Assassin 40

[Andrew]

Not sure that I consider myself an Advanced Player but I took up the challenge and it's the first time that I've finished an Assassin within a few hours of it being posted.

A nice smooth one Ruud! It just seemed to flow!

Over to you Ed for a V2. This Assassin needs one.

Here is my walkthrough.

I've had feedback that there was a flaw in this walkthrough at step 32a. Thanks Para. I've re-written the later stages and also taken the opportunity to include the steps that were only comments before. I hope it is now correct.

Clean-up is used in various steps, using the combinations in steps 1 and 6 for further eliminations from these two cell cages; it is also used for the two cell sub-cages that are produced by applying the 45 rule.

1. R6C34 = {15/24}

2. R6C67 = {79}, locked for R6

3. R67C2 = {18/27/36/45}, no 9, no 2 in R7C2

4. R67C8 = {14/23}

5. R78C3 = {89}, locked for C3 and N7, clean-up: no 1 in R6C2

6. R78C7 = {59/68}

5. 21(3) cage in N1 = {489/579/678}, no 1,2,3

6. 20(3) cage in N3 = {389/479/569/578}, no 1,2

7. 10(3) cage in N14 = {127/136/145/235}, no 8,9

8. 19(3) cage in N36 = {289/379/469/478/568}, no 1

9. 11(3) cage in N47 = {128/137/146/236/245}, no 9 [Para pointed out that R5C2 is now a hidden single 9 in N4. I only saw that at step 32!]

10. 11(3) cage in N69 = {128/137/146/236/245}, no 9

11. 14(4) cage in N56 = {1238/1247/1256/1346/2345}, no 9

12. 14(4) cage in N8 = {1238/1247/1256/1346/2345}, no 9

13. 45 rule on N1 1 outie R1C4 – 7 = 1 innies R3C1 -> R1C4 = {89}, R3C1 = {12}

14. 45 rule on R123 1 outie R4C5 – 4 = 2 innies R3C19, min R3C19 = 3 -> min R4C5 = 7, max R4C5 = 9 -> max R3C19 = 5 -> max R3C9 = 4, R3C19 = [12/13/14/23]

15. 45 rule on N3 1 innie R3C9 = 1 outie R1C6 -> R1C6 = {234}

16. 45 rule on N7 1 outie R9C4 – 3 = 2 innies R7C12, min R7C12 = 3 -> min R9C4 = 6, max R9C4 = 9 -> max R7C12 = 6, no 6,7, clean-up: no 2,3 in R6C2

17. 45 rule on N8 2 innies R9C46 – 11 = 1 outie R6C5, max R9C46 = 17 -> max R6C5 = 6, min R9C46 = 12, no 1,2

18. 45 rule on R12 2 innies R2C37 = 5 = [14/23]
18a. Killer pair 1/2 in R2C3 and R3C1 for N1
18b. 45 rule on R89 2 innies R8C37 = 14 = [86/95], clean-up: no 5,6 in R7C7
18c. Killer pair 8/9 in R7C37 for R7

19. 15(3) cage in N1 = {159/168/249/258/267} [7/8/9], no 3 in R3C23, no 4 in R3C2
19a. 21(3) cage in N1 = {489/579/678}, must contain two of 7,8,9 -> killer triple 7/8/9 in 15(3) and 21(3) cages for N1

20. 3 in N1 locked in R1C23, locked for R1 -> 16(3) cage = 3{49/58}, no 6
20a. R3C9 = {24} (step 14)
[Para pointed out that this can be used with the combinations at the end of step 14 to give R3C1 = 1 and then R1C4 = 8 from step 13. Very neat!]

21. 12(3) cage in N23 = {129/147/246}, no 5,8

22. 20(3) cage in N3 = {389/479} = 9{38/47} -> R3C78 = {789}, 9 locked for R3 and N3
22a. 15(3) cage in N1 now {168/258/267}, no 4, no 5 in R3C2

23. 5 in N3 locked in 13(3) cage = 5{17/26}, no 3,4,8

24. R2C7 = 3 (hidden single in N3), R3C78 = {89}, locked for R3

25. 15(3) cage in N1 = {267} -> R2C3 = 2, R3C23 = {67}, locked for R3 and N1, R3C1 = 1; clean-up: no 4 in R6C4
25a. R3C19 = 3 or 5 -> R4C5 = {79}
25b. Killer pair 7/9 in R4C5 + R6C8, locked for N5

26. R1C4 = 8 (step 13) -> R1C23 = {35} (step 2), locked for R1 and N1

27. Naked quad 2/3/4/5 in R1C6 + R3C456, locked for N2

28. 19(3) cage in N36 = {289/469/478} -> R4C89 = {6789}

29. R37C7 = {89}, locked for C7 -> R6C7 = 7, R6C6 = 9, R4C5 = 7, clean-up: no 2 in R4C12
[Edit. Step 29 rewritten after adding steps 18b and 18c. Steps resulting from R4C5 = 7 have been left until later since they weren’t in the original version of this walkthrough.]

30. 11(3) cage in N47 = {236/245} = 2{36/45}, no 7,8, 2 locked for C1

31. R2C1 = 8, R1C1 = 9 (hidden singles in C1) -> R2C2 = 4, clean-up: no 5 in R4C1, no 5 in R67C2

32. R5C2 = 9, R6C2 = 8 (hidden singles in C2), R7C2 = 1, clean-up: no 4 in R6C8
32a. R9C4 – 3 = R7C12 (step 16), R9C4 = {679} -> R7C1 = {235}
[Corrected from {245}, thanks Para. My only excuse for that error is that I was doing this puzzle too late at night! Steps 35 onward are new; the original step 35 no longer works.]

33. 16(3) cage in N7 = {367/457} = 7{36/45}, no 2, 7 locked for N7

34. 15(3) cage in N78 = {249/267/456} (cannot be {357} which would clash with 16(3) cage), no 3, no 6 in R9C2, no 5 in R9C3

35. R4C5 = 7 (step 29) -> R3C456 = 12 = {345}, locked for R3 and N2 -> R1C6 = 2, R3C9 = 2
35a. R1C6 = 2 -> R1C78 = 10 = {46}, locked for R1 and N3, R5C1 = 1
35b. R3C9 = 2 -> R4C89 = 17 = {89}, locked for R4 and N6

36. R9C2 = 2 (hidden single in C2), 15(3) cage in N78 (step 34) = 2{49/67} -> no 6 in R9C4

37. 2 in C1 locked in R56C1 -> R56C1 = {246}, no 3,5

38. 7 in C1 locked in R89C1 -> R3C2 = 7 (hidden single in C2), R3C3 = 6, R9C3 = 4, R9C4 = 9, clean-up: no 2 in R6C4

39. 16(3) cage in N7 (step 33) = {367}, locked for N7 -> R7C1 = 5 -> R56C1 = {24}, locked for N4, clean-up: no 5 in R4C2
39a. R6C34 = {15}, locked for R6, clean-up: no 4 in R7C8
39b. R4C12 = {36}, locked for R4 and N4
39c. R67C8 = {23}, locked for C8

40. R5C3 = 7 (hidden single in N4), R46C3 = {15}, locked for C3 -> R1C23 = [53]

41. R5C23 = [97] -> R4C34 = [54] (cage sum), R6C34 = [15], R4C67 = [12], R67C8 = [32]

42. R4C67 = [12] -> R5C78 = {56} (cage sum), locked for R5 and N6 -> R6C9 = 4, R5C9 = 1, R6C1 = 2, R5C1 = 4 (naked singles), R7C9 = 6

and the rest is naked and hidden singles, simple elimination and cage sums

[sudokuEd]

Pressure!

Here's a real hard V2 for Assassin 40 but it has a logical solve path. No chains necessary - but keep your eye out for those sneeky sub-sets

This Killer has 2 remote cages 29(6) r3c19 & r4c1289 and 22(4) r6c3467. They play havoc with your "45"'s

It also has a different final solution to the original puzzle.

I have included a census pic below the puzzle pic.

Assassin 40V2

[Nasenbaer]

Here is the code string for Assassin 40V2:

3x3::k:4864:35853585:640435893336:4864:4864:4363:6404:6404:6404:46233336:7442:4363:4363:4885:4885:4885:4623:4623:7442:7442:7442:6429:6429:4885:4128:4128:7442:74426429:642928554128:412828525679:5679:5681:5679:5679337218385681:5681:568113324671:46714162:4162:416233984671391341623661:3661

Peter

[Para]

Nice puzzle. Works very nicely. I'll check my walk-through somewhere tomorrow and post it then.

Para

[Nasenbaer]

Nice puzzle. Works very nicely.

I agree with you, Para. That was a wonderful puzzle. Thanks, Ed.

As you have solved it first I let you do the honors, Para.

Peter