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 Post subject: Re: Psycho Killer Jigsaw
PostPosted: Sun May 12, 2019 2:00 am 
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Posts: 1893
Location: Lethbridge, Alberta, Canada
SudokuPK-002 was a little bit harder than the demo version, but not difficult.

Here is my walkthrough for SudokuPK-002:
This puzzle is essentially a jigsaw killer with gaps to place the killer cage totals, in kakuro style. Since there are 11 rows and columns I’ve labelled them 1 to 9, then A and B. Jigsaw nonets have been identified by their upper left-hand cells.

Initial Placements.
a) 45 rule on R5 1 innie R5CB = 8, placed for NR3C8
b) R5CB = 8 -> R34CB = 14 = {59}, locked for CB and NR3C8
c) 45 rule on R7 1 innies R7C1 = 5, placed for NR7C1
d) 45 rule on C5 1 innie R8C5 = 6, placed for NR4C5
e) 45 rule on C7 1 innie R4C7 = 8, placed for NR4C5

Prelims, taking account of initial placements, with direct results.

a) R1C12 = {19/28/37/46}, no 5
b) R1C45 = {19/28/37}/[64], no 5, no 4 in R1C4
c) R12C7 = {16/25/34}, no 7,9
d) R2C9A = {17/26/35}, no 4,8,9
e) R3C12 = {13}, locked for R3 and NR1C1, clean-up: no 7,9 in R1C12
f) R5C89 = {12}, locked for R5 and NR3C8
g) R7C34 = {17/26}
h) R9CAB = [86], both placed for R8CA
i) RAC12 = {18/27/36/45}, no 9
j) RABC5 = {19/28/37}, no 4,5
k) RBC78 = {49/67}/[58], no 1,2,3, no 5 in RBC8
l) RBCAB = [47/74/92], RBCA = {479}, RBCB = {247}
m) 19(3) cage at R3C4 = {289/469/478/568}
n) 10(3) cage at R9C6 = {127/145/235}, no 9
o) 19(3) cage at R9C2 = {289/379/469/478/568}, no 1, clean-up: no 8 in RAC3

1a. Naked triple {467} in R3C89A, locked for R3 and NR3C8 -> R4C9 = 3, clean-up: no 5 in R2CA
1b. 19(3) cage at R3C4 = {289} (only remaining combination), locked for R3 and NR1C4 -> R34CB = [59], clean-up: no 1 in R1C45
1c. 1,5,9 in R1 only in R1C789AB, locked for NR1C7, clean-up: no 2,6 in R1C7, no 7 in R2C9, no 3,7 in R2CA
1d. Naked pair {26} in R2C9A, locked for R2 and NR1C7, clean-up: no 1,5 in R1C7
1e. Naked pair {34} in R12C7, locked for C7 and NR1C7, clean-up: no 9 in RBC8
1f. Killer pair 3,4 in R1C45 and R1C7, locked for R1, clean-up: no 6 in R1C12
1g. Naked pair {28} in R1C12, locked for NR1C1, 8 locked for R1
1h. R1C4 = 6 (hidden single in R1) -> R1C5 = 4, placed for NR1C4, R12C7 = [34]
1i. R7C3 = 6 (hidden single in NR6C1) -> R7C4 = 2, placed for NR7C1, clean-up: no 3 in RAC2
1j. Naked triple {579} in R2C123, 5,7 locked for R2 and NR1C1 -> R2C6 = 8
1k. Naked pair {13} in R2C45, locked for NR1C4
1l. Naked pair {57} in R45C4, locked for C4
1m. Naked pair {46} in R4C12, 4 locked for R4
1n. 1,3 in RB only in RBC12345, locked for NRAC2, clean-up: no 6,8 in RAC2, no 7,9 in RBC5
1o. 19(3) cage at R9C2 = {379/478} (cannot be {289} which clashes with R1C2, cannot be {469} which clashes with R4C2, cannot be {568} because no 5,6,8 in R9C2), no 2,5,6, 7 locked for C2, clean-up: no 4,7 in RAC3
1p. 7 of {379} must be in RAC2, 8 of {478} must be in RBC2 -> no 4,7 in RBC2

2. 3,4 in NR4C5, only in R5678C6, locked for C6
2a. 2,5 in R9 only in 10(3) cage at R9C6 = {235} -> R9C8 = 3, R9C67 {25}, locked for NR7C8, clean-up: no 8 in RBC8
2b. R8C13 = {38} (hidden pair in NR7C1), locked for R8
2c. 8 in NR4C3 only in R6C2345, locked for R6
2d. R7C9 = 8 (hidden single in NR6C7)
2e. RAC8 = 8 (hidden single in NR7C8), clean-up: no 2 in RBC5
2f. 4 in NR7C8 only in R78BC8, locked for C8

