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Hello All,

First things first...Congratulations to Afmob on his hard-earned diploma!
I'm thrilled for you, and so glad to have you back to make another puzzle for us!!



OK, Ed. For me, I always need a spark to help me think up a new puzzle idea, and
it's usually something visual. For A193, it was one of Ruud's old "X-File" puzzles,
published on 4/18/07. For those who might not know, Ruud's X-File series were
vanilla sudokus, with the addition of a diagonal constraint. I was intrigued by the
way so many of the "givens" hugged the / diagonal. It became the starting point
for this Assassin's design. Here's Ruud's puzzle, in case you would like to try it:





So now, for

Assassin 193X
Many Thanks to Børge for the great pics










SS Score: 1.21

I have no V2 planned, so take a stab if you wish.

Enjoy!

Ronnie

Thanks for the new Killer, Ronnie! It offered some nice moves.

Edit: I deleted a wrong step. Cheers for telling me, Ed!

A193 Walkthrough:

1. N28
a) 17(2) = {89} locked for C5+N8
b) 5(2) = {23} locked for C5+N2 since {14} blocked by 7(3)
c) 7(3) = {124} -> R5C4 = 2; CPE: R1C5+R456C6 <> 1,4
d) Outies N2 = 9(2+1) -> R1C7 <> 7,8,9 and R4C4 <> 8,9

2. N79
a) 22(3) = 9{58/67} -> 9 locked for N9
b) Innies C123 = 8(2) <> 4,8,9
c) Hidden Single: R9C7 = 9 @ R9

3. C789 !
a) Innies+Outies N69: -3 = R3C9 - R4C7: R3C9 <> 6; R4C7 <> 1,2,3
b) Outies C89 = 9(2): R2C7 <> 6,7,8; R4C7 <> 4
c) Innies C89 = 19(3) <> 1
d) Innies+Outies N69: -3 = R3C9 - R4C7: R3C9 <> 1
e) ! 1 locked in R123C7 @ N3 for C7 -> Either Outies C89 = 9(2) or Innies C789 = 9(2) must be {18}
-> 8 locked in R34C7 for C7; CPE: R4C6 <> 8, R2C9+R3C8 <> 8
f) Outies N69 = 15(3) = {249/267/357/456}
g) 11(2) <> {47} since it's a Killer pair of Outies N69
h) Innies+Outies C89: -9 = R2C7 - (R2C9+R3C8) -> R2C9+R3C8 <> 9 (IOU @ N3)
i) ! 11(2) <> {56} since it's blocked by Killer pair (56) in Outies N69

4. N23 !
a) ! Killer pair (89) locked in 11(2) + Innies C89 for N3
b) Innies C789 = 9(2) <> 1
c) Hidden Single: R2C7 = 1 @ N3 -> R1C8 = 9
d) 11(2) = {38} locked for N3+D/
e) Hidden Single: R4C7 = 8 @ C7
f) 18(3) = {468} -> 4,6 locked for N3
g) Innies C789 = 9(2) = {27} -> R1C7 = 2, R3C7 = 7
h) R3C9 = 5
i) 12(4) = {1245} -> 1,2,4 locked for N6; 2 also locked for R4
j) 8 locked in 25(4) @ C4 for N2

5. N7
a) 9(2) @ D/ = {45} locked for N7+D/
b) 25(5) = {12679} -> R7C3 = 2; 1,6,9 locked for N5
c) R4C5 = 4, R3C6 = 1
d) Innie N7 = R9C3 = 6
e) 9(2) @ R8C3 = {18} locked for N7

6. N25
a) 19(4) = {2467} -> 4,6,7 locked for N2; 4 also locked for C6
b) 25(4) = {3589} -> R4C4 = 3
c) 18(3) = 6{48/57} -> R7C4 = 6
d) 18(3) = {567} -> 5,7 locked for N5
e) R6C6 = 8

7. N79
a) 20(3) = {479} -> R7C3 = 4; 7,9 locked for N7
b) 12(4) = {1245} -> R5C8 = 4; 1 locked for R4
c) Innies N9 = 11(3) = {146} since R78C7 <> 1,2 -> R7C7 = 4, R7C8 = 1, R8C7 = 6

8. Rest is singles without considering diagonals.

I would like to add my congratulations to Afmob for finishing your diploma!

This Assassin wasn't an easy peasy puzzle for me. I just could not find Afmob's step 3c, 3f or 3h. I knew they must have been there somewhere but was totally blinded. Had to put the creative hat on instead.

This walk-through is a two-for-one deal. An alternative (and much harder, though shorter) route from step 9 is also given. It's Over The Top (OTT) but I really enjoyed it. Couldn't make a V2 out of that move because it is in the same spot as the other doors.

