Here's a nice hard and fun puzzle - the last inspired from that wonderful samurai killer with all those confusing diagonal cages. No need for a V2 on this one (wasn't really any need for SampuZ4 either in hindsight).
Very nice, Ed. Easy start with a lot of eliminations for N123 but then you have to take your time until it falls.
Here is a walkthrough, as always in tiny font. (Edit: tiny font removed)
Walkthrough SampuZ5
1. N1 : 7(3) = {124} -> 1,2,4 locked for N1
2. N3 : 30(4) = {6789} -> 6,7,8,9 locked for N3
3. N23 : 12(2) = [75|84|93]
4. N2 : 5(2) = {14|23}
5. N3 : 6(2) = {15|24}
6. N2 : 10(2) = {19|28|37|46}
7. N4 : 7(2) = {16|25|34}
8. N45 : 14(2) = {59|68}
9. N47 : 15(2) = {69|78}
10. N5 : 9(2) = {18|27|36|45}
11. N8 : 9(2) = {18|27|36|45}
12. N6 : 7(2) = {16|25|34}
13. N6 : 11(3) : no 9
14. N89 : 20(3) : no 1,2
15. N9 : 1 locked in 19(5) for N9
16. N56 : 19(3) : no 1
17. 45 on N1 : r3c45 = 8(2) = {17|26|35}
18. N12 : 33(6) = 89{1267|1357|2356} -> 8,9 locked for N1 in 33(6)
19. N1 : 13(2) = {67} -> 6,7 locked for N1
20. N12 : 33(6) : {3589} in N1 -> no 3,5 in r3c45
21. N2 : 1,2 locked in 5(2) and r3c45 for N2
22. N2 : 10(2) = {37|46} -> 6,7 locked in 10(2) and r3c45 for N2
23. N23 : 12(2) = [84|93]
24. N2 : 5 locked in 19(4) for N2 -> no 5 in r2c7 r3c8
25. N3 : 5 locked in 6(2) = {15} -> 1,5 locked for N3
26. 5 locked in r3c13 for N1 and r3
27. N23 : 19(4) = 25{39|48} -> no 3,4 in r1c5 r2c6
(other way: N2 : 3,4 locked in 10(2) and 5(2) for N2)
28. c9 : 16(3) has at most one of {6789} because of 30(4) in N3 -> 16(3) = {259|349|358|457} -> no 1,6 -> 6 locked in r123c9 for N3 and c9 -> no 6,7,8,9 in r489c9 (Para's suggestion, much clearer: Killer Quad {6789} in R123C9 + 16(3) which eliminates 6,7,8,9 from r489c9 -> 6 locked in r123C9 for N3)
29. 45 on N6 : r5c6 + r7c9 = 8(2) = [62]|{35|44}
30. N56 : 19(3) : max r5c6 = 6 -> min r45c7 = 13 -> no 2,3 in r45c7
31. N6 : 11(3) = {128|137|146|245} ({236} blocked by 7(2))
32. 45 on N4 : r6c2 + r5c3 = 15(2) = [78]|{69} -> no 7 in r7c2, no 9 in r4c4
33. c2 : 6,7 locked in r167c2 for c2 -> no 1 in r5c1
34. N4 : combination check for 23(5) : 23(5) = {12569|12578|13469|13478|23459} , others blocked
35. 45 on N7 : r6c2 + r78c4 = 22(3) = [679|7{69}|778|9{49|58}|976] -> no 1,2,3 in r78c4, no 7 in r8c4
36. 45 on N78 : r7c2 + r8c6 = 13(2) = [67|85|94] -> r8c6 = {457}
37. N89 : 20(3) = {479|569|578} -> no 3
38. N8 : 16(4) must have two of {123} (three not possible) -> {1456} not possible for 16(4) -> 9(2) must have one of {123} -> {45} not possible for 9(2) -> no 4,5 in 9(2)
Edit: Explanation by sudokuEd:
16(4) cannot have {123} since = 6 -> only other place for {123} in n8 is 9(2) -> no {45} in 9(2). Also, 9(2) can only have 1 of {123} -> 16(4) must have 2 of -> no {1456} in 16(4).
