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Joe Casey
 Post subject: Re: JFFK 7
PostPosted: Thu Jul 09, 2009 10:14 am 
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This is how I cracked it (expanding my hint from earlier):
R9C1 is 5 or 9
R6C6 = R9C6 + 6
R1C9 + R7C9 = 9
R2C6 + R2C9 = 13
N9 outie-sum = 6
If R9C1 = 9 then:
R9 is 9{38}{27}[1;46]5
R9C6=1, so R6C6 = 7
R6C8 = 5
so R7C9 is neither 3 nor 6
so R2C9 = 6 and R2C6 = 7
This eliminates 9 from R9C1

I don't see this in the tag, but then I can't read WTs fluently.
I do understand that spotting a problem 6 moves deep isn't a favourite technique here (I gather it's admirable in chess though); but I wonder if my lemma can be translated into one of the standard techniques. Although I can spot a contradiction 6 moves deep on a good day, I can't spot a swordfish to save my life.

cheers

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manu
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PostPosted: Fri Jul 17, 2009 9:03 am 
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Very happy with all the work you have done on this puzzle guys ! I much love the tag concept.

Here is how I solved this puzzle. I have no merit with this solving path since this killer was made with the intention to use some particular moves.

Edit : a sub-step has been missed (2)e). Thanks Afmob to have pointed out this problem.

JFFK7 solving path

Hidden Text:
Steps 1)+2)+ 3)a)->d) are mainly used to prove that 5 is locked at r3c78.
The puzzle is cracked after step 6)b) with a killer pair {39} that was not easy to see (I think it's the hardest move)
1) a) Innies for r9 : r9c1+r9c9=14 : r9c19=[59/68/95] (no 6 at r9c9)
b) 13(6)n7 <> {67} since {67} blocks both cages 8(2) of c1 -> r9c19={59} (no 6,8), locked for r9, r8c1=(84) and r8c9=(37)

2) a) Innies for r12 : r2c6+r2c9=13=h13(2) : no 1,2,3
b) r2c9<>9 -> r2c6<>4
c) There is only one permutation of h13(2) without one of {57} : [94]. But r2c9=4 -> r3c9=5 (cage 9(2)), so
r2c6+r2c9+r3c9 must contain one of {57}. Since these last three cells "see" cage 12(2)n3, we deduce 12(2) <> {57}
d) 12(2)n3={39/48}
e) h13(2) = {58/67} : {49} would block cage 12(2)n3. r2c9<>4 -> r3c9<>5 (edit)
f) IO for n3 : r4c8=4+r1c7 : r1c7=(1234) -> r4c8=(5678)
g) IO for n8 : r6c6=6+r9c6 : r6c6=(789), r9c6=(123)

3) a) IO for n1 : r3c4=r3c1+r2c3-4
b) r3c4<>r3c1, so r2c3<>4 (IOU)
c) 4 is locked for n1/r3 at r3c123 : clean-up, no 4 at r3c9, no 5 at r2c9
d) 5 is locked for n3/r3 and the rest of 18(3) at r3c78 :
-> r4c8<>5 , so (step2)e)) r1c7<>1
-> r4c8<>8 since 18(3) cannot contain both {58}, so r1c7<>4
e) r1c6=(23), so 5(2)n2={23} locked for r1
f) 9(2)n3=[81/72/63]
g) Last combination for 18(3)n3 : {567}.

4) a) Outies for n89 : r6c6+r6c8=12 -> r6c68=[75/84/93]
b) Combinations of 10(2)n3 : {19/46}
c) r1c8<>6 since r1c8 see all cells of 18(3)n3={567}; clean up, r1c9<>4
d) Innies for c9 : r1c9+r7c9=9 : no 9 at r1c9,r7c9; clean up, r1c8<>1
e) We deduce from the previous steps that 10(2)n3=[91/46], and r17c9=[18/63]

5) a) 4 is locked for c9/n6 at r456c9
b) r6c8<>4 ->(step 4)a)) r6c6<>8
c) Min r6c8+r7c9=5+3=8 -> max r7c8=15-8=7 : no 8,9.

