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Andrew
PostPosted: Sun May 05, 2013 2:11 am 
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Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Texas Jigsaw Killer 4 by Ruud (June 2006)
Puzzle Diagrams:
ImageImage
Code: Select, Copy & Paste into solver:
SumoCueV1=8J0=11J0=11J0+2J0=9J1=11J2+5J2=6J2=13J2+0J0+1J0=9J1+11J1+4J1=12J1+14J1+7J2+8J2=7J0+18J3=17J3=15J1+21J1+21J1=9J3=13J3+25J2=21J0+27J4+20J3=9J3+30J3+30J3+24J3=21J5+34J2+27J0+27J4=22J4+38J4=28J6=15J5+41J5+34J5+34J2=7J7+38J4+38J4+40J4+40J6+40J5+41J5+41J5=9J8+45J7=10J4+55J7=14J6+57J6+57J6=8J8+60J5+53J8=15J7=15J4+64J7=13J6+66J6+66J6=28J8+69J5=8J8+63J7+64J7+64J7=11J7+75J6+75J8+69J8+69J8+71J8
Solution: 
+-------+-------+-------+
| 1 6 2 | 9 7 8 | 3 5 4 |
| 7 5 3 | 6 2 4 | 8 1 9 |
| 3 4 8 | 1 5 9 | 2 6 7 |
+-------+-------+-------+
| 8 2 9 | 5 3 1 | 7 4 6 |
| 4 7 5 | 3 8 6 | 1 9 2 |
| 2 8 6 | 4 9 7 | 5 3 1 |
+-------+-------+-------+
| 5 9 1 | 7 4 3 | 6 2 8 |
| 9 1 7 | 2 6 5 | 4 8 3 |
| 6 3 4 | 8 1 2 | 9 7 5 |
+-------+-------+-------+

Quote:
SSscore: 0.85

Andrew (in 2013): Just a little harder.

Andrew's walkthrough:
Prelims

a) R12C1 = {17/26/35}, no 4,8,9
b) R12C2 = {29/38/47/56}, no 1
c) R1C34 = {29/38/47/56}, no 1
d) R12C5 = {18/27/36/45}, no 9
e) R1C67 = {29/38/47/56}, no 1
f) R12C8 = {15/24}
g) R12C9 = {49/58/67}, no 1,2,3
h) R2C34 = {18/27/36/45}, no 9
i) R2C67 = {39/48/57}, no 1,2,6
j) R3C12 = {16/25/34}, no 7,8,9
k) R34C3 = {89}
l) R34C7 = {18/27/36/45}, no 9
m) R3C89 = {49/58/67}, no 1,2,3
n) R67C1 = {16/25/34}, no 7,8,9
o) R67C9 = {18/27/36/45}, no 9
p) R7C23 = {19/28/37/46}, no 5
r) R7C78 = {17/26/35}, no 4,8,9
s) R89C1 = {69/78}
t) R89C9 = {17/26/35}, no 4,8,9
u) 9(3) cage at R4C4 = {126/135/234}, no 7,8,9
v) 11(3) cage at R9C4 = {128/137/146/236/245}, no 9
w) 28(4) cage at R5C5 = {4789/5689}, no 1,2,3
x) 28(4) cage at R8C7 = {4789/5689}, no 1,2,3

1. Naked pair {89} in R34C3, locked for C3 and NR3C2, clean-up: no 2,3 in R1C4, no 1 in R2C4, no 1 in R34C7, no 4,5 in R3C9, no 1,2 in R7C2

2. 45 rule on R789 2 outies R6C19 = 3 = {12}, locked for R6, R7C1 = {56}, R7C9 = {78}
2a. R89C9 = {26/35} (cannot be {17} which clashes with R67C9), no 1,7

3. 9(3) cage at R4C4 = {126/135} (cannot be {234} which clashes with R34C7), no 4, 1 locked for R4 and NR3C2, clean-up: no 6 in R3C1
3a. R34C7 = {27/45} (cannot be {36} which clashes with 9(3) cage), no 3,6
3b. Killer pair 2,5 in R34C7 and 9(3) cage, locked for NR3C2, clean-up: no 2,5 in R3C1, no 8 in R3C9
3c. Killer pair 4,6 in R3C12 and R3C89, locked for R3, clean-up: no 5 in R4C7