A wonderful Assassin. Really enjoyed your reminder of Ruud's X files too Ronnie. Used to enjoy those. The pic of Ruud's SudoCue shows what a master he was at presenting software. Very easy to look at.

Start to A193Cheers
Ed

Thanks Ronnie for another challenging Assassin. You seem to have a knack of creating puzzles which I find hard but this time it was my fault. Having come back to it this week and now finished it I've discovered from looking at the posted WTs that I missed R9C7 = 9 (hidden single in R9) (or maybe that should be ?) so that made it a much harder puzzle for me.

Afmob has posted a nice direct walkthrough with some neat steps in C789. Ed also had some neat steps in that area; as for his alternative OTT ending I can only say WOW!

The key area for both Afmob and Ed, using that early placement in R9C7, was C789. For me, without that placement, the key steps were in C46 and the relationships between R3C67 and R4C45, making it a very different puzzle.


Here is my walkthrough for A193X. It's much harder than Afmob's and Ed's posted ones but I think there are some interesting steps. I've also commented after step 14 on something I looked at but was unable to find a way to use it.

Prelims

a) 10(2) cage at R1C8 = {19/28/37/46}, no, 5
b) 11(2) cage at R1C9 = {29/38/47/56}, no 1
c) R23C5 = {14/23}
d) R78C5 = {89}
e) 9(2) cage at R8C2 = {18/27/36/45}, no 9
f) 9(2) cage at R8C3 = {18/27/36/45}, no 9
g) 7(3) cage at R3C6 = {124}
h) 22(3) cage at R7C9 = {589/679}
i) 20(3) cage at R6C3 = {389/479/569/578}, no 1,2
j) 12(4) cage at R3C9 = {1236/1245}, no 7,8,9

Steps resulting from Prelims
1a. Naked pair {89} in R78C5, locked for C5 and N8
1b. Naked triple {124} in 7(3) cage at R3C6, CPE no 1,2,4 in R456C6
1c. 22(3) cage at R7C9 = {589/679}, 9 locked for N9
1d. 12(4) cage at R3C9 = {1236/1245}, CPE no 1,2 in R56C9

2. R23C5 = {23} (cannot be {14} which clashes with 7(3) cage at R3C6, ALS block), locked for C5 and N2
[I accidentally overwrote this walkthrough file so had to start again. I’ve moved this step up slightly; I originally did a few routine 45s before I spotted it.]

3. 7(3) cage at R3C6 = {124}, naked pair {14} in R3C6 + R4C5 -> R5C4 = 2, CPE no 1,4 in R1C5

4. 45 rule on C123 2 innies R79C3 = 8 = {17/26/35}, no 4,8,9
[At this stage I missed R9C7 = 9 (hidden single in R9), which would have made this puzzle a lot easier.]

5. 45 rule on C789 2 innies R13C7 = 9 = {18/27/36/45}, no 9

6. 45 rule on N14 1 innie R6C3 = 1 outie R7C1 + 1, no 1,9 in R7C1
6a. 9 in N7 only in R7C2 + R8C1, locked for 20(3) cage at R6C3, no 9 in R6C3, clean-up: no 8 in R7C1
6b. 45 rule on N14 3 outies R7C12 + R8C1 = 19 = {289/379/469}, no 5, clean-up: no 6 in R6C3

7. 45 rule on N69 1 innie R4C7 = 1 outie R3C9 + 3, no 1,2,3 in R4C7

8. 45 rule on N2 2(1+1) outies R1C7 + R4C4 = 1 innie R3C6 + 4
8a. Max R3C6 = 4 -> max R1C7 + R4C4 = 8, no 8,9, clean-up: no 1 in R3C7 (step 5)

9. 45 rule on N2369 2 outies R4C45 = 1 innie R3C7
9a. Min R4C45 = 4 -> min R3C7 = 4, clean-up: no 6,7 in R1C7 (step 5)

10. 45 rule on N2369 2 innies R3C67 = 1 outie R4C4 + 5
10a. R3C67 cannot be [14] because min R3C67 = 6 and cannot be [44] -> no 4 in R3C7, clean-up: no 5 in R1C7 (step 5)

11. 25(4) cage at R1C4 = {1789/3589/3679/4579/4678}
11a. 1 of {1789} must be in R123C4 (R123C4 cannot be {789} which clashes with 19(4) cage at R1C5 which must contain at least one of 7,8,9), no 1 in R4C4

12. 18(3) cage at R5C6 = {369/378/459/468/567} (cannot be {189} because 8,9 only in R5C6), no 1
12a. 8,9 of {369/378} must be in R5C6 -> no 3 in R5C6

