Special Killer X - January 27

[Nasenbaer]

A nice puzzle, Ruud. I like Killer-X. Thanks a lot.

But the cages lying directly on the diagonals and minimal 45-checks made it too easy.

OK, here is a walkthrough

Edit: Preliminary steps included and typo corrected

Walkthrough SKX 4

0. Preliminary steps (as requested by Andrew because I'm too lazy )
0a. 11(3) at r1c1 : no 9
0b. 10(2) at r2c1, r3c8, r9c2 : no 5
0c. 14(2) at r1c2, r2c9 : no 1,2,3,4,7
0d. 11(2) at r3c2, r7c1, r6c8, r9c7 : no 1
0e. 8(2) at r2c3, r7c9 : no 4,8,9
0f. 19(3) at r9c1 : no 1
0g. 26(4) at r4c3 : no 1
0h. 13(2) at r2c6 : no 1,2,3
0i. 12(2) at r8c3 : no 1,2,6
0j. 20(3) at r7c7 : no 1,2
1. r67c2 = {12} -> 1,2 locked for c2
1a. -> no 9 in r34c2
2. r8c67 = {12} -> 1,2 locked for r8
3. r1c78 = {13} -> 1,3 locked for r1 and N3
4. 45 on N7 : r7c2 + r8c3 = 5(2) = [14|23]
5. 45 on N9 : r8c7 + r7c8 = 6(2) = [15|24]
6. 45 on N3 : r2c7 + r3c8 = 14(2) = [59]|{68}
7. 45 on N1 : r2c3 + r3c2 = 10(2) = [28|64]|{37}
8. Cleanup: r8c4 = {89}, r7c9 = {1235}, r6c8 = {67}, r4c8 = {124}, r2c6 = {578}, r2c4 = {1256}, r4c2 = {3478}
9. 5,6,8,9 locked in r2c79 and r3c89 for N3
10. N3 : 13(3) = {247} -> 2,4,7 locked for N3 and D/
11. N7 : 19(3) = {568} -> 5,6,8 locked for N7 and D/
12. 45 on D/ : r6c4 + r5c5 + r4c6 = 13(3) = {139} -> 1,3,9 locked for N5 and D/
13. 45 on D\ : r4c4 + r5c5 + r6c6 = 14(3) -> N5 : 26(5) = 139{58|67} -> r5c5 = 1, r4c4 = {5678}, r6c6 = {5678} (OK, I now know that this is the long way around, thanks Ed. Sometimes I'm a little thickheaded )
14. 2 locked in r1c1 and r3c3 for N1 and D\
15. no 8 in r23c1, no 6 in r2c4, no 8 in r3c2, no 3 inr4c2
16. N1 : 11(3) = 2{36|45}
17. (step 7) [64] not poss., conflict with 11(3) -> 3,7 locked in r2c3 and r3c2 -> 11(3) = {245} -> 2,4,5 locked for N1 and D\
18. 6,7 locked in r4c4 and r6c6 for N5 and D\
19. -> N9 : 20(3) = {389} -> 3,8,9 locked for N9 and D\
20. r1c23 = {68} -> 6,8 locked for r1 and N1
21. r23c1 = {19 -> 1,9 locked for c1 and N1
22. r78c1 = {47} -> 4,7 locked for c1 and N7
Now its only cleanup
23. r8c34 = [39], r9c23 = [91], r67c2 = [12], r2c34 = [71], r23c1 = [91], r34c2 = [38], r1c23 = [68], r8c2 = 5, r7c3 = 6, r9c1 = 8, r25c2 = [47], r28c8 = [28], r9c9 = 3, r7c7 = 9, r78c9 = [17], r8c67 = [12], r78c1 = [74], r8c5 = 6, r6c4 = 3, r4c6 = 9, r1c9 = 4, r3c7 = 7
I leave the rest to you.

Comments and/or corrections are appreciated.

Peter

[Para]

Yes, i enjoyed it.
It was a smooth puzzle. But i didn't use any 45-tests. Wasn't really any need for it. I've posted my walkthrough too in tiny text. Tell me what you think of it.
Just hope i didn't make any mistakes this time.


