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 Post subject: Assassin 53 V3 Revisit
PostPosted: Thu Apr 01, 2021 6:29 pm 
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Assassin 53 v3 Revisit

Easter and killer sudoku go together in my history so hope this one is worthy! This puzzle is over the target score range (2.20) for these Revisits but JSudoku gets it out pretty easily with just 2 'complex intersections'. Also, the human raters found this one more satisfying than the misnomered v0.1 even though its score is lower (2.05). JSudoku has a very hard time with it.
Code: Select, Copy & Paste into solver:
3x3::k:4096:4096:4096:5123:5123:5123:4102:4102:4102:1289:1289:5899:5123:6992:5123:4623:6737:6737:2834:5899:5899:2837:6992:6992:4623:4623:6737:2834:5899:2837:2837:3359:6992:4641:4623:6737:6948:6948:6948:6948:3359:4641:4641:4641:4641:6482:3630:6948:5711:3359:5170:5170:5428:2357:6482:3630:3630:5711:5711:5170:5428:5428:2357:6482:6482:3630:6210:5711:6210:5428:2886:2886:3912:3912:3912:6210:6210:6210:3406:3406:3406:
Solution:
+-------+-------+-------+
| 8 6 2 | 1 9 3 | 7 4 5 |
| 4 1 7 | 5 6 2 | 3 9 8 |
| 5 3 9 | 7 4 8 | 6 1 2 |
+-------+-------+-------+
| 6 4 1 | 3 5 9 | 2 8 7 |
| 3 9 8 | 2 7 6 | 4 5 1 |
| 7 2 5 | 8 1 4 | 9 6 3 |
+-------+-------+-------+
| 1 5 4 | 9 3 7 | 8 2 6 |
| 9 8 3 | 6 2 1 | 5 7 4 |
| 2 7 6 | 4 8 5 | 1 3 9 |
+-------+-------+-------+
Cheers
Ed


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PostPosted: Sun Apr 04, 2021 11:07 pm 
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Grand Master
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Location: Lethbridge, Alberta, Canada
Thanks Ed for this latest Revisit. My most interesting steps were 4a and 4b, although they didn't help with the later steps.

Here's how I solved Assassin 53 V3 Revisit:
Prelims

a) R2C12 = {14/23}
b) R34C1 = {29/38/47/56}, no 1
c) R67C9 = {18/27/36/45}, no 9
d) R8C89 = {29/38/47/56}, no 1
e) 11(3) cage at R3C4 = {128/137/146/236/245}, no 9
f) 20(3) cage at R6C6 = {389/479/569/578}, no 1,2
g) 27(4) cage at R2C5 = {3789/4689/5679}, no 1,2
h) 26(4) cage at R2C8 = {2789/3689/4589/4679/5678}, no 1
i) 14(4) cage at R6C2 = {1238/1247/1256/1346/2345}, no 9
j) 18(5) cage at R4C7 = {12348/12357/12456}, no 9

1a. 45 rule on R1 2 outies R2C46 = 7 = {16/25} (cannot be {34} which clashes with R2C12)
1b. Killer pair 1,2 in R2C12 and R2C46, locked for R2

2a. 45 rule on R1234 2 innies R4C57 = 7 = {16/25/34}, no 7,8,9
2b. 45 rule on R6789 2 innies R6C35 = 6 = {15/24}
2c. 45 rule on N9 2 outies R6C12 = 9 = {18/27/36} (cannot be {45} which clashes with R6C35), no 4,5,9
2d. 45 rule on N9 2 outies R6C89 = 9 = {18/27/36} (cannot be {45} which clashes with R6C35), no 4,5,9, clean-up: no 4,5 in R7C9
2e. Killer triple 1,2,3 in R6C12, R6C35 and R6C89, locked for R6
2f. 45 rule on N8 3 outies R6C467 = 21 = {489/579} (cannot be {678} which clashes with R6C12), no 6
2g. 45 rule on N8 1 outie R6C4 = 1 innie R7C6 + 1, R6C4 = {45789} -> R7C6 = {34678}, no 5,9
2h. Max R46C5 = 11 -> min R6C5 = 2

3a. 45 rule on C123 1 outie R5C4 = 1 innie R4C3 + 1, no 1 in R5C4
3b. 45 rule on C789 1 innie R6C7 = 1 outie R5C6 + 3, R6C7 = {45789} -> R5C6 = {12456}

[The first interesting steps …]
4a. R4C7 ‘sees’ both R4C5 and R5C6, R4C57 (step 2a) = 7 -> R5C6 + R4C7 cannot total 7 (combination crossover clash, CCC) -> R5C789 cannot total 11
Note. This doesn’t eliminate 8 from R5C789, which can still total more than 11
4b. R6C5 ‘sees’ both R5C4 and R6C3, R6C35 (step 2b) = 6 -> R5C4 + R6C3 cannot total 6 (CCC) -> R5C123 cannot total 21