13. 45 rule on N1478 2 innies R7C34 = 1 outie R6C6
13a. Min R7C34 = 4 -> no 3 in R6C6
13b. Max R7C34 = 9 -> no 7 in R7C3, clean-up: no 1 in R9C3 (step 4)

14. 45 rule on N69 4 innies R4C789 + R5C8 = 15 = {1239/1248/1257/1356/2346} (cannot be {1347} which clashes with combinations for 12(4) cage at R3C9)
14a. 6 of {1356/2346} must be in R4C89 + R5C7 (R4C89 + R5C7 cannot be {135/234} which clash with combinations for 12(4) cage at R3C9) -> no 6 in R4C7, clean-up: no 3 in R3C9 (step 7)

[At this stage I looked at
12(4) cage + 23(4) cage cannot form an 8-cell combined cage with all numbers different because the minimum total for a normal 8-cell cage is 36
R3C9 “sees” all of the 23(4) cage except from R67C8 and R7C8 “sees” all of the 12(4) cage except for R34C9. This means that at least one of R34C9 must be the same as one of R67C8 but R4C9 cannot be the same as R6C8.
However I couldn’t see how I could use this.]

15. 25(4) cage at R1C4 (step 11) = {1789/3589/3679/4579/4678}
15a. 7 of {1789} must be in R4C4, 3 of {3589/3679} must be in R4C4, 4 of {4579/4678} must be in R4C4 (4 cannot be in R123C4 because R3C6 + R4C5 = [14] and R4C45 cannot be more than 8, step 9, because max R3C7 = 8) -> R4C4 = {347}, no 4 in R123C4
15b. 4 in N2 only in R123C6, locked for C6

16. R4C45 = R3C7 (step 9)
16a. R4C45 = [34/41/71] (cannot be [31/74] because min/max R3C7 = 5,8) = 5,7,8 -> R3C7 = {578}, no 6, clean-up: no 3 in R1C7 (step 5)

17. 2 in N8 only in R789C6 -> 18(4) cage at R6C6 = {1269/1278/2358/2367}
17a. 8 of {2358} must be in R6C6 -> no 5 in R6C6

18. 1 in N8 must be in 18(4) cage at R6C6 or 18(4) cage at R8C4
18a. 18(4) cage at R8C4 = {1467/2457/3456} (cannot be {2367} which clashes with 18(4) cage at R6C6 which must be {1269/1278} when 18(4) cage at R8C4 doesn’t contain 1), 4 locked for N8

19. 45 rule on C4 4 innies R6789C4 = 18 = {1458/1467/3456} (cannot be {1359/1368} which clash with 18(4) cage at R6C6), no 9, 4 locked for C4
19a. 9 in C4 only in R123C4, locked for N2
19b. R4C45 (step 16a) = [34/71] = 7,8 -> R3C7 = {78}, no 5, clean-up: no 4 in R1C7 (step 5)
19c. 10(2) cage at R1C8 = {19/37/46} (cannot be {28} which clashes with R13C7), no 2,8

20. 25(4) cage at R1C4 (step 15) = {1789/3589/3679}
20a. 19(4) cage at R1C5 = {1567/2458/2467} (cannot be {1468} which clashes with 25(4) cage at R1C4)
20b. R1C7 = {12} -> no 1 in R12C6

21. Hidden killer pair 1,3 in R34C6 and R789C6 for C6, R789C6 contains one of 1,3 -> R34C6 must contain one of 1,3
21a. R3C6 = 1 => R4C45 = [34] or R4C6 = 3
21b. -> 3 locked in R4C46, locked for R4 and N5
[Maybe steps 21a and 21b are a sort of Killer ALS-xz step.]
21c. 12(4) cage at R3C9 = {1236/1245}
21d. 3 of {1236} must be in R5C8 -> no 6 in R5C8

22. 45 rule on N69 3 outies R2C9 + R3C89 = 15
22a. 18(3) cage at R2C9 = {189/279/459/468/567} (cannot be {369} because R2C9 + R3C89 = 15 cannot contain both of 3,6, cannot be {378} which clashes with R3C7), no 3

23. 3 in N3 only in 10(2) cage at R1C8 = {37} or 11(2) cage at R1C9 = {38} -> 11(2) cage at R1C9 = {29/38/56} (cannot be {47}, locking-out cages) no 4,7
23a. Killer pair 7,8 in 10(2) cage at R1C8 + 11(2) cage at R1C9 and R3C7 (locking cages), locked for N3