39. 45 on N789 : r7c279 = 19(3) -> r7c7 = {6789}
Edit: Explanation by sudokuEd:
Max r7c29 = [85/94] = 13 -> min r7c7 = 6
40. N6 : combination check: 2 is in 11(2) or 7(2) -> no 2 in r56c9
41. r3 : 1,2,3,4 locked in r3c24578 -> no 3 in r3c13
42. r3 : naked triple {589} -> no 8,9 i r3c9
43. 45 on N47 : r478c4 = 21(3) = [579|8{49] ({678} blocked by 10(2) at r1c4) -> r4c4 = {58}, r7c4 = {479}, r8c4 = {49} ->9 locked in r78c4 for c4 and N8, 4,7 locked in r1278c4 for c4
44. clean-up: no 2 in r9c5, no 1 in r3c5, no 8 in r5c3
45. from step 32: r6c2 + r5c3 = 15(2) = {69} -> 6,9 locked for N4
46. hidden single : r4c7 = 9
47. N47 : 15(2) = {69} -> 6,9 locked for c2
48. r1c2 = 7, r2c1 = 6
49. clean-up: no 1 in r4c2, no 5 in r5c67, no 8 in r5c7
50. 7 locked in r23c9 for c9
51. c9 : 16(3) = {358} -> 3,5,8 locked for c9, 8 locked for N6
52. r1c8 = 8
53. from step 39: r7c279 = 19(3) = [973|685] -> r7c7 = {78}
54. from step 36: r8c6 = {47} -> 4,7,9 locked in r78c4 r8c6 for N8 -> no 2 i r9c4
55. N89 : 20(3) = 7{49|58} -> 7 locked for 20(3) -> no 7 in r8c78, no 5 in r9c7
56. 3 locked in r3c78 for r3 and N3
57. N59 : 18(3) = {189|279|378|468|567}
58. N9 : 6 locked in 19(5) = {12367} -> 1,2,3,6,7 locked for N9
The rest is clean-up
59. r7c79 = [85], r9c78 =[49], r8c6 = 7, r67c2 = [96], r5c3 = 6, r4c4 = 8, r5c67 = [37], r3c67 = [93], 19(4) at r1c5 = [5824], ...
I know there are still a lot of cells to fill but it can be done with simple checks.
As always feel free to comment/correct.
Peter
Last edited by Nasenbaer on Sat Feb 17, 2007 7:14 pm, edited 4 times in total.
I think mine covers a lot more steps but follows basically the same route.
I didn't include the primary eliminations and started my walkthrough from the mark-up pic.
Walk-through SampuZ5
1. {124} locked in 7(3) in R1C3 for N1.
1a. Clean up: no 9 in 13(2) in R1C2
1b. 3 and 9 locked in N1 for 33(6) in R1C1. No 3 or 9 in R3C45.
1c. 33(6) = {135789/234789/235689} -->> 8 obligated in 33(6)
2. {6789} locked in 30(4) for N3.
2a. Clean up: no 3, 4 or 5 in R3C6
3. 45 on N1: 2 outies R3C45 = 8 = {17/26}
3a. 8 locked in 33(6) for N1.
3b. 13(2) in R1C2 = {67} -->> locked in N1
3c. 33(6) in R1C1 = {3589}+{17/26}
4. Killer Pair {67} in R1C2 + 15(2) in R6C2 -->> no 6 or 7 anywhere else in C2
4a. Clean up: No 1 in R5C1
5. 45 on N2: 3 innies: R1C5 + R23C6 = 22 = {589/679}-->> no 1,2,3,4 + 9 locked for N2
5a. 5 locked in R1C5 + R2C6 -->> R1C5 + R23C6 = {589} -->> no 6,7 + 8 locked for N2 + 5 locked in 19(4) in R1C5 -->> no 5 in R2C7 and R3C8
5b. Clean up: no 1 or 2 in R12C4
5c. Clean up: no 5 in R3C7
5d. 5 locked in 6(2) in R1C7: 6(2) = {15} -->> locked for N3
6. Hidden Killer Pair {67} in R3C45 + R3C9 -->> R3C9 = {67} : R3C45 contains either a 6 or a 7. Only other option for a 6 or a 7 in R3 is in R3C9
7. 45 on N4: 2 innies R5C3 + R6C2 = 15 = {69}/[87]
7a. Clean up: R4C4: no 9 ; R7C2: no 7
8. 45 on N5: 4 outies: R5C3 + R457C7 = 30 = 9{489}; 9{579}; 9{678}; 8{589};8{679}; 6{789} -->> no 1, 2 or 3 in R457C7
9. 45 on N6: 2 outies: R5C6 + R7C9 = 8 = [71]/{26/35/44} -->> no 8 or 9 in both cells and no 7 in R7C9
9a. 45 on N6: 4 innies: R45C7 + R56C9 = 27 = {9873/9864/9765} -->> no 1,2
10. 45 on N7: 3 outies: R6C2 + R78C4 = 22 = {994/985/976/877} -->> no 1,2,3
11. 19(5) in R7C8 = {12349/12358/12367/12457/13456} -->> 1 locked in 19(5) for N9
11a. Clean up: no 7 in R5C6 (Step 9)
12. 45 on N569: 2 outies R5C3 + R8C6 = 13 = [67/85/94] -->> R8C6 = {457}
12a. 20(3) in R8C6 = {479/569/578} -->> no 3 in R9C78
13. 45 on N47: 3 outies R478C4 = 21 = {489/579/678} -->> no 5 in R78C4: {579} no possible that way.