5a. 45 rule on N1 2 outies R4C12 = 10 = {28/37/46}/[91], no 5, no 9 in R4C2, clean-up: no 6 in R3C1
5b. 45 rule on N3 2 outies R4C89 = 15 = {69/78}
5c. Min R2C7 + R4C8 = 9 -> max R3C78 = 9, no 9 in R3C78

6a. R6C35 (step 2b) = {15/24}, R6C7 = R5C6 + 3 (step 3b)
6b. Consider position of 1 in N6
1 in R4C7 + R5C789, locked for 18(4) cage at R4C7, no 1 in R5C6
or 1 in R6C89, locked for R6 => R6C35 = {24}, 4 locked for R6, no 4 in R6C7 => no 1 in R5C6
-> no 1 in R5C6, clean-up: no 4 in R6C7
6c. 18(5) cage at R4C7 = {12348/12357/12456}, 1 locked for N6, clean-up: no 8 in R6C89 (step 2d), clean-up: no 1,8 in R7C9
6d. Killer pair 6,7 in R4C89 and R6C89, locked for N6, clean-up: no 1 in R4C5 (step 2a), no 4 in R5C6
6e. 18(5) cage at R4C7 = {12348/12456}
6f. 6 of {12456} must be in R5C6 -> no 5 in R5C6, clean-up: no 8 in R6C7
6g. 45 rule on C789 3 outies R567C6 = 17 = {269/278/368/467} (cannot be {359/458} because R5C6 only contains 2,6), no 5

7a. 18(5) cage at R4C7 (step 6e) = {12348/12456}, R4C89 = 15 (step 5b), R6C89 = 9 (step 2d), R6C7 = R5C6 + 3 (step 3b)
7b. Consider combinations for R6C467 (step 2f) = {489/579}
R6C467 = {489} => R6C7 = 9 => R5C6 = 6 => 18(5) cage = {12456}
or R6C467 = {579}, 7 locked for R6 => R6C89 = {36}, 3 locked for N6 => 18(5) cage = {12456}
-> 18(5) cage = {12456} -> R5C6 = 6, R6C7 = 9, clean-up: no 1 in R2C4 (step 1a), no 1 in R4C7 (step 2a), no 6 in R4C89, no 5 in R4C3 (step 3a), no 7 in R6C4 (step 2g), no 8 in R7C6 (step 2g)
7c. Naked pair {78} in R4C89, locked for R4 and N6, clean-up: no 2,3 in R4C12 (step 5a), no 3,4,8,9 in R3C1, no 8,9 in R5C4 (step 3a), no 2 in R6C89, no 2,7 in R7C9
7d. Naked pair {78} in R4C89, CPE no 7,8 in R2C8
7e. Naked pair {36} in R6C89, locked for R6, 3 locked for N6, clean-up: no 4 in R4C5 (step 2a)
7f. R67C9 = {36}, locked for C9, clean-up: no 5,8 in R8C8
7g. 1 in N6 only in R5C789, locked for R5
7h. 13(3) cage at R4C5 must contain one of 7,8,9 -> R5C5 = {789}

8a. 45 rule on N2 1 outie R4C6 = 1 innie R3C4 + 2 -> R3C4 = {1237}
8b. 11(3) cage at R3C4 = {137/146/236} (cannot be {245} = [245] which clashes with R4C57), no 5
8c. 6 of {146/236} must be in R4C3 -> no 2,4 in R4C3, clean-up: no 3,5 in R5C4 (step 3a)
8d. 45 rule on C123 3 outies R345C4 = 12 = {147/237}, 7 locked for C4
8e. 3 in N5 only in R4C456, locked for R4, clean-up: no 4 in R5C4 (step 3a)
8f. 9 in N5 only in R4C6 or 13(3) cage at R4C5 = [391] -> no 3 in R4C6 (locking-out cages), clean-up: no 1 in R3C4
8g. 11(3) cage = {137/236} (cannot be {146} because R3C4 only contains 2,3,7), no 4
8h. R345C4 = {237}, 2,3 locked for C4, clean-up: no 5 in R2C6 (step 1a)
8i. 1 in R4 only in R4C23, locked for N4, clean-up: no 8 in R6C12 (step 2d), no 5 in R6C5 (step 2b)
8j. 1 in R4 only in R4C23, CPE no 1 in R3C3
8k. Naked pair {27} in R6C12, locked for R6 and N4, clean-up: no 4 in R6C35 (step 2b)
8l. R6C35 = [51] -> R45C5 = 12 = [39/57], clean-up: no 5 in R4C7 (step 2a), no 4 in R7C6 (step 2g)
8m. 5 in R4 only in R4C56, CPE no 5 in R23C5
8n. Naked pair {48} in R6C46, 4 locked for N5, clean-up: no 2 in R3C4
8o. Naked pair {27} in R6C12, CPE no 2,7 in R8C2
8p. 45 rule on R9 2 outies R8C46 = 7 = [43/52/61]

