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remote killer X - Black-hole X

 
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sudokuEd
Grandmaster
Grandmaster


Joined: 19 Jun 2006
Posts: 257
Location: Sydney Australia

PostPosted: Tue Feb 20, 2007 1:08 am    Post subject: remote killer X - Black-hole X Reply with quote

Nasenbaer has unleashed a new phenomena with his CDK: the remote cage killer. Thanks for showing how to get SumoCue to make remote cages Peter (Shift-click).

This diagonals killer (1-9 cannot repeat on the diagonals) has 3 remote cages - each has 4 cells: 24(4)@r1c1 (r19c19), 21(4)@r2c2 (r28c28), 26(4)@r3c3 (r37c37). Confused yet? Wait till you try and solve it Twisted Evil . I've had a good go at it - but was defeated. Have some ideas on how to make the remote cages interact: but couldn't convince myself.

If others find it difficult enough, perhaps we can help each other 'tag' style: especially on the weekend.

BTW - when using SumoCue to confirm that it has a unique solution, I get an error message: "Unhandled Exception". Can anyone show me how to fix this? PS4 confirms that it is unique.

So here is Black-hole X. This is a remote X killer: (1-9 cannot repeat on the diagonals and it has 3 remote cages @r1c1, r2c2 and r3c3).

3x3:d:k:6144:1793:1793:3331:3331:3331:2566:2566:6144:3337:5386:3586:3586:3853:3076:3076:5386:3089:3337:3859:6676:3853:3853:3853:6676:3609:3089:3337:3859:3859:11550:11550:11550:3848:3609:3089:5156:5156:5156:11550:11550:11550:3848:3848:3848:3373:1070:5156:11550:11550:11550:5171:5171:5685:3373:1070:6676:3129:3129:3129:6676:5171:5685:3373:5386:2881:2881:3129:2882:2882:5386:5685:6144:1541:1541:5383:5383:5383:2373:2373:6144:

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Para
Yokozuna
Yokozuna


Joined: 08 Nov 2006
Posts: 384
Location: The Netherlands

PostPosted: Tue Feb 20, 2007 7:15 pm    Post subject: Reply with quote

Hey Ed

Nice Killer. Had to result to one ugly move. Must be a nicer way through it.
So here is my walk-through. Any comments or corrections are appreciated.

