Ruudiculous tag Killer - PANIV

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sudokuEd
Grandmaster
Grandmaster
Posts: 257
Joined: Mon Jun 19, 2006 11:06 am
Location: Sydney Australia

Post by sudokuEd »

Congratulations guys for finishing it off - great way for Peter to bring up his 100 and Para's 50 =D> .

PANIV is the hardest of the tag Killers - at least according to the amount of grunt time for SumoCue to find a solution- just piping UTA. However, still way short of nd's #9 (still one of my all time favs) - takes SumoCue over twice as long to get it out. (BTW - good luck nd on your new job.)

Here's a condensed walk-through for PANIV, with just the essential steps (just about all of them!). I've taken the liberty of slightly changing a couple to make them clearer and added some at the end just to finish.

PANIV - condensed walkthrough : (1-9 cannot repeat on diagonals)
Preliminary steps (easy way, without writing down all poss. combinations)
0a. 10(2) at r6c5, r7c4, r8c4, r8c5 : no 5
0b. 10(3) at r1c2 : no 8,9
0c. 11(2) at r3c2, r5c3, r4c7 : no 1
0d. 9(2) at r1c4 : no 9
0e. 21(3) at r1c7 : no 1,2,3
0f. 8(3) at r4c5 : no 6,7,8,9
0g. 8(2) at r8c8 : no 4,8,9
0h. 14(2) at r7c6 : no 1,2,3,4,7
0i. 19(3) at r5c8 : no 1

1. 45 on r123456 : r56c1 + r6c2 = 15(3)
1a. N7 is 45(9) cage

2. 45 on N4 : r4c2 + r5c3 = 5(2) = {23} -> 2,3 locked in N4

3. 45 on N6 : r3c9 + r5c6 = 15(2) = {69|78}

4. 11(2) at r3c2 : r3c2 = {89}, 11(2) at r5c3 : r6c4 = {89}
4a. -> no 8,9 at r3c4 and r6c2
4b. no 8,9 for R8C2 (and theoretically for R3C7), over D/

5. 8(3) at r4c5 : 8(3) = 1{25|34} -> 1 locked in 8(3) -> no 1 in r5c5 because of D/

6. 45 on r123 : r3c279 = 18(3) -> min. r3c29 = 14 -> r3c7 = {1234}

7. 12(3) at r5c6 : r56c7 = {12345}

9. N4 : 15(3) = {159|168|456} -> no 7

10. N4 : 25(4) = 7{189|459|468} -> 7 locked in 25(4)

11. 45 on N5 (2 innies, 1 outie) : r3c7 + 14 = r5c6 + r6c4
11a. r5c6 + r6c4 : minmax 15..17
11b. r3c7 : minmax 1..3 -> no 4 in r3c7

12. 45 on N5 (4 outies) : r5c3 + r356c7 = 9(4) (doubles allowed!) -> r5c3 = {23} -> r356c7 = 6 or 7 -> 1,2 locked in r356c7 for c7, no 5 in r56c7, no 3 in r5c7

13. Cleanup : no 6,7 in r8c8, no 9 in r4c8

15. 45 on N9 : r7c78 + r8c7 = 21(3) = {489|579|678} -> no 1,2,3

16. 45 on N8 : r78c6 + r9c5 = 15(3) = 5{19|28|37|46} -> 5 locked in 15(3) -> no 5 in r7c8 (seen by all poss. for 5 in N8)

17. 45 on N12 : r3c2 + r2c6 = 15(2) = [87]|[96] -> r2c6 = {67}

18. 21(3) at r1c7 : 21(3) = 7{59|68} (no 4)-> 7 locked in 21(3) -> no 7 in r2c789 and r1c456

19. no 2 in r1c45

20. N3 : 4 locked in 21(5) = 4{1259|1268|1358|1367|2357}

22. N2 : combination check {67} in r2c6 : 20(4) : {2567|3467} not poss.

23. N9 : combination check between 16(4) and 8(2) : {1258|1456|2347 not poss. for 16(4)

25. 45 n3 -> r2c6 + 3 = r3c79
25a. r2c6 = 6 -> r1c78 = {78} and r3c79 = 9 = [36] ([18/27] blocked by r1c78)
25b. r2c6 = 7 -> r1c78 = {59} and r3c79 = 10 = [28/37] ([19] blocked by r1c78) [postcript: [28] also blocked by step 17!]
....................................= {68} and r3c79 = 10 = [19/37] ([28] blocked by r1c78)

26. from step 3 r5c6 + r3c9 = 15(2) = {69|78}. combining this with steps 25ab ->
26a. r5c6 + r3c9 = [69] -> r3c79 = [19] -> r2c6 = 7
26b....................= [96] -> r3c79 = [36] -> r2c6 = 6
26c....................= [78] -> r3c79 = [28] -> r2c6 = 7 -> blocked - 2 7's in c6
26d....................= [87] -> r3c79 = [37] -> blocked - r45c7 = {13} with 8 in r5c6

steps 27-31 come from steps 26 - 26d.
27.-> r5c6 = {69}
27a. r45c7 = 2{1/4}: 2 locked for c7,n6
27b. no 9 r4c7

28. -> r3c9 = {69}

29. -> r25c6 = [76/69] = 6{7/9}: 6 locked for c6
29a. no 4 r6c5
29b. no 8 r7c7
29c. no 4 r8c5

30. -> combined with step 25ab -> r1c78 = {68/78} = 8{6/7}:8 locked for r1, n3
30a. -> no 1 r1c45

31. -> 4 innies n3 = {1689/3678} = 68{19/37}: 6 locked for n3

32. 21(3)n23 = {678}
32a. -> no 6 r1c456

33. 9(2)n2 = {45}:locked for n2, r1

34. 20(4)n2 = {1289/1379/2369/2378}

37. no 6,9 in r5c9 and no 9 in r3c6 because r3c9 and r5c6 are {69}

38. 45 on N5 (1 outie, 2 innies) : r3c7 + 14 = r5c6 + r6c4
38a. if r3c7 = 1 then r5c6 + r6c4 = 15(2) = [96]
38b. if r3c7 = 3 then r5c6 + r6c4 = 17(2) = [89]
38c. -> 9 locked in r5c6 and r6c4 for N5

39. no 1 in r6c56

42. {47} not poss. in r4c78
Explanation: 1 in r3c7 means {24} in r56c7, 3 in r3c7 means {14} in r4c56 -> no 4 in r4c78

43. N6 : 19(3) : {568} not poss. because of 11(2) -> no 5 in 19(3)

44. 8(3) at r3c7 is {134} -> 4 locked for N5 and r4 and no 3 in r5c5 and r4c7
Explanation: 8(3) = {125} means r3c7 = 1, r4c56 = {25}, r4c2 = 3 -> no poss. combination left for r4c78

45. no 8 in r4c8, no 6 in r6c5

46. 5 in N5 in 13(3) = 5{17|26} no 3,8
46a. -> 8 locked in r6c456 for N5 and r6

47. 5 locked in c45 for N2 and N5 -> 5 locked in r78c6 for N8 and c6

48. 5 locked in r45 for N5 and N6 -> 5 locked in r6c123 for N4 and r6

50. R3C7 = 3
50a.R4C56 is not 3. R4C56=3 -->> R4C2 = 2 -->> R3C2 = 9 -->> R3c9 = 6 -->> R3C7=3 (step 26b) -->> contradiction 2 3's in 8(3) R3C7
50b R4C56={14} locked for N5 and R4

51. r3c9 = 6 (step 26b), r1c67 = {78}:locked for r1,n3 and r2c6 = 6, 13(3)n5 = {256}..the rest unravels pretty quickly - so when you get stuck, try these:
{56} is blocked from 11(2)r4 by r4c5,
hidden single 9 in r1c9
{1357} is blocked from 16(4)n9
hidden single 4 on D\ in r3c3,
that horrible zig-zag cage 23(4)n1 = {1679}only, then its singles :D
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