[With hindsight, it would probably have been quicker to do step 10a now.]
9a. R4C12 (step 5a) = 10
9b. Consider permutations for 11(3) cage at R3C4 (step 8g) = {137/236} = [362/713]
11(3) cage = [362] => R4C12 = [91]
or 11(3) cage = [713] => R4C12 = [64]
-> R4C12 = [64/91], clean-up: no 7 in R3C1
9c. Max R4C2 = 4 -> min R2C3 + R3C23 = 19, no 1 in R3C2
9d. 1 in R3 only R3C78, locked for N3
9e. 18(4) cage at R2C7 contains 1 = {1278/1368/1458/1467}
9f. 1,2 of {1278} must be in R3C78, 7,8 of {1368/1458/1467} must be in R4C8 -> no 7,8 in R3C78

10a. 27(4) cage at R2C5 = {4689/5679} (cannot be {3789} = {378}9 which clashes with R3C3), no 3, 6 locked for N2, clean-up: no 1 in R2C6 (step 1a)
10b. R2C46 = [52], clean-up: no 3 in R2C12
10c. Naked pair {14} in R2C12, locked for N1, 4 locked for R2
10d. 27(4) cage = {4689} -> R4C6 = 9, 4 locked for R3 and N2, 6 locked for C2
10e. R2C46 = [52] = 7 -> R1C456 = 13 = {139} (only remaining combination), 3,9 locked for R1, 3 locked for N2
10f. R3C4 = 7 -> R45C3 = [32], R4C123 = [641] -> R3C1 = 5, R2C12 = [41], R45C5 = [57]
10g. 16(3) cage at R1C1 = {268} (only remaining combination), locked for R1 and N1
10h. Naked triple {457} in 16(3) cage at R1C7, 7 locked for N3
10i. Naked pair {39} in R3C23, locked for R3 and N1 -> R2C3 = 7
10j. 14(4) cage at R6C2 = {2345} -> R6C2 = 2, R7C2 = 5, R78C3 = {34}, locked for N7, 3 locked for C3
10k. R3C23 = [39], R5C123 = [398]
10l. R9C2 = 7 (hidden single in C2) -> R9C13 = 8 = [26]
10m. R8C46 (step 8b) = 7 -> R9C456 = 17 = {359/458} -> R8C46 = [61], R1C456 = [193], R7C6 = 7 -> R6C6 = 4 (cage sum), R3C6 = 8, R9C6 = 5, clean-up: no 5 in R8C9
10n. R8C12 = [98], clean-up: no 2,3 in R8C89
10o. R3C9 = 2 -> 26(4) cage at R2C8 = {2789} -> R2C89 = [98], R4C9 = 7

and the rest is naked singles.


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PostPosted: Mon Apr 12, 2021 6:40 pm 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
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Location: Sydney, Australia
Very worthy as an Easter puzzle. Loved it! So nice to have some big cages. I did the start pretty much exactly the same way as I did on the archive WT so have borrowed that one with a different middle crack.

Assassin 53 V3
WT:
1. "45" r6789: r6c35 = 6 = h6(2)r6 = {15/24}
1a. = [4/5]

2. "45" n7: r6c12 = 9 = h9(2)n4
2a. no 9

3. "45" n9: r6c89 = 9 = h9(2)n6
3a. no 9

4. "45" n8: r6c467 = 21 = h21(3)r6
4a. must have 9 for r6
4b. = 9{48/57}(no 1236)
4c. = [4/5]

5. Killer Pair 4/5 in h21(3)r6 and h5(2)r6
5a. 4 and 5 locked for r6

6. "45" n3: r4c89 = 15 = h15(2)n6
6a. = {69/78}

7. "45" n369: r5c6 + 3 = r6c7
7a. r5c6 = 1,2,4,5,6

8. 4 and 5 cannot be in r5c6. Here's how.
8a. 4 or 5 in r5c6 -> only place for 4/5 in n6 is in r6c7
8b. but this is impossible since r5c6 + 3 = r6c7 = 7/8(step 7)
8c. -> no 4 or 5 in r5c6
8d. -> no 7/8 r6c7 (step 7)

