Assassin 71
Posted: Fri Oct 05, 2007 2:29 pm
No, I haven't solved it yet! But the fact that no-one else has either shows either it's really difficult or you haven't had time yet. I'll have another look at it this evening.
Edit: This is definitely a tough one. 45 steps (about 3 hours) and counting.
I have c7 fixed and a few other placements and thought it would start falling into place but there's still work to do!
Edit 2: Finally! Took about 4 hours in total. At least 1.5 rating. I can't say I particularly want to go through it again so if there's any corrections required, I'll just take your word for it.
Prelims
a) 14(4) @ r1c7 and r8c3: no 9
b) 12(3) r34c3 = {39/48/57}
c) 10(2) @ r3c4 and r3c6: no 5
d) 19(3) @ r3c5: no 1
e) 13(2) @ r3c7 and r6c6 = {49/58/67}
f) 8(2) @ r5c3 and r5c6 = {17/26/35}
g) 27(4) @ r4c8 = {3789/4689/5679} -> 9 not elsewhere in N6 -> r3c7 <> 4
h) 9(2) r67c3: no 9
i) 11(2) r67c4 and r67c5: no 1
j) 5(2) r67c7 = {14/23}
1. Innies r12: r2c18 = 12 = {39/48/57}
2. Innies r89: r8c29 = 8 = {17/26/35}
3. Outies c12: r29c3 = 10 = {19/28/37/46} -> r158c3 = 14
4. Outies c89: r18c7 = 7 = {16/25} ({34} blocked by 5(2))
a) KP with 5(2) -> 1,2 not elsewhere in c7 -> r5c6 <> 6,7
b) r259c7 = 20 = {389/479/578} ({569} blocked by 13(2) -> r259c7 <> 6 -> r5c6 <> 2
5. Innies r6789: r6c29 = 15 = {69/78}
6. Outies c1234: r29c5 = 7 = {16/25/34}
7. Outies c6789: r18c5 = 8 = {17/26/35}
8. O-I N1: r4c23 – r1c3 = 7 -> r4c2 <> 7
9. O-I N3: r2c7 – r4c79 = 1
a) r4c79 max 8 -> r4c7 = (4567), r4c9 = (123) -> r3c7 <> 5
b) r2c7 min 6 -> r2c7 = (789)
10. O-I N7: r6c13 – r8c3 = 5 -> r6c1 <> 5
11. O-I N9: r9c7 – r6c78 = 1
a) r6c78 is max 8 -> r6c8 <> 8
b) 8 locked to 27(4) in N6 = {3789/4689} (eliminate 5)
12. O-I r1234: r4c18 – r5c5 = 2 -> r4c1 <> 9
13. Innies N69: r4c9 + r459c6 = 19
a) 5(2) r67c7 must have one of 3,4
b) split 19(4) must have one of 3,4 within r459c6 -> split 19(4) <> {1567}
14. 27(4) N6 must have one of 3,4
a) From step 9, O-I N3 <> [843]
15. Split 19(4) = 1[639/738/459], 2[539/638/458], 3{57}4 -> r9c7 <> 5,7
16. Split 20(3) r259c7 = [839/938/974/758]
17. 27(4) N6 must have one of 3,6
a) Split 19(4) can’t have both 3,6 within N6 -> 19(4) <> [1639/2638]
b) r4c7 <> 6, r3c7 <> 7
18. Killer combo N6: 27(4) must have one of 3,4; split 19(4) must have one of 3,4 within N6
a) r6c78 <> 3,4 -> r7c7 <> 1,2
b) 21(4) N9 and 18(4) @ r6c8 can’t have both 3,4
c) 16(4) @r6c1 can’t have both 3,4 within r7c12
19. Innies N36: r256c7 + r6c8 = 19
a) Can’t have both 3,6 in N6 because of 27(4) -> {1369/2368} blocked.