3. RAC6 = 6 (hidden single in C6), placed for NRAC2
3a. 6 in RB only in RBC78 = {67}, 7 locked for RB and NR7C8, clean-up: no 4 in RBCAB
3b. RBCAB = [92], both placed for NR8CA
3c. RBC3 = 5 (hidden single in RB), RAC3 = 2 -> RAC2 = 7, RAC5 = 9 -> R8C5 = 1, R2C45 = [13], RAC7 = 1, placed for NR7C8
3d. Naked pair {49} in R78C8, 9 locked for C8
3e. R8CAB = {17} (hidden pair in NR8CA), locked for R8
3f. Naked pair {17} in R18CB, locked for CB
3g. R2C2 = 5 (hidden single in R2)
3h. 2 in R4 only in R4C56, locked for NR4C5
3i. R8C9 = 2 (hidden single in R8), placed for NR6C7, R2C9A = [62], R5C89 = [21]
3j. R1C9 = 9 (hidden single in R1)

4a. R9C7 = 2 (hidden single in C7) -> R9C6 = 5
4b. R8C7 = 5 (hidden single in R8), placed for NR4C5
4c. 9 in NR4C5 only in R567C6, locked for C6 -> R3C456 = [982]
4d. Naked pair {17} in R4C36 -> R4C45 = [52], R5C4 = 7

5a. R6C2 = 2 (hidden single in R6) -> R1C12 = [28], RBC2 = 3, R3C12 = [31], R8C13 = [83], RBC14 = [48], R4C12 = [64], R5C123 = [964], 4,9 placed for NR4C3, R2C13 = [79], R5C6 = 3
5b. R9C1234 = [1974], R56C5 = [57], R4C36 = [17], R6C34 = [83]

6a. R3C9 = 7 (hidden single in C9) -> R3C8A = [64]
6b. R123CA = 13, R23CA = [24] -> R1CA = 7

and the rest is naked singles.


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 Post subject: Re: Psycho Killer Jigsaw
PostPosted: Sun May 12, 2019 6:28 pm 
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Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Mathimagics wrote:
This puzzle should be anything but routine: (for SudokuPK-004)

and

Oh dear, I seem to have lost my audience ... :(

Did I make the puzzles too hard? Not hard enough? Not interesting enough? :?:

I used one somewhat more advanced step for SudokuPK-004, which I've explained in my walkthrough for those unfamiliar with it. The rest of my solving path was about the same level as SudokuPK-002.

Here is my walkthrough for SudokuPK-004:
This puzzle is essentially a jigsaw killer with gaps to place the killer cage totals, in kakuro style. Since there are 11 rows and columns I’ve labelled them 1 to 9, then A and B. Jigsaw nonets have been identified by their upper left-hand cells.

Initial Placements.
a) 45 rule on R3 1 innie R3C1 = 4, placed for NR1C1
b) 45 rule on R7 1 innie R7C1 = 5, placed for NR7C1
c) 45 rule on R9 1 innie R9CB = 8, placed for NR8C9
d) 45 rule on C5 1 innie R8C5 = 3, placed for NR4C6
e) 45 rule on C7 1 innie R4C7 = 7, placed for NR4C6

Prelims, including hidden pairs, taking account of initial placements.

a) R12C2 = {19/28/37}, no 5,6
b) R1BC6 = 15 = {69/78}
c) R12C7 = {59/68}
d) R13C9 = 5 = [23/32/41], R1C9 = {234}, R3C9 = {123}
e) R23C4 = 6 = [15/42/51] -> R2C4 = {145}, R3C4 = {125}
f) R2C78 = [56/65/83/92] -> R2C8 = {2356}
g) R2CAB = {29/47/56}/[83], no 1, no 3 in R2CA
h) R4CAB = [39/84/93], R4CA = {389}, R4CB = {349}
i) R7C34 = {19/28/37/46}
j) R8C12 = [29/74/92], R8C1 = {279}, R8C2 = {249}
k) R9BC3 = 10 = {19/37/46}/[28], no 2,5 in RBC3
l) R9AC8 = [59/68/95] -> R9C8 = {569}, RAC8 = {589}
m) RAC12 = {69/78}
n) RABC5 = {15/24}
o) RAC45 = {25}/[34/61] -> RAC4 = {2356}
p) RABCA = 9 = {27/36/45}, no 1,9
q) 8(3) cage at R4C2 = {125/134}
r) 27(4) cage at R8C2 = {3789/4689/5679}, no 1,2