9. 1 cannot be in r5c6. Here's how.
9a. 1 in r5c6 -> 4 in r6c7 (step 7) and 1 in n6 in r6c89.
9b. -> r6c789 = {14}
9c. but this clashes with h6(2) r6 = [1/4..]
9d. no 1 r5c6
9e. no 4 r6c7 (step 7)

10. 2 cannot be in r5c6. You've probably guessed how by now.
10a. 2 in r5c6 -> r6c7 = 5 (step 7) and 2 for n6 in r6c89
10b. -> r6c789 = {25}
10c. but this clashes with h6(2)r6 = [2/5..]
10d. no 2 r5c6

11. r5c6 = 6, r6c7 = 9 (step 7)
11a. split-cage 11(2)r6c6 = [83]/{47}
11b. r6c6 = 478, r6c7 = 347

12. split-cage 12(4)r4c7 = {1245}: all locked for n6

13. h15(2)n6 = {78}: both locked for n6 & r4
13a. r2c8 sees both those so has no 7,8

14. r6c89 = {36}: both locked for r6

15. 9(2)r6c9 = {36}: both locked for c9

16. "45" r1234: r4c57 = 7 = h7(2)r4
16a. = {25}/[34], r4c5 = 235, r4c7 no 1
16b. -> 1 in n6 only in r5: 1 locked for r5

17. "45" n8: r6c46 = 12 = {48}/[57](no 7 r6c4)
17a. = [4/7..]

18. 13(3)n5 = [391/571/382] ({247} blocked by r6c46 step 17a)
18a. r4c5 = {35}, r5c5 = {789}, r6c5 = {12}
18b. r6c3 = {45} (h6(2)r6)
18c. r4c7 = {24} (h7(2)r4)

19. 5 in n6 only in r5: 5 locked for r5

20. 27(5)n4 = 5{...}
20a. ->r6c3 = 5

21. r6c5 = 1 (h6(2)r5)
21a. r45c5 = [39/57](no 8)
21b. 8 in r5 only in split-cage 22(4)r5c1 = 8{239/347}

22. r6c12 = h9(2) = {27}: both locked for n4, r6
22a. and not in r8c2 (CPE)

23. r6c46 = naked pair {48}: both locked for n5
23. r67c6 = [83/47]

24. "45" n147: r5c4 - 1 = r4c3
24a. r5c4 = {27}, r4c3 = {16}

25. "45" n1: r4c12 = 10 = [91]/{46} (no 3, no 9 in r4c2)

26. 2 in n5 only in c4: 2 locked for c4

27. "45" n2: 3 outies r4c346 = 13 = [139/625]
27a. r4c4={23}, r4c6 = {59}

28. "45" n2: r4c6 - 2 = r3c4
28a. r3c4 = {37}

29. naked triple {237} r345c4: all locked for c4

30. 5(2)n1 = {14/23}
30a. = [3/4..]

31. "45" r1: 2 outies r2c46 = 7 = h7(2)n2
31a. = [61/52] ([43] blocked by 5(2)n1 step 30a)

New ending from here
32. 11(3)r3c4 = [713/362] = 7 in r3 or 6 in r4
32a. -> combined half cage r34c1+r4c2, [746] blocked
32b. -> r34c1 = [29/56]
32c. r4c2 = (14)

33. 23(4)n1 must have 1 or 4 for r4c2
33a. can't have both 1,4 since other two can't = 18
33b. -> no 1,4 in r2c3 + r3c23

34. 16(3)n1 can't have both 1,4 and make the cage sum
34a. -> 5(2) must have both = {14}(only other place in n1): both locked for n1 and r2
34b. r2c46 = [52]

35. 27(4)n2: {3789} blocked by r3c4 = (37)
35a. = {4689/5679}(no 3)
35b. must have 6: locked for c5 and n2

36. sp13(3)r1c456 = {139/148}(no 7)
36a. 1 locked for r1

37. 16(3)n1: {259} blocked by r3c1 = (25)
37a. {358} blocked by r1c456 = 3 or 8
37b. = {268/367}(no 5,9)
37c. 6 locked for n1 and r1

38. 5 in r1 only in 16(3)n7
38a. but {358} blocked by r1c456
38b. = {259/457}(no 3,8)
38c. 5 locked for n3

39. 26(4)n3: {3689} blocked by 3,6 only in r2c8
39a. = {2789/4679}(no 3)
39b. 9 locked for n3

40. 16(3)n3 = {457} only: 4,7 both locked for r1 and n3
40a. -> 7 which must be in 26(4)n3 must be in r4c9
40b. r4c8 = 8
40c. -> 18(4)r2c7: must have 3 or 6 for r2c7 = {136}[8]
40d. 6 locked for n3
40e. -> 26(4)n3 = [9827]

On from there. Sorry, ran out of time for any more
Cheers
Ed


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