SampuZ4 V2 was solved as a tag solution with an excellent condensed walkthrough from Ed. Having gone through both the tag solution and the condensed walkthrough, after completing the original puzzle, I felt that there were actually three "money" moves in the condensed walkthrough. Step 22a, which I don’t remember being in the tag solution, was a really powerful typical Ed move. Nice one!sudokuEd wrote: Tried very hard to make a V2 for Special Killer X 4: couldn't find one hard enough.
So instead, here's a really nice hard Killer - another one inspired by the Killer Samurai from Flower-sudoku with lots of diagonal cages. Found it a terrible struggle to solve - but suspect I missed something.
So, as insurance, have included a V2 that slams shut a couple of front doors.
The original puzzle did have "a couple of front doors" but was still a very hard puzzle needing a lot of the moves that were used for V2. If you want a slightly easier puzzle with crossover cages, I recommend SampuZ5 which is another excellent puzzle from Ed; it is in its own thread on this forum.
No walkthrough was ever posted for the original SampuZ4 puzzle so here’s my one. I must thank Ed for his encouragement when I was stuck, feedback on my partial walkthrough and a few corrections. Without him I would never have finished his excellent puzzle. Very many thanks Ed!
I wonder if I found any moves that Ed suspected he had missed?
Steps 1 to 12 set up Ed’s “cell population” diagram and provide some extra eliminations.
1. R3C34 = {12}, locked for R3
2. 7(2) cage in N8 = {16/25/34}, no 7,8,9
3. 8(2) cage in N2 = {17/26/35}, no 4,8,9
4. 9(2) cages in N3, N4 and N5 = {18/27/36/45}, no 9
4a. Clean-up: no 7,8 in R2C7
5. 10(2) cage in N69 = {19/28/37/46}, no 5
6. 11(2) cage in N56 = {29/38/47/56}, no 1
7. 12(2) cage in N1 = {39/48/57}, no 1,2,6
8. 13(2) cage in N2 = {49/58/67}, no 1,2,3
9. 15(2) cage in N6 = {69/78}
10. 8(3) cage in N4 = 1{25/34} [2/3, 4/5], 1 locked for N4, clean-up: no 8 in R6C23
10a. No 4,5 in R6C23 (these clash with the 8(3) cage)
10b. Killer pair 2,3 in 8(3) and 9(2) cages for N4
11. 10(3) cage in N9 = {127/136/145/235}, no 8,9
12. 21(3) cage in N47 = {489/579/678}, no 1,2,3
13. 45 rule on R123 1 outie R4C9 = 4, clean-up: no 5 in R4C45, no 7 in 11(2) cage in N56, no 6 in R7C8
13a. 8(3) cage in N4 = 1{25/34} (step 10), 4 only in R5C2 -> no 3 in R5C2
14. 45 rule on N12 1 outie R3C7 = 4 -> R3C56 = 14 = {59/68}, clean-up: no 5 in 9(2) cage in N3
15. 45 rule on N6 2 remaining innies R5C7 + R6C8 = 7 = [52/61], clean-up: R7C8 = {89}, R4C6 = {56} -> no 5,6 in R4C78 and R5C456 (all the cells “seen” by both R4C6 and R5C7), clean-up: no 9 in R5C9
16. 45 rule on N4 2 outies R5C4 + R7C1 = 7 = [16/25/34]
17. R7C1 = {456} -> R56C1 = {789} (from combinations in step 12)
18. 45 rule on N1 3 outies R1C5 + R23C4 = 10 = {127/136/145/235}, no 8,9
19. R3C56 contains 8/9, only other 8,9 in N2 is in R12C6 -> no 6,7 in R12C6
19a. R3C56 = {68} (cannot be {59} which clashes with R12C6), locked for R3 and N2
19b. R12C6 = {49}, locked for C6 and N2
19c. Clean-up: no 2 in 8(2) cage in N2, no 1,3 in R2C7, no 3 in R9C5
19d. R1C5 + R23C4 (step 18) = 2{17/35}
20. 3 in N6 locked in 19(4) cage, valid combinations are 3{169/178/259} (cannot be {2368} which clashes with the 15(2) cage)
21. 17(3) cage in N3 and 19(4) cage in N36 must each contain 8 or 9 (neither can contain both)
21a. Only valid combinations for the 19(4) cage are 4{159/258} (cannot be {1468} because no 1,4,6,8 in R3C9) = 45{19/28}, [1/2], no 3,6,7, 5 locked for N3
21b. Only valid combinations for the 17(3) cage are {179/278/368}(cannot be {269} which clashes with R2C7)
22. 45 rule on N1 3 innies R2C3 + R3C23 = 15, R3C3 = {12} -> R2C3 + R3C2 = 13 or 14, no 1,2,3
22a. Only valid combinations with R3C2 = {579} and R3C3 = {12} are {159/249/258/267}
22b. 6 only in R2C3 -> no 7 in R2C3
23. 45 rule on N7 4 innies R7C13 + R9C23 = 15, min. R7C1 = 4 -> max. R7C3 + R9C23 = 11, no 9 -> 9 locked in 30(5) cage
[This is the alternative to Para’s neat move]
23a. Valid combinations for 30(5) cage are 9{1578/2478/2568/3468/3567}Para wrote: "Ok was just looking over this puzzle quickly and found an interesting elimination. Just as a headstart for everyone.