b) Options for split 19(4) = {1279/1378/1567/2359/2377}
20. Innies N14: r6c1 + r156c3 = 19 -> can’t have both 1,2 within r6c13
21. Innies N47: r4c2 + r458c3 = 21
22. Innies r1234: r34c5 + r4c18 = 21
23. Conflicting combo: Split 19(4) r256c7, r6c8 <> [7516] since would block both options for split 7(2) r18c7
a) r5c7 <> 5 -> r5c6 <> 3
b) r6c8 <> 6
24. 27(4) N6 = {4689}(only available combo since r5c7 = (37)) -> r4c7 <> 4 -> r3c7 <> 9
a) Clean up: r6c2 <> 8
25. 4 locked r79c7 n/e N9
26. Split 20(3) r259c7 = [839/938/974] -> r2c7 <> 7
a) 7 locked r45c7 -> r6c8 <> 7
b) Split 19(4) r4c9 + r569c7 must have 7 = [1738/3574] -> r9c7 <> 9
27. HS r2c7 = 9
a) split 12(2): r2c18 <> 3
b) split 10(2) r29c3: r9c3 <> 1
c) r4c79 = [53/71] -> 2 locked r6c78 n/e r6 -> clean up: r7c45 <> 9, r7c3 <> 7
28: r4c79 = [53/71], r5c67 = [17/53]
a) r4c6 <> 1 -> r3c6 <> 9
b) r4c5 <> 5
c) r4c4 <> 1 -> r3c4 <> 9
29. 9 locked r789c6 -> r46c6 <> 9 -> r7c6 <> 4; r3c6 <> 1
30. 1 locked r5c46 -> r5c123 <> 1 -> r5c4 <> 7
31. Conflicting combo N6:
a) r4c9 = 1 -> r4c7 = 7, r5c7 = 3 -> Conflict for 5(2)
b) Therefore: r4c9 = 3 -> r4c7 = 5, r5c7 = 7, r5c6 = 1, r3c7 = 8, r9c7 = 4, r7c7 = 3, r6c7 = 2, r6c8 = 1
c) Clean up: r2c1 <> 4, r3c46 <> 7, r4c46 <> 2, r6c45 <> 8, r6c3 <> 6, r7c3 <> 8, r3c3 <> 7,9, r4c3 <> 4,
32. HS r1c8 = 3
33. 14(4) N3 = {1346} only possible combo, -> r2c8 = (57), r3c89 = (257)
a) 2 locked r3c89 n/e r3
b) Clean up: r4c46 <> 8
c) 4 locked r45c8 -> r5c9 <> 4
d) Split 12(2) r2c18 = {57} n/e r2
34. 10(2) r34c6 = [37]/{46} -> KP 13(2) r67c6 <> {67}
35. 1 locked r7c123 n/e N7
36. Split 8(2) r8c29 = {26} only possible combo -> n/e r8
a) r8c7 = 1 -> r1c7 = 6
b) 25(4) N7 <> {2689} -> r9c123 <> 2
c) 2 locked r9c456 -> r7c45 <> 2 -> r6c45 <> 9
37. 1 locked r4c12 -> r3c1 <> 1
38. Grouped Turbot (5): r2c1 = r2c8 – r89c8 = r9c9
-> r9c1 <> 5
39. 9 locked to 19(3) r345c5 = {289/379/469}
40. 5 locked r1c456 -> r1c123 <> 5
41. Split 8(2) r18c5 = [17/53]
42. 14(4) @ r8c3 = {1238/1247/1346/2345} Must have one of 3,7
a) Since r8c5 = (37), r8c6 <> 3,7
43. Grouped Turbot (9): r3c12 = r3c5 – r45c5 = r4c4
-> r4c2 <> 9
44. Split 10(2) r29c3 = [19/28/37/46]
45. Split 7(2) r29c5 = [16/25/43/61]
46. Pointing cells: 6 locked r2c2, r3c12 -> r4c2 <> 6
47. 14(4) @ r8c3 must have 1 within r9c45 -> {2345} blocked -> 14(4) <> 5
a) clean up: r2c5 <> 2
48. 2 locked r45c5 n/e N5 – r5c3 <> 6
a) 19(3) r345c5 = 9{28}
b) 11(2) r67c5 <> [38]
c) 13(2) r67c6 <> [85]
49. HS r4c4 = 9 -> r3c4 = 1, r1c5 = 5, r8c5 = 3
50. 11(2) r67c5 = {47} -> r2c5 = 6, r9c5 = 1
51. r12c6 of 20(4) = {24} n/e N2 -> r3c6 = 3, r4c6 = 7, …
All singles from here.