Walk-through Black Hole Killer

1. R1C23 = {16/25/34}
2. R1C78 = {19/28/37/46}
3. R2C34 and R34C8 = {59/68}
4. R2C67 = {39/48/57}
5. R37C37 = 26(4): no 1
6. 20(3) in R6C7 = {389/479/569/578}
7. 22(3) in R678C9 = {589/679} -->> 9 locked for C9
8. R8C34 and R8C67 = {29/38/47/56}
9. R9C23 = {15/24}
10. R9C456 = {489/579/678}
11. R9C78 = {18/27/36} : {45} clashes with 6(2) in R9C2
12. 12(4) in R7C4 = {1236/1245} -->> 1 and 2 locked for N8
12a. Clean up : R8C37: no 9
13. R67C2 = {13} locked for C2
13a. Clean up : R1C3: no 4,6; R9C3: no 5
14. Sum 3 remote cages = 71 -->> 2*R5C5 + R46C46 = 19: min. R46C46 = 10; max. R5C5 = 4: no 5,6,7,8,9
14a. Max R46C46 + R5C5 = 18: no 9
14b. 45 on N5: Min. R46C5 + R5C46 = 27 : no 1 or 2
15. 45 on R1: 2 innies: R1C19 = 15 = {78}/[96]
15a. 45 on R1: 2 outies: R9C19 = 9 = {18/27/36}: {45} clashes with 6(2) in R9C2
16. 45 on N2: 2 innies: R2C46 = 17 = {89}: locked for N2 and R2
16a. Clean up : R2C3 = {56}; R2C7 = {34}
17. 9 locked in R9 and 21(3) in R9C4 for N8
17a. 21(3) in R9C4 = {489/579}: no 6
18. 45 on N8: 2 innies: R8C46 = 12 = {48/57}
18a. Clean up: R8C37 : no 2,5,8
19. 6 locked in N8 for 12(4) in R7C4: 12(4) = {1236}
19a. 1 and 3 canít both be in R7C456: clashed with R7C2: R8C5 = {13}
19b. 2 and 6 locked in N8 for R7
19c. Killer Pair {13} in R7C2 + R7C456
20. Killer Pair {67} in R1C19 and 13(3) in R1C4 for R1
20a. Clean up: R1C3: no 1; R1C78: no 3,4
21. 45 on C9: 3 innies: R159C9 = 11 = [8]{12}/[7]{13}/[6]{23}/[41]
21a. R5C9 = {1234}; R9C9 = {123}; R9C1 = {678}
21b. R59C9 always has 1 or 3(or both): 12(3) in R2C9 canít be {138}: no 8 in R234C9
22. 45 on C1: 3 innies: R159C1 = 19: [928]/[937]/{8[4]7}/[856] -->> R5C1 = {2345}
22a. R159C1 = [937] -->> R159C9 = [632] : 2 3ís in R5: R159C5 canít be [937]: R5C1: no 3
23. 24(4) in R1C1 = {1689/2679/3678}: 6 locked in 24(4) for D/
24. 1 locked in N1 for C1 and 13(3) in R2C1
24a. 13(3) in R2C1 = {139/148/157}: no 2,6
24b. 1ís in R8: R8C58: crossover: no 1 in R5C5
24c. Max. R46C46 + R5C5 = 17: no 8 (step 14)
24d. Min R5C46+R46C5 = 28: no 3 (step 14)
25. 13(3) in R6C1 = {238/247/256/346}: no 9
25a. 9 locked in N7 for D/: R3C7: no 9
26. 3 locked in R9 for N9
26a. Clean up: R8C6: no 8; R8C4: no 4; R8C3: no 7
27. Hidden killer Triple {123} in N9 in R8C8 + 9(2) in R9C7 +R9C9 -->> R8C8 = {12}
28. R8C3: no 6
28a. R8C3 = 6 -->>R8C46 = [57] -->> R8C7 = 4
28b. R8C3 = 6 -->>R2C3 = 5 -->> R2C46 = 98 -->> R2C7 = 4 : 2 4ís in C7
28c. Clean up: R8C4: no 5; R8C6: no 7; R8C7: no 4
29. Killer Triple {134}for N7 in R7C2 + R8C3 + 6(2) in R9C2
30. 13(3) in R6C1 = [382]/[472]/{2[5]6} (needs 5, 7 or 8 in R7C1)
30a. R6C1 = {2346}; R8C1 = {26}
30b. 2 locked in 13(3) in R6C1 for C1: R5C1: no 2
31. R159C1 = {8[4]7}/[856] (step 22): R1C1: no 9
31a. R1C19 = {78} -->> locked for R1 and 24(4) in R1C1 (step 15)
31b. Naked single 6 in R1C9 -->> R9C9 = 3 (step 15a)
31c. R8C1 = 2; R9C23 = [51]; R67C2 = [13]
31d. R8C34 = [47]; R8C67 = [56]; R8C58 = [31];
32. 9 locked in 13(3) in R2C1 -->> 13(3) = {139} locked for C1
32a. R67C1 = [47]; R5C1 = 5; R1C1 = 8; R1C9 = 7; R1C78 = [19]
32b. R4C6 = 1; R5C9 = 1; R6C4 = 3; R2C7 = 3; R5C8 = 3 (hidden singles)
32c. R2C6 = 9; R2C34 = [68]; R2C1 = 1
33. Naked Pair {89} in R7C2 + R8C2 for D/
33a. Hidden single 8 in R3C8; R4C8 = 6; Hidden single 6 in R3C9 and R5C2
33b. Hidden single 6 in R6C6 for D\; R7C6 = 2
34. 9ís on D\ in R3C3 + R7C7 locked for 26(4) -->> R7C2: no 9
34a. R7C3 = 8; R8C2 = 9; R8C9 = 8; R4C2 = 8 (hidden)
34b. 15(3) in R3C2 = [438] -->> R3C2 = 4; R4C3 = 3
And the rest is singles or cage sums.

There must be a nicer way past step 28.

Ok here is the cleaned up and nicer walk-through. Without the ugly moves.