Check out how the 9 is locked in N7 for 30(5) and R7C1. So no 9's anywhere else in N7.
Explanation 30(5) = 9{....}/{87654}(either a 9 in 30(5) or {87654} in 30(5) and {87654} -->> R7C1 = 9
No clue how useful it is, but it just struck me as an interesting move.
24. 45 rule on N5 2 innies R4C6 + R5C4 – 5 = 1 outie R7C3, max R4C6 + R5C4 = 9 -> max R7C3 = 4
25. 45 rule on N7 2 innies R7C13 – 1 = 1 outie R8C4, min R7C13 = 5 -> min R8C4 = 4
26. 45 rule on N9 2 outies R78C6 = 1 innie R7C8, R78C6 = 8 or 9
27. 45 rule on N8 3 innies R8C4 + R78C6 = 15, R78C6 = 8 or 9 (step 26) -> R8C4 = {67}
[Alternatively 45 rule on N89 2 innies R7C8 + R8C4 = 15 -> R8C4 = {67}]
27a. Valid combinations for 14(3) cage in N78 with R8C4 = {67} are {167/257/347/356} [1/2/3], no 8
27b. 8 locked in 30(5) cage, valid combinations 89{157/247/256/346} [1/2/3]
27c. 30(5) contains [1/2/3], R9C23 contains [1/2/3] -> R7C3 = {123}
27d. 15(3) cage in N57 = {159/168/249/258/267/348/357}, R7C3 = {123} -> no 1,2,3 in R6C45
28. Valid combinations for 14(3) cage in N45 are {149/158/248/257/347/356} (cannot be {167} which would clash with R6C23, cannot be {239} because 2,3 only in R5C4)
28a. 4 only in R5C3 -> no 9 in R5C3
29. R3C4 = {12}, 8(2) cage in N2 must contain 1/3 and 5/7 -> 22(4) cage must contain 1/2/3 and 5/7 in N2, valid combinations {1579/2479/2578} (cannot be {2569/3478} because R1C5 + R23C4 must total 10 (step 18), cannot be {3568} because 6,8 only in R2C3) = 7{159/249/258}, no 3,6
29a. {1579} can only have 1,7 in R1C5 + R2C4 (1,5 in R1C5 + R2C4 clashes with the 8(2) cage)
29b. {2578} can only have 2,7 in R1C5 + R2C4 (2,5 in R1C5 + R2C4 -> R3C4 = 1 clashes with the 8(2) cage)
[Alternatively steps 29a and 29b are clashes with step 18 for the invalid cases.]
29c. From steps 29a and 29b no 5 in R1C5 + R2C4 -> 8(2) cage in N2 = {35} (hidden pair)
29d. From steps 29a and 29b no 7 in R3C2
29e. Naked pair {59} in R3C29, locked for R3
[I originally had “29. ...-> 22(4) cage must contain 5/7 in N2, valid combinations {1579/2479/2569/2578/3478/3568}” and Ed commented “Hint: Not all of these combinations are valid”. He added in a later message that it was deliberately phrased that way after I’d assumed he meant one combination was invalid. After looking in more detail, I managed to eliminate 3 of the 6 listed combinations; the 3 explained in step 29.]