24. 25(5) cage at R3C7 = {12679/13678/14578/34567} (cannot be {12589/13579/23569/23578/24568} which clash with 11(2) cage at R1C9, cannot be {14569} because R3C7 only contains 7,8, cannot be {13489} which clashes with R4C5 because 9 must be in R4C6 and 3 in R7C3, cannot be {23479} because 2,3,9 only in R4C6 + R7C3), 7 locked for D/, clean-up: no 2 in 9(2) cage at R8C2
[I originally had
11(2) cage at R1C9 and 9(2) cage at R8C2 must each contain one even number -> 25(5) cage at R3C7 must contain two even numbers for D/ so cannot be {13579} which doesn’t contain any even numbers, cannot be {24568} which contains four even numbers, cannot be {23578} because cannot place 9 for D/ but after step 23 these all clash with 11(2) cage at R1C9, which is technically simpler.]
24a. 11(2) cage at R1C9 (step 23) = {29/38} (cannot be {56} which clashes with 25(5) cage at R3C7), no 5,6

25. Killer pair 2,8 in R13C7 and 11(2) cage at R1C9, locked for N3, clean-up: no 5 in R4C7 (step 7)
25a. 8 in N3 only in R1C9 + R2C8 + R3C7, locked for D/, clean-up: no 1 in 9(2) cage at R8C2
25b. 12(4) cage at R3C9 = {1236/1245}, 2 locked for R4 and N6

26. R79C3 (step 4) = {17/26} (cannot be {35} which clashes with 9(2) cage at R8C2), no 3,5
26a. R7C12 + R8C1 (step 6b) = {289/379} (cannot be {469} which clashes with 9(2) cage at R8C2), no 4,6, clean-up: no 5,7 in R6C3 (step 6)
26b. Killer pair 2,7 in R7C12 + R8C1 and R79C3, locked for N7

27. 8 in C4 only in R123C4, locked for N2
27a. 25(4) cage at R1C4 (step 20) = {1789/3589}, no 6
27b. R4C4 = {37} -> no 7 in R123C4

28. 19(4) cage at R1C5 (step 20a) = {1567/2467}
28a. 18(4) cage at R6C6 (step 17) = {1269/1278/2358} (cannot be {2367} which clashes with 19(4) cage at R1C5, ALS block)
28b. 8,9 only in R6C6 -> R6C6 = {89}

29. 1 in D/ only in 25(5) cage at R3C7 (step 24) = {12679/14578} (cannot be {13678} which clashes with R4C4 because 8 must be in R3C8), no 3
29a. 9 of {12679} must be in R4C6 -> no 6 in R4C6

30. R4C4 = 3 (hidden single in N5), placed for D\
30a. 25(4) cage at R1C4 (step 27a) = {3589} (only remaining combination), 5 locked for C4 and N2

31. R3C6 = 1 (hidden single in N2), R4C5 = 4
31a. R4C45 = [34] = 7 -> R3C7 = 7 (step 9), placed for D/, R1C7 = 2 (step 5), clean-up: no 9 in 11(2) cage at R1C9, no 3 in 10(2) cage in R1C8

32. Naked pair {38} in 11(2) cage at R1C9, locked for D/, clean-up: no 6 in 9(2) cage at R8C2
32a. Naked pair {45} in 9(2) cage at R8C2, locked for N7 and D/ -> R4C6 = 9, R4C7 = 8, R3C9 = 5 (step 7), R6C6 = 8, placed for D\, clean-up: no 7 in R7C1 (step 6)
32b. Naked pair {16} in R5C5 + R6C4, locked for N5 and D/ -> R7C3 = 2, R9C3 = 6 (step 4), R7C1= 3, R6C3 = 4 (step 6), R3C3 = 9, placed for D\, R3C4 = 8
32c. Naked pair {18} in 9(2) cage at R8C3, locked for N7

33. 18(4) cage at R6C6 (step 28a) = {2358} (only remaining combination) -> R7C6 = 5, R5C6 = 7, R6C5 = 5, R7C4 = 6, R6C4 = 1, R5C5 = 6, placed for D\, R1C5 = 7, R9C5 = 1, R9C2 = 8, R8C3 = 1

34. 22(3) cage at R7C9 = {589} (only remaining combination) -> R7C9 = 8, R78C5 = [98], R7C2 = 7, R8C1 = 9, R8C8 = 5, placed for D\, R9C7 = 9, R1C9 = 3, R2C8 = 8, R8C2 = 4, R9C1 = 5, R89C4 = [74]

35. R1C3 = 8 (hidden single in R1), R2C2 + R3C1 = 6 -> R2C2 = 2, placed for D\, R3C1 = 4, R1C1 = 1, placed for D\
35a. R1C1 = 1 -> R1C2 + R2C1 = 13 = [67]

and the rest is naked singles without using the diagonals.