Edit: This is definitely a tough one. 45 steps (about 3 hours) and counting.
I have c7 fixed and a few other placements and thought it would start falling into place but there's still work to do!
Edit 2: Finally! Took about 4 hours in total. At least 1.5 rating. I can't say I particularly want to go through it again so if there's any corrections required, I'll just take your word for it.
Prelims
a) 14(4) @ r1c7 and r8c3: no 9
b) 12(3) r34c3 = {39/48/57}
c) 10(2) @ r3c4 and r3c6: no 5
d) 19(3) @ r3c5: no 1
e) 13(2) @ r3c7 and r6c6 = {49/58/67}
f) 8(2) @ r5c3 and r5c6 = {17/26/35}
g) 27(4) @ r4c8 = {3789/4689/5679} -> 9 not elsewhere in N6 -> r3c7 <> 4
h) 9(2) r67c3: no 9
i) 11(2) r67c4 and r67c5: no 1
j) 5(2) r67c7 = {14/23}
1. Innies r12: r2c18 = 12 = {39/48/57}
2. Innies r89: r8c29 = 8 = {17/26/35}
3. Outies c12: r29c3 = 10 = {19/28/37/46} -> r158c3 = 14
4. Outies c89: r18c7 = 7 = {16/25} ({34} blocked by 5(2))
a) KP with 5(2) -> 1,2 not elsewhere in c7 -> r5c6 <> 6,7
b) r259c7 = 20 = {389/479/578} ({569} blocked by 13(2) -> r259c7 <> 6 -> r5c6 <> 2
5. Innies r6789: r6c29 = 15 = {69/78}
6. Outies c1234: r29c5 = 7 = {16/25/34}
7. Outies c6789: r18c5 = 8 = {17/26/35}
8. O-I N1: r4c23 – r1c3 = 7 -> r4c2 <> 7
9. O-I N3: r2c7 – r4c79 = 1
a) r4c79 max 8 -> r4c7 = (4567), r4c9 = (123) -> r3c7 <> 5
b) r2c7 min 6 -> r2c7 = (789)
10. O-I N7: r6c13 – r8c3 = 5 -> r6c1 <> 5
11. O-I N9: r9c7 – r6c78 = 1
a) r6c78 is max 8 -> r6c8 <> 8
b) 8 locked to 27(4) in N6 = {3789/4689} (eliminate 5)
12. O-I r1234: r4c18 – r5c5 = 2 -> r4c1 <> 9
13. Innies N69: r4c9 + r459c6 = 19
a) 5(2) r67c7 must have one of 3,4
b) split 19(4) must have one of 3,4 within r459c6 -> split 19(4) <> {1567}
14. 27(4) N6 must have one of 3,4
a) From step 9, O-I N3 <> [843]
15. Split 19(4) = 1[639/738/459], 2[539/638/458], 3{57}4 -> r9c7 <> 5,7
16. Split 20(3) r259c7 = [839/938/974/758]
17. 27(4) N6 must have one of 3,6
a) Split 19(4) can’t have both 3,6 within N6 -> 19(4) <> [1639/2638]
b) r4c7 <> 6, r3c7 <> 7
18. Killer combo N6: 27(4) must have one of 3,4; split 19(4) must have one of 3,4 within N6
a) r6c78 <> 3,4 -> r7c7 <> 1,2
b) 21(4) N9 and 18(4) @ r6c8 can’t have both 3,4
c) 16(4) @r6c1 can’t have both 3,4 within r7c12
19. Innies N36: r256c7 + r6c8 = 19
a) Can’t have both 3,6 in N6 because of 27(4) -> {1369/2368} blocked.