14. 5 locked in R3C13 for N1, nowhere else in N1
14a. Hidden Killer Pair {89} in R3C13 + R3C6 -->> R3C13 has to contain 8/9
14b. R3C13 = {589} -->> no 3 in R3C13
14c. 3 locked in R3C78 for N3 -->> no 3 in R2C7
15. 45 on C1234: 3 outies: R359C5 = 18 = {189/279/369/378/468/567} -->> R5C5: no 1,2 ; R9C5: no1 : {189} or {279} not possible with these placements
15a. Clean up: R9C4: no 8
16 Building on step 13: R478C4 = 22
16a. No {678} -->> clashes with 10(2) in R1C4
16b. 9 locked in R78C4 for C4 and N8
16c. No 6 in R478C4
16d. Clean up: R5C3: no 8; R6C2: no 7 (step7); R7C2: no 8
16e. Naked Pair {69} in R5C3 + R6C2 for N4
16f. Naked Pair{69} in R67C2 for C2
16g. R1C2 =7; R2C1 = 6
16h. Clean up: R1C4: no 4; R2C4: no 3; R4C2: no 1
17. Clean up on step 16
17a. R478C4 = {489/579} :R4C4 = {58} -->> R78C4 = {479}
18. 45 on N8: 3 innies R78C4 + R8C6 = 20 = {479} locked for N8 -->> no 5 in R8C6
18a. 20(3) in R8C6 = {479/578} -->> no 6 in R9C78
19. 7 locked in N3 for C9 -->> nowhere else in C9
20. 16(3) in R5C9 = {259/349/358}: {268} clashes with 30(4) : no 6
20a. 30(4) can’t have both 8 and 9 in C9: would clash with 16(3) -->> R1C8 has to contain 8 or 9 -->> R1C8 = {89}
20b. Killer Pair {89} in R123C9 + 16(3) for C9 -->> no {89} anywhere else in C9
20c. 6 locked in N3 for C9 -->> no 6 anywhere else in C9
21. Naked Quad {3689} in R1C1489 -->> not anywhere else in R1
21a. R1C5 = 5 ; R1C7 = 1; R2C8 = 5
21b. Clean up: R2C5 = {13}
21c. Naked Pair {89} in R23C6 for C6
22. Hidden single 9 in R4C7
22a. 9 locked in N9 for C8 -->> R1C8 = 8
23. 16(3) = {358} -->> locked for C9
23a. 8 locked in C9 for N6 -->> no 8 in R5C7
23b. Clean up: R5C6 = {35} (step 9)
23c. 19 (3) in R4C7 = {379} -->> R5C67 = [37]
23d. R7C9 = 5; R5C9 = 8; R6C9 =3
24. 11(3) in R4C8 = {146} -->> locked for N6
24a. 7(2) in R6C7 = [52]
24b. 6 locked in N6 for C8
24c. 2 locked in C9 for N9
24d. Hidden single 2 in R2C7
24e. Naked Pair {34} in R3C78 for R3
24f. 4 locked in N1 for C3
25. Clean up on step 18
25a. 9(2) in R9C4 = [18]/{36}
25b. Hidden single 5 in R9C6
I only tried this puzzle recently, after completing SampuZ4V1. This was a lot easier, about the level of a moderate Assassin whereas SampuZ4 was at Assassin V2 level. I can strongly recommend SampuZ5 for anyone who wants to try a puzzle with crossover puzzles. Great puzzle Ed!