Walk-through Black Hole Killer

1. R1C23 = {16/25/34}
2. R1C78 = {19/28/37/46}
3. R2C34 and R34C8 = {59/68}
4. R2C67 = {39/48/57}
5. R37C37 = 26(4): no 1
6. 20(3) in R6C7 = {389/479/569/578}
7. 22(3) in R678C9 = {589/679} -->> 9 locked for C9
8. R8C34 and R8C67 = {29/38/47/56}
9. R9C23 = {15/24}
10. R9C456 = {489/579/678}
11. R9C78 = {18/27/36} : {45} clashes with 6(2) in R9C2
12. 12(4) in R7C4 = {1236/1245} -->> 1 and 2 locked for N8
12a. Clean up : R8C37: no 9
13. R67C2 = {13} locked for C2
13a. Clean up : R1C3: no 4,6; R9C3: no 5
14. Sum 3 remote cages = 71 -->> 2*R5C5 + R46C46 = 19: min. R46C46 = 10; max. R5C5 = 4: no 5,6,7,8,9
14a. Max R46C46 + R5C5 = 18: no 9
14b. 45 on N5: Min. R46C5 + R5C46 = 27 : no 1 or 2
15. 45 on R1: 2 innies: R1C19 = 15 = {78}/[96]
15a. 45 on R1: 2 outies: R9C19 = 9 = {18/27/36}: {45} clashes with 6(2) in R9C2
16. 45 on N2: 2 innies: R2C46 = 17 = {89}: locked for N2 and R2
16a. Clean up : R2C3 = {56}; R2C7 = {34}
17. 9 locked in R9 and 21(3) in R9C4 for N8
17a. 21(3) in R9C4 = {489/579}: no 6
18. 45 on N8: 2 innies: R8C46 = 12 = {48/57}
18a. Clean up: R8C37 : no 2,5,8
19. 6 locked in N8 for 12(4) in R7C4: 12(4) = {1236}
19a. 1 and 3 canít both be in R7C456: clashed with R7C2: R8C5 = {13}
19b. 2 and 6 locked in N8 for R7
19c. Killer Pair {13} in R7C2 + R7C456
20. Killer Pair {67} in R1C19 and 13(3) in R1C4 for R1
20a. Clean up: R1C3: no 1; R1C78: no 3,4
21. 45 on C9: 3 innies: R159C9 = 11 = [8]{12}/[7]{13}/[6]{23}/[41]
21a. R5C9 = {1234}; R9C9 = {123}; R9C1 = {678}
21b. R59C9 always has 1 or 3(or both): 12(3) in R2C9 canít be {138}: no 8 in R234C9
22. 45 on C1: 3 innies: R159C1 = 19: [928]/[937]/{8[4]7}/[856] -->> R5C1 = {2345}
23. 45 on C19: 6 innies = 30: R5C19 = 30 Ė 24(4) in R19C19 = 6 = {24}/[51]
23a. R159C1 : not [937]
24. 24(4) = {1689/2679/3678}: 6 locked in 24(4) for D/
25. Combining step 15 and 21-24
25a. 24(4) = [9681/8763]: [9672] clashes with step 23a.; [7863] clashes with step 21
25b. R1C1 = {89}; R1C9 = {67}; R5C1 = {25}; R5C9 = {14}; R9C1 = {68}; R9C9 = {13}
25c. 22(3) in R6C9 = {589}-->> locked for C9: {679} clashes with R1C9
25d. 2 locked in 12(3) in R2C9-->> 12(3) = {237/246}: no 1
26. 1 locked in N1 for C1 and 13(3) in R2C1
26a. 13(3) = {139/148/157} : no 2 or 6
26b. 13(3) in R6C1 = {238/247/256/346}: no 9
26c. 9 locked in N7 for D/: R3C7: no 9
27. 3 locked in R9 for N9
27a. Clean up: R8C6: no 8; R8C4: no 4; R8C3: no 7
27b. Hidden Killer Triple {123}in N9 in R8C8 + R9C9 + 9(2) in R9C7 -->> R8C8 = {12}
28. {4,7} locked in R8C3467 for R8
28a. R8C67 = {47}/[56]; R8C67 = [56] -->> R8C34 = [47] (step 18)
28b. 7 locked in N7 for R7
28c. Naked quad {4589} in R7C789 + R8C9 for N9
28d. Clean up: R9C78: no 1; R8C6: no 7; R8C4: no 5; R8C3: no 6
29. Killer Triple {134}for N7 in R7C2 + R8C3 + 6(2) in R9C2
30. 13(3) in R6C1 = [382]/[472]/{2[5]6} (needs 5, 7 or 8 in R7C1)
30a. R6C1 = {2346}; R8C1 = {26}
30b. 2 locked in 13(3) in R6C1 for C1: R5C1: no 2
31. R5C19 = [51]; R19C9 = [73] (step 21); R19C1 = [86] (step 22)
31a. R678C1 = [472]; R9C23 = [51]; R67C2 = [13]
31b. R8C34 = [47]; R8C67 = [56]; R8C8 = 1; R8C5 = 3
31c. R1C78 = [19]; R4C6 = 1(hidden)
32. Crossover 9ís on D\ in R3C3 and R7C7 -->> R7C3: no 9
32a. R7C3 = 8; R8C29 = [98]
32b. R3C8 = 8(hidden); R4C8 = 6
33. 20(4) = 5{267} -->> locked for N4
33a. R4C2 = 8
33b. 15(3) in R3C2 = 8{34} -->> R3C2 = 4; R4C3 = 3
33c. R3C1 = 9; R1C23 = [25]; R2C34 = [68]; R3C67 = [93]
33d. R23C1 = [13]; R2C2 = 7; R3C3 = 9; R5C2 = 6; R2C8 = 4
And the rest is singles and cage sums.

greetings

Para
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