b) Options for split 19(4) = {1279/1378/1567/2359/2377}
20. Innies N14: r6c1 + r156c3 = 19 -> can’t have both 1,2 within r6c13
21. Innies N47: r4c2 + r458c3 = 21
22. Innies r1234: r34c5 + r4c18 = 21
23. Conflicting combo: Split 19(4) r256c7, r6c8 <> [7516] since would block both options for split 7(2) r18c7
a) r5c7 <> 5 -> r5c6 <> 3
b) r6c8 <> 6
24. 27(4) N6 = {4689}(only available combo since r5c7 = (37)) -> r4c7 <> 4 -> r3c7 <> 9
a) Clean up: r6c2 <> 8
25. 4 locked r79c7 n/e N9
26. Split 20(3) r259c7 = [839/938/974] -> r2c7 <> 7
a) 7 locked r45c7 -> r6c8 <> 7
b) Split 19(4) r4c9 + r569c7 must have 7 = [1738/3574] -> r9c7 <> 9
27. HS r2c7 = 9
a) split 12(2): r2c18 <> 3
b) split 10(2) r29c3: r9c3 <> 1
c) r4c79 = [53/71] -> 2 locked r6c78 n/e r6 -> clean up: r7c45 <> 9, r7c3 <> 7
28: r4c79 = [53/71], r5c67 = [17/53]
a) r4c6 <> 1 -> r3c6 <> 9
b) r4c5 <> 5
c) r4c4 <> 1 -> r3c4 <> 9
29. 9 locked r789c6 -> r46c6 <> 9 -> r7c6 <> 4; r3c6 <> 1
30. 1 locked r5c46 -> r5c123 <> 1 -> r5c4 <> 7
31. Conflicting combo N6:
a) r4c9 = 1 -> r4c7 = 7, r5c7 = 3 -> Conflict for 5(2)
b) Therefore: r4c9 = 3 -> r4c7 = 5, r5c7 = 7, r5c6 = 1, r3c7 = 8, r9c7 = 4, r7c7 = 3, r6c7 = 2, r6c8 = 1
c) Clean up: r2c1 <> 4, r3c46 <> 7, r4c46 <> 2, r6c45 <> 8, r6c3 <> 6, r7c3 <> 8, r3c3 <> 7,9, r4c3 <> 4,
32. HS r1c8 = 3
33. 14(4) N3 = {1346} only possible combo, -> r2c8 = (57), r3c89 = (257)
a) 2 locked r3c89 n/e r3
b) Clean up: r4c46 <> 8
c) 4 locked r45c8 -> r5c9 <> 4
d) Split 12(2) r2c18 = {57} n/e r2
34. 10(2) r34c6 = [37]/{46} -> KP 13(2) r67c6 <> {67}
35. 1 locked r7c123 n/e N7
36. Split 8(2) r8c29 = {26} only possible combo -> n/e r8
a) r8c7 = 1 -> r1c7 = 6
b) 25(4) N7 <> {2689} -> r9c123 <> 2
c) 2 locked r9c456 -> r7c45 <> 2 -> r6c45 <> 9
37. 1 locked r4c12 -> r3c1 <> 1
38. Grouped Turbot (5): r2c1 = r2c8 – r89c8 = r9c9
-> r9c1 <> 5
39. 9 locked to 19(3) r345c5 = {289/379/469}
40. 5 locked r1c456 -> r1c123 <> 5
41. Split 8(2) r18c5 = [17/53]
42. 14(4) @ r8c3 = {1238/1247/1346/2345} Must have one of 3,7
a) Since r8c5 = (37), r8c6 <> 3,7
43. Grouped Turbot (9): r3c12 = r3c5 – r45c5 = r4c4
-> r4c2 <> 9
44. Split 10(2) r29c3 = [19/28/37/46]
45. Split 7(2) r29c5 = [16/25/43/61]
46. Pointing cells: 6 locked r2c2, r3c12 -> r4c2 <> 6
47. 14(4) @ r8c3 must have 1 within r9c45 -> {2345} blocked -> 14(4) <> 5
a) clean up: r2c5 <> 2
48. 2 locked r45c5 n/e N5 – r5c3 <> 6
a) 19(3) r345c5 = 9{28}
b) 11(2) r67c5 <> [38]
c) 13(2) r67c6 <> [85]
49. HS r4c4 = 9 -> r3c4 = 1, r1c5 = 5, r8c5 = 3
50. 11(2) r67c5 = {47} -> r2c5 = 6, r9c5 = 1
51. r12c6 of 20(4) = {24} n/e N2 -> r3c6 = 3, r4c6 = 7, …
All singles from here.