I was impressed by the fact that the first two walkthroughs were both posted within about half a day of the puzzle being posted and both had a neat elimination in C9 that I never spotted.
Here is my walkthrough.
1. 13(2) cage in N1 = {49/58/67}, no 1,2,3
2. R12C4 = {19/28/37/46}, no 5
3. 5(2) cage in N2 = {14/23}
4. 6(2) cage in N3 = {15/24}
5. R3C67 = {39/48/57}, no 1,2,6
6. 7(2) cage in N4 = {16/25/34}, no 7,8,9
7. 14(2) cage in N45 = {59/68}
8. R4C56 = {18/27/36/45}, no 9
9. R67C2 = {69/78}
10. R6C78 = {16/25/34}, no 7,8,9
11. R9C45 = {18/27/36/45}, no 9
12. 7(3) cage in N1 = {124}, locked for N1, clean-up: no 9 in 13(2) cage
13. 19(3) cage in N56 = {289/379/469/478/568}, no 1
14. 11(3) cage in N6 = {128/137/146/236/245}, no 9
15. 20(3) cage in N89 = {389/479/569/578}, no 1,2
16. 30(4) cage in N3 = {6789}, locked for N3, clean-up: no 3,4,5 in R3C6
17. 19(5) cage in N9 = 1{2349/2358/2367/2457/3456}, 1 locked for N9
18. 45 rule on N1 2 outies R3C45 = 8 = {17/26/35}, no 4,8,9
18a. Remaining part of 33(6) cage in N1 = 25(4) = {3589/3679} = 39{58/67} -> no 3 in R3C45, clean-up: no 5 in R3C45
18b. Remaining part of 33(6) cage in N1 {3589} (cannot be {3679} which clashes with R3C45), locked for N1 -> 13(2) cage = {67}
19. Killer pair 1/2 in 5(2) cage and R3C45 for N2, clean-up: no 8,9 in R12C4
20. Killer pair 3/4 in R12C4 and 5(2) cage for N2
21. Killer pair 6/7 in R12C4 and R3C45 for N2, clean-up: no 5 in R3C7
22. 5 in N2 locked in 19(4) cage -> no 5 in R2C7 + R3C8
22a. 19(4) cage = 5{149/239/248}
23. Killer quad 1/2/3/4 in R3C2, R3C45, R3C7 and R3C8 -> no 3 in R3C12
23a. Naked triple {589} in R3C136, locked for R3
23b. 5 in R3 locked in R3C13, locked for N1
24. 6(2) cage in N3 = {15} (only remaining 5s in N3), locked for N3
24a. 2 in N3 locked in 19(4) cage = 25{39/48}
25. 45 rule on N6 2 outies R5C6 + R7C9 = 8 = {26/35/44} (double possible), no 7,8,9
26. 45 rule on N4 2 innies R5C3 + R6C2 = 15 -> R5C3 = {689}, R6C2 = {679}, clean-up: no 9 in R4C4, no 7 in R7C3
28. 45 rule on N8 3 innies R78C4 + R8C6 = 20 = {479/569/578} (cannot be {389} because no 3,8,9 in R8C6), no 1,2,3
28a. No {45} in R9C45 (clashes with R78C4 + R8C6)
29. 20(3) cage in N89 = {479/569/578} (cannot be 3,8,9 because no 3,8,9 in R8C6), no 3
30. 45 rule on N9 2 innies R7C79 – 6 = 1 outie R8C6, min R8C6 = 4 -> min R7C79 = 10, no 2,3 in R7C7
31. 45 rule on N6 2 innies R45C7 – 11 = 1 outie R7C9, min R7C9 = 2 -> min R45C7 = 13, no 2,3
[Alternatively this comes from combinations for 19(3) cage in N56]
32. 45 rule on C123 5 outies R3C45 + R478C4 = 29, R3C34 = 8 (step 18) -> R478C4 = 21 = {489/579} (cannot be {678} which clashes with R12C4) = 9{48/57}, no 6, 9 locked in R78C4 for C4 and N8, clean-up: no 8 in R5C3, no 7 in R6C2, no 8 in R7C2, no 5 in R8C6 (step 27)
32a. R4C4 = {58} -> no 5,8 in R78C4