1. R1C78 = {13} 1,3 locked for R1 and N3
2. R67C2 and R8C67 = {12} 1,2 locked for C2 and R8
3. R1C23 and R23C9 = {59/86} : no 2,4,7
4. R23C1, R34C8 and R9C23 = {19/28/37/46}: no 5
5. R2C34 and R78C9 = {17/26/35}: no 4,8,9
6. R2C67 = {49/58/67}: no1,2,3
7. R34C2, R67C8, R78C1 and R9C78 = {29/38/48/56}: no 1
8. R8C34 = {39/48/57} : no 1,2,6
9. 26(4) in R4C3: no 1
10. 20(3) in R7C7: no 1,2
11. sum 5 cages on both diagonals = 89 -->>R5C5 = 90-89 = 1
12. 17(3) in R1C9 = {247} : {256} not possible because of 14(2) in R2C9 -->> 2,4,7 locked in D/ and N3
13. 19 (3) in R7C3 = {568} -->> 5,6,8 in D/ and N7
14. R4C6 and R6C4 = {3,9} -->> 3,9 locked for N5
15. R4C4 and R6C6 = {58/67}
16. 20(3) in R7C7 = {389/479}: {578} and {569} clash with step 15 -->> 9 locked in N9 and D\
17. 11(3) in R1C1 = {236/245} -->> 2 locked in N1
18. 10(2) in R9C2 = {37}/[91] -->> no 4 in R9C2 and no 2,4,9 in R9C3
19. 2 locked in N7 for R7 -->> no 2 anywhere else
20. 11(2) in R7C1 = [29]/{47} -->> killer pair {7,9} in N7 in R78C1 and R9C23 -->> no 7,9 anywhere else
21. Time for some clean up
21a. R23C1: no8
21b. R2C4: no6
21c. R2C6: no 6,9
21d. R34C2: no 9
21e. R4C8: no 3,6,7,8,9
21f. R6C8: no 2,9
21g. R7C1: no 9
21h. R7C9: no 6,7
21i. R8C4: no 3,4,5,7
21j. R8C9: no 6
21k. R9C78: no 2
22. hidden single 2 in R8C7 -->> R8C6 = 1
23. hidden single 1 in R7C9 and R9C3
24. R7C2 = 2 -->> R6C2 = 1
25. R8C9 = 7
26. R9C2 = 9
27. R78C1 = [74]
28. R8C34 = [39]
29. R6C4 = 3
30. R4C6 = 9
31. 20(3) in R7C7= {983} -->> R7C7 = 9; R8C8 = 8; R9C9= 3
32. R4C4 and R6C6 = {67} -->> locked for N5 and D\
33. 11(3) in R1C1 = {245} -->> 2,4,5 locked for N1
34. 14(2) in R1C2 = {68} -->> locked in N1 and R1 -->> naked single 7 in R2C3 -->> R2C4 = 1
35. R23C1 = {19} = [91]
36. R9C78 = {56} -->> locked for N9 -->> single 4 in R7C8
37. R2C67 = {58} -->> locked for R2
And the rest is singles.


Just edited it a little to make it more clear, after a few comments.

Para

[Andrew]

Wow! That was quick. I also enjoyed it. I'd been hoping to post the first walkthrough but Peter and Para both beat me to it by several hours.

Some general comments

I like the basic concept of the diagonal-connections on the two main diagonals. I'm sure there is potential for a harder puzzle using the same basic layout. What made this one easy was that one diagonally-connected cage combination got fixed early and that in turn fixed another one on the same diagonal. If the cages on the diagonals were made harder to solve then we could have an Assassin level puzzle. How about it Ruud?

This is the 4th SKX. The 1st and 3rd were both Assassin level with the 2nd, which I haven't yet solved at Super Assassin level, I think that one was solved jointly by Ed and Peter.

[Andrew]

Ed suggested to me that I move my walkthrough to a separate message because it was originally posted as an edit to my previous message. As he pointed out, editing can be missed by those looking for new messages.

I've also made a few corrections and added some comments based on Ed's feedback. Thanks Ed.

Here is my walkthrough. I'll convert it to normal text next week.

I took a fairly similar solving route to Peter.

Clean-up is used in various steps, using the combinations in preliminary steps 1 to 16 for further eliminations from these two cell cages. In some of the later steps, clean-up is followed by further moves and sometimes more clean-up.