6) a) 9 is locked for n9 at 13(3)+12(2)
b) Either 13(3) contains 9 and 13(3)={139}, either 12(2) contains 9 and 12(2)={39}. So, 13(3)+12(2)
contain 3 : killer pair {39} locked for n9 at 13(3)+12(2)
c) r7c9=8, r1c9=1 (step 4)d)) and r1c8=9
d) 8 is locked for n3 at 12(2) : 12(2)={48} locked for n3/r2
e) Hidden single for r1 : r1c4=4
f) Last combination for h13(2) at r2 (step 2)a)) : Naked pair {67} locked for r2 at r2c69
g) Last combination for cage 12(3) at n2 : {345}. Naked pair {35} locked for r2 at r2c34
h) Hidden single for r2 : r2c2=9
i) 8 locked for r1 at 22(3) : 22(3)={589}, {58} locked for r1/n1
j) r2c34=[35]

7) a) 8(2)n1={17/26} : contains one of {12}
b) r3c23<>{12} ->(11(3)) r3c4<>8
c) Naked pair {89} locked for r3/n2 and the rest of 24(4) at r3c56.
d) Last combo for 24(4)n2 : {1689}. r2c6=6, r4c6=1
e) Naked single : r4c4=2 -> r4c3=4
f) r2c9=7. 9(2)c9=[72] -> 12(2)c9=[39] -> 15(3)c9={456} locked for c9/n6
g) r4c8=7, r6c8=3 -> r6c6=9 (step 4)a))
h) 8 is locked at r456c7+r5c8 for n6 and the rest of 45(9) -> Hidden single for n5 : r6c4=8

The rest follows easily
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Andrew
 Post subject: Re: JFFK 7
PostPosted: Mon Nov 29, 2010 5:54 am 
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After managing to finish JF"F"K6 I thought I ought to have another try at finishing JFFK7.

Thanks manu for a challenging and interesting puzzle. My solving path had some similarity to the "tag" solution by Ed and Afmob but my main work was in different areas, N3, N9 and C8. I'm not sure whether I ever spotted their 4 outies for R123, which was a key part of the "tag" walkthrough; if I did I didn't get anything out of if although I did use an innie-outie difference for R123 to make one elimination.

From an early stage I was looking to apply the Law of Leftovers to the 45(9) cage; I could see that R4C7 must equal one of R6C46 and similarly R6C7 must be the same as one of R4C46 but I never found a way to apply this.

manu wrote:
Here is how I solved this puzzle. I have no merit with this solving path since this killer was made with the intention to use some particular moves.
I really enjoyed your solving path. The interesting step 2)c) it made it a simpler puzzle than in either the "tag" or my solving path.

Rating Comment:
I'll rate my walkthrough for JFFK7 at 1.5. I used some combined cages and a short forcing chain.

I think 1.5 is also an appropriate rating for both the "tag" solution and manu's one.

Here is my walkthrough for JFFK7.

Prelims

a) R12C1 = {17/26/35}, no 4,8,9
b) R12C5 = {17/26/35}, no 4,8,9
c) R1C56 = {14/23}
d) R1C89 = {19/28/37/46}, no 5
e) R2C78 = {39/48/57}, no 1,2,6
f) R23C9 = {18/27/36/45}, no 9
g) R4C34 = {15/24}
h) R67C1 = {17/26/35}, no 4,8,9
i) R89C1 = {49/58/67}, no 1,2,3
j) R89C9 = {39/48/57}, no 1,2,6
k) R9C23 = {29/38/47/56}, no 1
l) R9C45 = {18/27/36/45}, no 9
m) 22(3) cage in N1 = {589/679}, 9 locked for N1
n) 11(3) cage at R3C2 = {128/137/146/236/245}, no 9
o) 20(3) cage at R6C6 = {389/479/569/578}, no 1,2
p) 11(3) cage at R9C6 = {128/137/146/236/245}, no 9

1. 45 rule on R1234 3 innies R4C579 = 20 = {389/479/569/578}, no 1,2

2. 45 rule on R6789 3 innies R6C579 = 10 = {127/136/145/235}, no 8,9

3. 45 rule on N8 1 outie R6C6 = 1 innie R9C6 + 6, R6C6 = {789}, R9C6 = {123}

4. 45 rule on N89 2 outies R6C68 = 12 = [75/84/93], R6C8 = {345}

5. 4 in N1 locked in R2C3 + R3C123
5a. 45 rule on N1 4 innies R2C3 + R3C123 = 15 = {1248/1347/2346}, no 5

6. 45 rule on N3 1 outie R4C8 = 1 innie R1C7 + 4, R4C8 = {5678}

7. Combined cage R1267C1 = 16 = {1267/1357/2356}
7a. R89C1 = {49/58} (cannot be {67} which clashes with R1267C1), no 6,7

8. 45 rule on R9 2 innies R9C19 = 14 = {59} locked for R9, R8C1 = {48}, R8C9 = {37}, clean-up: no 2,6 in R9C23, no 4 in R9C45
8a. Killer pair 4,8 in R8C1 and R9C23, locked for N7

9. 11(3) cage at R9C6 = {128/146/236} (cannot be {137} which clashes with R9C23), no 7

10. 45 rule on C9 2 innies R17C9 = 9 = {18/27/36}/[45], no 9, no 4 in R7C9, clean-up: no 1 in R1C8

[This is how far I got originally. I ought to have seen some of the next steps sooner.]