33. Naked triple {479} in R78C4 + R8C6, locked for N8, clean-up: no 2 in R9C45
34. Killer pair 4,7 in R12C4 and R78C4 for C4, clean-up: no 1 in R3C5
35. 20(3) cage in N89 (step 29) = {479/578} (cannot be {569} because no 5,6,9 in R8C6) = 7{49/58}, no 6
36. Naked pair {69} in 15(2) cage in N4, locked for N4, clean-up: no 1 in 7(2) cage
37. Naked pair {69} in R67C2, locked for C2 -> R1C2 = 7, R2C1 = 6, clean-up: no 4 in R1C4, no 3 in R2C4
37a. 7 in N3 locked in R23C9, locked for C9
38. 45 rule on R789 3 innies R7C279 = 19 = [685/694/946/964/973/982], no 5 in R7C7
38a. If R7C2 = 9, R8C6 = 4 (step 27) => R9C78 = {79} -> R7C279 cannot be [973]
-> no 7 in R7C7, no 3 in R7C9; clean-up: no 5 in R5C6 (step 25)
38b. 19(5) cage (step 17) = 13{258/267/456} (cannot be {12349} which would make R9C78 = {58} (step 35) and then there is no 7 in N9), no 9
39. 45 rule on C1234 3 outies R359C5 = 18 = {369/378/468/567} (cannot be {189} because no 1,8,9 in R3C5, cannot be {279} because no 2,7,9 in R9C5, cannot be {459} because 4,5,9 only in R5C5), no 1,2, clean-up: no 6 in R3C4, no 8 in R9C4
39a. 4,5,9 only in R5C5 -> no 6 in R5C5
39b. 5 only in R5C5 and {378} must have 7 in R3C5 -> no 7 in R5C5
40. 5,8 in C4 locked in R456C4, locked for N5, clean-up: no 1,4 in R4C56
41. 15(3) cage in N5 = {159/348/456} (cannot be {168} because no 1,6,8 in R5C5, cannot be {249} because 4,9 only in R5C5, cannot be {258} which clashes with R4C4), no 2
41a. No 4 in R56C4 -> no 3 in R5C5
42. R3C4 = 2 (hidden single in C4) -> R3C5 = 6 (step 18), R3C9 = 7, clean-up: no 3 in 5(2) cage in N2, no 3 in R4C6, no 3 in R9C4
43. R2C7 = 2 (hidden single in N3), clean-up: no 5 in R6C8
44. R1C3 = 2 (hidden single in N1)
45. R1C6 = 4 (hidden single in R1), R2C5 = 1 (these are, of course, a naked pair but I was looking for hidden singles and R1C6 was one), R2C4 = 7, R1C4 = 3, R2C3 = 4, R3C2 = 1, R2C8 = 5, R1C7 = 1, R8C6 = 7, clean-up: no 2 in R4C5, no 6 in R6C8, R7C2 = 6 (step 27), R6C2 = 9, R5C3 = 6, R4C4 = 8, no 2 in R5C6 (step 25) -> R5C6 = 3 -> R7C9 = 5 (step 25), R4C5 = 7, R4C6 = 2 (cage sum), R6C5 = 4, R5C5 = 9, clean-up: no 4 in R4C2, no 5 in R5C1, no 3 in R6C78
45a. R8C6 = 7 -> R9C78 = 13 = {49}, locked for R7 and N9-> R7C7 = 8, R7C6 = 1, R6C6 = 6, R6C78 = [52], R56C4 = [51], R9C45 = [63], R7C5 = 2
45b. R7C9 = 5 -> R56C9 = 11 = [83], R2C9 = 9, R1C9 = 6, R1C8 = 8, R1C1 = 9, R2C6 = 8, R1C5 = 5, R2C2 = 3, R3C6 = 9, R3C78 = [34], R9C8 = 9, R9C7 = 4, R5C7 = 7, R5C8 = 1, R4C89 = [64], R4C7 = 9, R8C7 = 6, R4C2 = 5, R5C1 = 2 (cage sum), R5C2 = 4, R8C5 = 8, R89C2 = [28], R89C9 = [12], R8C8 = 3, R7C8 = 7, R9C6 = 5
1794
4868
1542:7687:7687
2563
7687:8448
3095:4868:7687:5915
5915
2335
4897
2850
4897:4897
5915
1843:4140
3886:4664:4664:4154:4154:4657:4925:4140
2379:4154:5188:5188:4925:
