359/368/458}
5a. 18(3) cage at R2C4 = {279/369/378/459/468} (cannot be {189/567} which clash with 17(3) cage), no 1
5b. 1 in N2 only in R23C6, locked for C6, clean-up: no 9 in R78C6
5c. 45 rule on N2 3 innies R2C6 + R3C46 = 10 contains 1 = {127/145}, no 3
5d. 5 of {145} must be in R3C6 -> no 4 in R3C6
5e. 2 of {127} must be in R2C6 (cannot be [172] which clashes with R2C6 + R3C7 = [17], step 3), no 2 in R3C6
5f. 45 rule on N23 3 innies R3C467 = 16 = [457/718], 7 locked for R3
5g. 45 rule on C789 3 outies R234C6 = 10 = [217/154]
5h. Killer pair 2,4 in R234C6 and R78C6, locked for C6

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

7. 21(4) cage at R5C7 must contain 5 = {1569/2568/3459/3567} (cannot be {1578} which clash 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 = 17, no 5,6 in R19C6
8d. 5 in C6 only in R56C6 -> R56C6 = {35}, locked for C6 and N5
8e. R23C6 = [21] -> R3C4 = 7 (step 5c), R4C6 = 7 (step 5g), R3C7 = 8, clean-up: no 4 in R2C1
8f. R5C5 = 6
8g. R78C6 = {46} (hidden pair in C6), locked for N8, clean-up: no 1 in R8C45
8g. Naked pair {23} in R8C45, locked for R8 and N8, clean-up: no 9 in R7C45
8h. R7C45 = [57]
8i. Naked triple {189} in 18(3) cage at R9C4, locked for R9
8j. 36(8) cage at R2C2 = {12345678} -> R6C3 = 7
8k. 32(7) cage at R1C3 contains 7 so must contain 6 in R1234C3, locked for C3
8l. 4 in N5 only in R6C45, locked for R6 and 36(8) cage at R2C2, no 4 in R234C2

9. 7 in C1 only in 16(3) cage at R7C1 = {367/457}, no 2,8,9
9a. 45 rule on R9 1 innie R9C1 = 1 outie R8C3 + 1 -> R8C3 = {45}, R9C1 = {56}
9b. 11(3) cage at R8C3 = {245} (only remaining combination), locked for N7
9c. R9C1 = 6 -> R8C3 = 5, R9C23 = {24}, locked for R9, R78C1 = [37], clean-up: no 9 in R2C1
9d. R23C1 = [84], R4C1 = 5
9e. Naked pair {29} in R56C1, locked for N4

10a. 36(8) cage at R2C2 = {12345678}, 8 locked for C2 and N4
10b. 32(7) cage R1C3 = {1234679} -> R4C3 = 4, R9C23 = [42]
10c. Naked triple {369} in R123C3, locked for C3 and N1 -> R23C2 = [52], R5C34 = [12], R8C8 = 8, R56C1 = [92], R5C7 = 5, R8C34 = [32]
10d. 8 in R6 only in R6C89, locked for 23(3) cage at R6C8
10e. 8 in N9 only in 14(3) cage at R7C9 = {248} -> R7C9 = 2, R8C89 = {48}, locked for R8 and N9
10f. Naked triple {169} in R678C7, locked for C7
10g. 4 in C7 only in R12C7, locked for N3

11a. 18(3) cage at R2C4 (step 5a) = {369/459}, 9 locked for R2 and N2
11b. 3 of {369} must be in R3C5 -> no 3 in R2C5

12a. R2C8 = 1 (hidden single in N3)
12b. 7 in R2 only in R2C79 -> 16(4) disjoint cage at R1C9 = {2347} -> R1C9 = 3, R2C79 = [47], R1C7 = 2, R13C8 = {56}, locked for C8
12c. R1C6 = 8 -> R1C45 = 9 = [45]

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough at Easy 1.25.


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