11. 45 rule on C1 1 innie R5C1 = 1 outie R4C2 + 1, no 9 in R4C2, no 1 in R5C1
11a. 45 rule on C1 3 innies R345C1 = 16 = {178/268/349/358} (cannot be {169/259/367/457} which clash with combined cage R1267C1)
11b. 7 of {178} must be in R5C1 (15(3) cage at R3C1 cannot contain both of 1,7 or both of 7,8) -> no 7 in R34C1
11c. 4 of {349} must be in R34C1 (R34C1 cannot be [39] because 15(3) cage at R3C1 cannot be [393]) -> no 4 in R5C1, clean-up: no 3 in R4C2 (step 11)

12. 45 rule on R12 2 innies R2C69 = 13 = {58/67}/[94], no 1,2,3, no 4 in R2C6, clean-up: no 6,7,8 in R3C9

13. 15(3) cage at R6C8 = {159/249/258/348/357/456} (cannot be {168/267} because R6C8 only contains 3,4,5)
13a. 9 of {159} must be in R7C8 -> no 1 in R7C8

14. Hidden killer pair 1,8 in R17C9, R23C9 and 15(3) cage at R4C9, R17C9 and R23C9 can only contain both or neither of 1,8 -> 15(3) cage at R4C9 must contain both or neither of 1,8
14a. 15(3) cage at R4C9 = {168/249/267/456} (cannot be {159/258/348} which only contain one of 1,8, cannot be {357} which clashes with R8C9), no 3

15. 3 in N6 only in R4C7 + R5C78 + R6C78, CPE no 3 in R6C5
15a. R6C579 (step 2) = {127/136/145/235}
15b. 3 of {136} must be in R6C7 -> no 6 in R6C7

16. 45 rule on N7 2 innies R7C13 = 1 outie R6C2 + 1
16a. Min R7C13 = 3 -> min R6C2 = 2

17. 45 rule on C9 3 outies R167C8 = 16 = {259/349/358/367/457} (cannot be {268} because R6C8 only contains 3,4,5)
17a. 6 of {367} must be in R1C8 (R67C8 cannot be [36] because 15(3) cage at R6C8 cannot be [366]), no 6 in R7C8

18. 45 rule on N12 2(1+1) outies R1C7 + R4C6 = 1 innie R3C1
18a. Max R3C1 = 8 -> max R1C7 + R4C6 = 8, no 8,9 in R4C6
18b. Min R1C7 + R4C6 = 2 -> min R3C1 = 2

19. 45 rule on N1 2 innies R2C3 + R3C1 = 1 outie R3C4 + 4, IOU no 4 in R2C3
19a. 4 in N1 only in R3C123, locked for R3, clean-up: no 5 in R2C9, no 8 in R2C6 (step 12)

20. 45 rule on N3 3 innies R1C7 + R3C78 = 14 = {149/167/239/257/356} (cannot be {158/248} because 18(3) cage at R3C7 cannot be {58}5/{28}8, cannot be {347} which clashes with R2C78), no 8

21. 45 rule on R123 2 outies R4C68 = 1 innie R3C1 + 4
21a. R3C1 = {23468} -> R4C68 = 6,7,8,10,12 -> no 6 in R4C6 (because R4C68 cannot be [66] and min R4C8 = 5)

22. 45 rule on N9 4 innies R7C89 + R9C78 = 20 = {1289/1469/1478/1568/2369/2468/2567} (cannot be {1379/2378/3467} which clash with R8C9, cannot be {2459} which clashes with R9C9, cannot be {3458} which clashes with R89C9)
22a. 9 of {2369} must be in R7C8 -> no 3 in R7C8

23. R1C7 + R3C78 (step 20) = {149/167/239/257/356}, R2C78 = {39/48/57} -> combined cage R1C7 + R2C78 + R3C78 = {149}{57} and all other combinations for R1C7 + R3C78 contain one of 3,7 -> R1C89 = {28/46}/[91] (cannot be {37} which clashes with R1C7 + R2C78 + R3C78), no 3,7, clean-up: no 2,6 in R7C9 (step 10)

24. R1C67 = {14/23}, R1C89 (step 23) = {28/46}/[91] -> combined cage R1C6789 = {14}{28}/{23}{46}/{23}[91], 2 locked for R1, clean-up: no 6 in R2C1, no 6 in R2C5

25. R167C8 (step 17) = {259/349/358/367/457}
25a. 4 of {457} must be in R1C8, 3 of {349} must be in R6C8 -> no 4 in R6C8, clean-up: no 8 in R6C6 (step 4), no 2 in R9C6 (step 3)
25b. 8 of {358} must be in R1C8 -> no 8 in R7C8

26. 11(3) cage at R9C6 (step 9) = {128/146/236}
26a. R9C6 = {13} -> no 1,3 in R9C78
26b. 1 in R9 only in R9C456, locked for N8

27. 45 rule on N8 3 innies R7C56 + R9C6 = 14 = {149/158/347/356} (cannot be {167} because 20(3) cage at R6C6 cannot be 6{67})
27a. R9C6 = {13} -> no 3 in R7C56

28. 8 in R6 only in R6C234
28a. 45 rule on N7 4 outies R6C1234 = 23 = {2489/2678/4568} (cannot be {3578} which clashes with R6C8, cannot be {1589} which clashes with R6C68), no 1,3, clean-up: no 5,7 in R7C1

29. 3 in R6 only in R6C78, locked for N6
29a. 1 in R6 only in R6C579, CPE no 1 in R5C78

30. R7C89 + R9C78 (step 22) = {1289/1469/2468/2567} (cannot be {1478/1568} because max R9C78 = 10, cannot be {2369} because 15(3) cage at R6C8 cannot be [393]), no 3, clean-up: no 6 in R1C9 (step 10), no 4 in R1C8

31. 20(3) cage at R6C6 = {479/569/578}
15(3) cage at R6C8 (step 13) = {159/258/348/357} (cannot be {249} because 2,4,9 only in R7C8)
31a. Consider placements for R6C6
R6C6 = 7 => R6C8 = 5 (step 4) => 15(3) cage at R6C8 cannot be {357} (because 3 of {357} only in R6C8)
R6C6 = 9 => R7C56 = {47/56} => 15(3) cage at R6C8 cannot be {357} (because 5,7 of {357} must be in R7C89)
31b. -> 15(3) cage at R6C8 = {159/258/348}, no 7, clean-up: no 2 in R1C9 (step 10), no 8 in R1C8
31c. R6C8 = {35} -> no 5 in R7C89, clean-up: no 4 in R1C9 (step 10), no 6 in R1C8

32. Naked pair {18} in R17C9, locked for C9
[I overlooked a few clean-ups (for R2C69 and for R1C7 + R4C8) from here onward but they don’t make much difference so I haven’t re-worked the remaining steps.]

33. R6C7 = 1 (hidden single in N6), clean-up: no 4 in R1C6
33a. R6C579 (step 2) = {127/145}, no 6

34. R6C8 = 3 (hidden single in R6), R6C6 = 9 (step 4), clean-up: no 9 in R2C7
34a. 15(3) cage at R6C8 (step 31b) = {348} (only remaining combination) -> R7C89 = [48], R1C9 = 1, R1C8 = 9, clean-up: no 4 in R1C7, no 7 in R2C1, no 7 in R2C5, no 3,8 in R2C7
34b. 20(3) cage at R6C6 (step 31) = {569} (only remaining combination) -> R7C56 = {56}, locked for R7 and N8, clean-up: no 2 in R6C1, no 3 in R9C45

35. R6C6 = 9 -> R9C6 = 3 (step 3), R1C67 = [23], clean-up: no 6 in R1C5, no 5 in R2C1, no 5 in R2C5, no 6 in R2C9, no 8 in R9C23

36. R2C8 = 8 (hidden single in N3), R2C7 = 4, R2C9 = 7, R3C9 = 2, R8C9 = 3, R9C9 = 9, R9C1 = 5, R8C1 = 8, clean-up: no 3 in R2C1, no 3 in R7C1

37. Naked pair {26} in R9C78, locked for R9 and N9 -> R7C7 = 7, R8C78 = [51], R3C78 = [65], R4C8 = 7, R9C78 = [26], R5C8 = 2, clean-up: no 7 in R6C5 (step 33a), no 7 in R9C45

38. Naked pair {89} in R45C7, locked for 45(9) cage at R4C5
38a. Naked quad {34567} in R4C5 + R5C456 + R6C5, locked for N5 -> R4C6 = 1, R4C4 = 2, R4C3 = 4, R6C4 = 8, R7C4 = 9, R9C23 = [47], R9C45 = [18]

39. R8C5 = 2 (hidden single in N8)

40. R8C23 = {69} = 15 -> R67C2 = 5 = [23]

41. Naked pair {45} in R6C59, locked for R6 -> R6C3 = 6, R6C1 = 7, R7C1 = 1, R7C3 = 2, R12C1 = [62]

42. 22(3) cage in N1 = {589} (only remaining combination) -> R2C2 = 9, R1C23 = {58}, locked for R1 and N1 -> R1C5 = 7, R2C5 = 1, R1C4 = 4, R2C3 = 3, R2C4 = 5 (cage sum)

43. R3C1 = 4 -> R4C12 = 11 = [38]

and the rest is naked singles.
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