30. 6 in N1 locked in 18(4) cage
30a. R3C3 = {12} -> 18(4) cage in N1 must contain 1/2, combinations with R3C1 = {37} are 6{138/147/237}, no 5,9
31. 4 in R6 locked in R6C45, locked for N5
31a. 15(3) cage in N57 = 4{29/38} -> R7C3 = {23}, R6C45 = {489}
32. 5 in N5 locked in R46C6, locked for C6, clean-up: no 2 in R9C5
33. R5C4 = {123}, R4C45 contains [1/2/3] -> 16(3) cage in N5 must contain [1/2/3], valid combinations {169/178/259/358/367} (cannot be {268} which clashes with R4C45)
33a. 5,6 only in R6C6 -> no 2,3 in R6C6
34. 9 in N8 locked in 23(4) cage, valid combinations 9{158/248/257/347/356} (cannot be {1679} which clashes with R8C4) [1/2/3], R9C56 contains [1/2/3] -> R78C6 must contain [1/2/3]
35. 16(3) in N5 contains [1/2/3] (step 33), 7(2) cage in N8 contains [1/2/3] and R78C6 must contain [1/2/3] (step 34) -> the [1/2/3] in the 16(3) cage must be in C6 -> no 1,2,3 in R5C5, the [1/2/3] in 7(2) cage must be in C6 -> R9C6 = {123}, R9C5 = {456}
36. 45 rule on C6789 3 outies R359C5 = 19 = [685/694/874], no 6 in R9C5, clean-up: no 1 in R9C6
37. 30(5) cage in N7 = 89{157/247/256/346} (step 27b) -> R7C13 + R9C23 = {1257/1347/1356/2346}
37a. R7C1 = {456}, R7C3 = {23} and R9C23 = 7 or 8 (because R8C4 = {67}) -> R9C23 = {16/17/26/34} (cannot be {35} because {1356} has 1 in R9C23), no 5
37b. 14(3) cage in N78 (step 27a) = {167/347}, no 2 -> R9C23 = {16/17/34}
[At this stage Ed suggested Hint "look at the combo's in the 18(4)n1 and 21(3)n4" after I’d showed him my changes to step 29. I’m sure I would have found this but the hint focussed my thoughts.]
38. 18(4) cage in N1 (step 30a) = 6{138/147/237}
38a. R123C1 must contain 6, 7 and/or 8 -> R567C1 cannot be {678} -> no 6 in R7C1, no 1 in R5C4 (step 16)
38b. R567C1 = {489/579} = 9{48/57}, 9 locked for C1 and N4
38c. For the {1467} combination, R3C1 = 7 -> R567C1 = {489} -> R1C2 = 4 -> no 4 in R12C1
39. 9 in R4 locked in R4C78, locked for N6
39a. 19(4) cage (step 20) = 3{169/178/259}, 9 only in R4C7 -> no 2 in R4C7
40. 4 in C1 locked in R789C1, locked for N7
41. R7C13 + R9C23 (step 37) = {1257/1347/1356} (cannot be {2346} because R7C13 = [42] clashes with step 25) = 1{257/347/356}, 1 locked in R9C23 for R9 and N7
41a. 14(3) cage in N78 (step 37b) = {167}, no 3, no 6,7 in R8C123 and R9C4
41b. 30(5) cage (step 37) = 89{247/256/346}
42. 14(3) cage in N45 (step 28) = {248/257/347/356}
42a. 45 rule on N4 4 innies R45C3 + R56C1 = 28 = {4789/5689}, R56C1 = {79/89} (step 38b) -> R45C3 = {47/48/56} -> 14(3) cage = {248/347/356}
42b. 4 only in R5C3 -> no 7,8 in R5C3
[I said to Ed "Looks like I'm now at the next hurdle." He replied "Couple more yet. Very Vague Hint: Richard took the next hurdle" (in the V2 tag solution)]
43. 5 in R6 locked in R6C679
43a. If R6C6 = 5 => R4C6 = 6 => R5C7 = 5 => no 5 in R5C8
43b. If R6C79 = 5 => no 5 in R5C8
43c. No 5 in R5C8
[Step 44 is fairly heavy innie/outie and combination work with a summary after sub-step 44e. If you want to skip this, go to the comment after step 47 and then look at step 47.]
44. 45 rule on R6789 3 innies R6C679 – 6 = 1 outie R5C1 -> R6C679 = 13, 14 or 15 = 5{17/18/27/28/36} (cannot be 5{26/37} which clash with R6C23)
Examining each of these combinations separately, noting that 19(4) cage in N6 (step 39a) = 3{169/178/259}
44a. {157} can only have 5 in R6C6 (1,7 in R6C6 don’t give valid combinations for 19(4) cage) => R6C79 = {17}, R67C8 = [28], R4C7 = 8, R5C8 = 3
44b. {158} can only have 5 in R6C6 (1,8 in R6C6 don’t give valid combinations for 19(4) cage) => R6C79 = {18}, R67C8 = [28], R4C7 = {37}, R5C8 = {37}
44c. {257} can only have 7 in R6C6 (5 in R6C6 doesn’t give valid combination for 19(4) cage) => R6C79 = {25}, R67C8 = [19], R4C7 = 9, R5C8 = 3
44d. {258} can only have 8 in R6C6 (5 in R6C6 doesn’t give valid combination for 19(4) cage) => R6C79 = {25}, R67C8 = [19], R4C7 = 9, R5C8 = 3
44e. {356} can have 5 or 6 in R6C6
44ea. If 5 in R6C6 => R6C79 = {36}, R4C7 = 9, R5C8 = 1
44eb. If 6 in R6C6 => R6C79 = {35}, R4C7 = 9, R5C8 = 2
Summary of sub-steps 44a to 44e, R6C6 = {5678}, R4C7 = {3789}, R5C8 = {1237}, R6C79 unchanged
44f. 1 in R6 locked in R6C789, locked for N6 -> no 1 in R5C8 -> R6C79 cannot be {36} (step 44ea) -> no 6 in R6C79 -> 6 in N6 locked in R5C79, locked for R5
44g. 19(4) cage in N6 = 3{178/259}
45. 14(3) cage in N45 (step 42a) = {248/347/356}
45a. 6 only in R4C3 -> no 5 in R4C3
46. 16(3) cage in N5 (step 33) = {169/178/259/358/367}
46a. 1,2,3 only in R5C6 -> no 7,8 in R5C6
[Alternatively R4C45 contains 1/2/3, R5C4 = {23} -> R5C6 = {123}]
47. 16(3) cage in N5 (step 33) = {169/178/259/358/367}
47a. {259} => R4C6 = 6 => R4C45 = {18} clashes with R6C45
47b. {358} => R4C6 = 6 => R4C45 = {27} clashes with R5C4
Summary 16(3) cage = {169/178/367}, no 2,5
[Ed said “This is the key move.” He added that “big step 44” isn’t really necessary. I’ve checked that and he’s correct. Step 47 can be done directly after step 43. In that case there will be detail changes to the remaining steps to remove the candidates eliminated in steps 44, 45 and 46.
Maybe I sometimes suffer from "Assassin 42V2 Syndrome", as in step 44, but that's better than not having learned how to do those sort of steps.]
48. R4C6 = 5 (hidden single in N5) -> R5C7 = 6, R2C7 = 2, R3C8 = 7, R3C1 = 3, clean-up: no 9 in 12(2) in N1, no 9 in R4C8 -> R4C8 = 8, R5C9 = 7, R7C8 = 9, R6C8 = 1, R2C8 = 5, R3C9 = 9, R1C7 = 1 (cage sum), R3C2 = 5, R2C5 = 3, R1C4 = 5, clean-up: no 7 in 12(2) cage in N1, no 1 in R4C45, no 6 in R4C4
48a. Naked pair {48} in 12(2) cage in N1, locked for N1 -> R2C3 = 9, R12C6 = [94], R2C2 = 8, R1C3 = 4, R5C3 = 5
49. R4C7 = 9 (hidden single in N6)
50. Naked pair {23} in R5C48, locked for R5 -> R5C6 = 1, R5C2 = 4
50a. R5C7 + R6C8 = 15 = [87/96], no 8 in R6C8
50b. R5C2 = 4 -> R4C12 = 4 = [13], clean-up: no 6 in R4C5, no 6 in R6C23
50c. Naked pair {27} in R4C45, locked for R4 and N5 -> R4C3 = 6, R5C4 = 3, R5C8 = 2
50d. Naked pair {27} in R6C23, locked for R6 -> R6C6 = 6, R5C5 = 9 (cage sum), R56C1 = [89], R7C1 = 4 (cage sum), R3C56 = [68]
50e. R6C45 = {48} -> R7C3 = 3 (cage sum)
51. 2,3,7 in C6 locked in R789C6, locked for N8-> R8C4 = 6
52. R78C6 = R7C8 (step 26) = 9 = {27} (only remaining combination) -> R9C56 = [43], R9C8 = 6, R1C8 = 3, R8C8 = 4
52a. R9C8 = 6 -> R78C9 = 4 = [13], R6C79 = [35], R9C9 = 2 (hidden single in C9), R8C6 = 7, R9C7 = 8 (cage sum), R7C6 = 2, R78C7 = [75], R8C1 = 2, R8C23 = [98], R8C5 = 1, R7C45 = [85], R6C45 = [48], R9C4 = 9
and the rest is naked and hidden singles
Thanks again Ed. You were a great help for reviewing my partial walkthroughs and providing good cryptic hints. All the moves are my own so any errors in them are mine.