1. R7C1 = 5 -> R89AC1 = 12, R8AC1 cannot total 11 which clashes with R8C12, combination crossover clash (CCC) -> no 1 in R9C1
[For those unfamiliar with CCC, R8C12 cannot have the same total as R8AC1 because they share a common cell R8C1 while R8C2 and RAC1 are in the same nonet; note that it’s not necessary for R8C1 to be in the same nonet although in this case it is.]
1a. R89AC1 = 12 = {237} (only remaining combination) = R89AC1 = [237], R8C2 = 9, all placed for NR7C1, clean-up: no 1 in R12C2, no 2 in RBCA
1b. RAC1 = 7 -> RAC2 = 8, clean-up: no 2 in R12C2, no 6 in R9C8
1c. Naked pair {37} in R12C2, locked for C2 and NR1C1
1d. Naked pair {46} in R9BC2, locked for C2 and NR7C1 -> R9C3 = 1, R9BC3 = 10 -> RBC3 = 9, placed for NR6C4, clean-up: no 6 in R1C6, no 1 in R7C4
1e. Naked triple {125} in R456C4, locked for NR4C1, clean-up: no 8 in R7C4
1f. R12C1 = {19} (hidden single in NR1C1), 9 locked for C1
1g. Naked pair {68} in R45C1, locked for NR4C1
1h. R5C4 = 9 (hidden single in NR4C1)
1i. R3C6 = 3 (hidden single in NR1C5), clean-up: no 2 in R1C9
1j. Naked pair {59} in R9AC8, locked for C8 and NR7C7, clean-up: no 6 in R2C7, no 8 in R1C7
1k. 7 in NR7C7 only in R9BC6, locked for C6, clean-up: no 8 in RBC6
1l. 8 in NR7C7 only in R78BC7, locked for C7, clean-up: no 6 in R1C7, no 3 in R2C8
1m. Naked pair {59} in R12C7, locked for C7
1n. 1,2,6,7,8 in NR1C7 only in R123456C8, locked for C8
1o. 1 in NR7C7 only in R78ABC7, locked for C7

2. 12(3) cage at R4C1 = {156} (only remaining combination) = [615], R5C1 = 8

3. 18(3) cage at R1C1 = {279/369} (cannot be {189} which clashes with R1C6, cannot be {378} which clashes with R2C2) -> R1C1 = 9, R2C1 = 1, R1C6 = 8 -> RBC6 = 7, 8 placed for NR1C5, R12C7 = [59], clean-up: no 2 in R2CAB, no 5 in R3C4, no 2 in RACA
3a. R6C5 = 8 (hidden single in C5)
3b. R7C9 = 8 (hidden single in C9), placed for NR5C9
3c. 7 in NR8C9 only in R89C9, locked for C9
3d. 21(4) cage at R4C5 contains 2 (for R4) and 7 = {2379/2478}
3e. 3,8 on in R4C8 -> R4C8 = {38}
[Alternatively hidden killer pair 3,8 in R4C8 and R4CAB for R4, R4CAB contains one of 3,8 -> R4C8 = {38}.]

4. 8 in RB only in RBC47
4a. 32(6) cage at RBC2 contains 7,8,9 = {134789} (cannot be {125789} because RBC2 only contains 4,6) -> RBC2 = 4, RBC5 = 1, placed for NR6C4, RBC47 = {38}, 3 locked for RB
4b. RBC5 = 1 -> RAC5 = 5, placed for NR6C4, R9AC8 = [59]
4c. R9C2 = 6
4d. Naked pair {24} in R9C67, locked for R9 and NR7C7 -> R9C49 = [79]
4e. R8C9 = 7 (hidden single in NR8C9)
4f. R23C4 = [51] (hidden pair in C4), R3C9 = 2 (placed for NR1CA) -> R1C9 = 3, placed for NR1C7, R12C2 = [73], R4C8 = 8, clean-up: no 6,8 in R2CA, no 6 in R2CB, no 4 in R4CB
4g. Naked pair {47} in R2CAB, locked for R2 and NR1CA
4h. Naked pair {39} in R4CAB, locked for R4 and NR1CA

5. Naked pair {56} in RBC9A, locked for NR8C9
5a. R9BCB = [82] = 10 -> R78ACB = 11 = {137/146}, no 9, 1 locked for CB
5b. R4CB = 9 (hidden single in CB) -> R4CA = 3, RACA = 4 -> RBCA = 5, RABC9 = [16]
5c. RACB = 3 -> R78CB = [71], both placed for NR5C9, R8CA = 6
5d. R7C8 = 3 (hidden single in C8)
5e. R3CA = 8 -> R3C38 = [67]

6. 45 rule on R5 3 innies R5C89B = 15 = {456} (only remaining combination), locked for R5
6a. R1C3A = [21]
6b. Naked pair {46} in R15C8, locked for C8

and the rest is naked singles.


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 Post subject: Re: Psycho Killer Jigsaw
PostPosted: Sun May 12, 2019 6:33 pm 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Additional Comment:
Note that Law of Leftovers applies to these puzzles because each row, column and jigsaw nonet contains 1 … 9.
I didn't use LoL for any of these three puzzles because the results came out easily enough.
However it can be useful in harder puzzles to make eliminations or just to indicate an area to search for a more routine step.


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