1. R1C23 = {59/68}

2. R1C78 = {13}, locked for R1 and N3

3. R23C1 = 10(2), no 5

4. R2C34 = {17/26/35}, no 4,8,9

5. R2C67 = {49/58/67}, no 1,2,3

6. R23C9 = {59/68}

7. R34C2 = {29/38/47/56}, no 1

8. R34C8 = 10(2), no 5, no 7,9 in R4C8

9. R67C2 = {12}, locked for C2; clean-up: no 9 in R34C2 (R9C3 cleaned-up in step 15)

10. R67C8 = {29/38/47/56}, no 1

11. R78C1 = {29/38/47/56}, no 1

12. R78C9 = {17/26/35}, no 4,8,9

13. R8C34 = {39/48/57}, no 1,2,6

14. R8C67 = {12}, locked for R8, clean-up: no 9 in R7C1, no 6,7 in R7C9

15. R9C23 = 10(2), no 5, no 8,9 in R9C3

16. R9C78 = {29/38/47/56}, no 1

17. 11(3) in N1, no 9

18. 19(3) in N7, no 1

19. 20(3) in N9, no 1,2

There’s one that I missed! 26(4) in N45, no 1. Fortunately it didn’t matter.

20. 45 rule on N1 2 innies R2C3 + R3C2 = 10 -> R2C3 = {2367}, R3C2 = {3478}, clean-up: R2C4 = {1256}, R4C2 = {3478}

21. 45 rule on N3 2 innies R2C7 + R3C8 = 14 = [59]/{68}, killer quad 5/6/8/9 in R2C7 + R3C8 and R23C9 for N3 -> 13(3) cage in N3 = {247}, locked for D/
21a. Clean-up: R2C6 = {578}, R4C8 = {124}

22. Only valid combination for 19(3) cage in N7 = {568}, locked for N7 and D/
22a. Clean-up: no 3 in R78C1, no 2,4 in R9C23, no 4,7 in R8C4

23. R4C6 + R5C5 + R6C4 = 13 = {139}, locked for N5

24. 45 rule on D\ 3 innies R4C4 + R5C5 + R6C6 = 14

25. Crossed 13(3) and 14(3) cages in 26(5) cage -> R5C5 = 1, locked for diagonals
25a. R4C4 + R6C6 = {58/67}

26. R23C1 = {19} (only remaining 1s in N1), locked for C1 and N1, clean-up: no 5 in R1C23, no 2 in R7C1
26a. R1C23 = {68}, locked for R1 and N1, clean-up: no 2 in R2C4, no 3 in R4C2 [Ed has pointed out no 2 in R3C2 and no 4 in R2C3 (step 20). I wish I’d seen that. It would lock 3,7 for N1 and therefore give quicker eliminations for D\]
26b. R78C1 = {47}, locked for C1 and N7, clean-up: no 5,8 in R8C4, no 3 in R9C23 -> R9C23 = [91], more clean-up: no 2 in R9C78
26c. R8C34 = [39], clean-up: no 5 in R2C4, no 5 in R7C9
26d. R67C2 = [12], clean-up: no 6 in R8C9

27. 3 in C1 locked in R456C1, locked for N4

28. 45 rule on N9 2 innies R7C8 + R8C7 = 6 = [42]/[51], clean-up: R6C8 = {67}

29. R7C7 = 9 (hidden single on D\), 20(3) cage in N9 = 9{38/47/56} -> no 8 in R9C9

30. 2 on D\ locked in 11(3) cage in N1 = {245}, locked for D\ and N1, clean-up: no 6 in R2C4, no 7 in R4C2
30a. R2C34 = [71], clean-up: no 6 in R2C7
30b. R34C2 = [38], R1C23 = [68]
30c. R8C2 = 5, R7C3 = 6, R9C1 = 8, clean-up: no 3 in R9C78
30d. R78C9 = [17], clean-up: no 4 in R9C78
30e. R23C1 = [91]

31. 14(3) diagonal sub-cage in N5 = {167}, locked for D\ and N5
31b. 20(3) cage in N9 = [983], clean-up: no 2 in R4C8

32. R3C7 = 7 (hidden single on D/)

33. R9C78 = {56}, locked for R9 and N9
33a. R67C8 = [74], R78C1 = [74]
33b. R8C5 = 6 (naked single) [corrected], R9C456 = {247}, locked for N8
33c. R8C67 = [12]

34. R2C8 = 2, R1C9 = 4, R2C2 = 4, R6C6 = 6, R4C4 = 7 (naked singles)

35. R5C2 = 7 (naked single), R456C1 = {236} (subtraction combo), locked for C1 and N4 -> R1C1 = 5, R3C3 = 2

36. R1C4 = 2 (naked single), R1C56 = {79}, locked for N2 -> R2C5 = 3

37. R2C67 = {58}, locked for R2 -> R23C9 = [68] (naked single in R2C9) -> R2C67 = [85] [Thanks Ed for correcting me on this step.]
37a. R34C8 = [91] -> R1C78 = [13]

38. R3C56 = {45} -> R3C4 = 6, R4C5 = 2

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