4. Killer triple 5,6,7 in R12C1, R7C1 and R89C1, locked for C1

5. 45 rule on C1 3 innies R345C1 = 15 = {249/348}, no 1, clean-up: no 6 in R3C2
5a. Naked pair {34} in R3C12, locked for R3, clean-up: no 9 in R3C9
5b. Naked pair {67} in R3C89, locked for R3, clean-up: no 2 in R4C7
5c. R12C9 = {49/58} (cannot be {67} which clashes with R3C9), no 6,7

6. 15(3) cage at R3C4 = {159} (only remaining combination, cannot be {258} which clashes with R3C7), locked for R3 and NR1C5 -> R34C3 = [89], R3C7 = 2, R4C7 = 7, both placed for NR3C2 -> R3C8 = 6, placed for NR3C2, R3C9 = 7, placed for NR1C6, clean-up: no 4,8 in R12C5, no 4,9 in R1C6, no 4 in R1C7, no 4 in R2C3, no 4,8 in R2C4, no 3,7 in R2C6, no 3 in R2C7, no 1 in R7C8
[Alternatively 1 in R3 only in 15(3) cage = {159} …]
6a. Naked pair {48} in R2C67, locked for R2, clean-up: no 3,7 in R1C2, no 2 in R1C8, no 5,9 in R1C9

7. R7C9 = 8, R6C9 = 1, both placed for NR6C9, R6C1 = 2, R7C1 = 5, both placed for NR6C1, R1C9 = 4, R2C9 = 9, placed for NR1C6, clean-up: no 3,6 in R12C1, no 2 in R1C2, no 7 in R1C34, no 2 in R1C6, no 7 in R2C2, no 2 in R2C8, no 3 in R7C7, no 3,7 in R7C8
7a. Naked pair {15} in R12C8, locked for C8 and NR1C6, clean-up: no 6 in R1C67
7b. Naked pair {38} in R1C67, locked for R1 and NR1C6, clean-up: no 3 in R2C2, no 6 in R2C5
7c. Naked pair {26} in R45C9, locked for C9 and 21(4) cage at R4C8

8. R45C9 = {26} = 8 -> R45C8 = 13 = [49], both placed for NR4C8, R9C8 = 7, R8C8 = 8, placed for NR4C8, R67C8 = [32], both placed for NR4C8, R7C7 = 6, placed for NR6C9, R56C7 = [15], clean-up: no 4 in R7C23
8a. Naked pair {49} in R89C7, locked for C7 -> R2C67 = [48], R1C67 = [83]
8b. Naked pair {67} in R56C6, locked for C6

9. Naked triple {135} in 9(3) cage at R4C4, locked for R4 and NR3C2 -> R3C2 = 4, R3C1 = 3, R45C1 = [84] = 12 -> R45C2 = 9 = [27/63], clean-up: no 7 in R8C1
9a. Killer pair 2,6 in R12C2 and R4C2, locked for C2
9b. Naked pair {69} in R89C1, locked for NR6C1

10. 4 in R7 only in 14(3) cage at R7C4, locked for NR5C5

11. Naked pair {35} in R89C9, locked for NR6C9 -> R9C6 = 2
11a. 2 in R8 only in 13(3) cage at R8C4 = {256} (only remaining combination) -> R8C6 = 5, placed for NR5C5, R8C45 = {26}, locked for R8 and NR5C5 -> R89C1 = [96], R89C7 = [49], R89C9 = [35]
11b. R9C6 = 2 -> R9C45 = 9 = {18}, locked for R9 -> R9C2 = 3, placed for NR6C1, R9C3 = 4, R5C2 = 7, R4C2 = 2 (step 10), R45C9 = [62], R5C5 = 8, R56C6 = [67], R6C5 = 9, placed for NR5C5, R6C234 = [864], R9C5 = 1, placed for NR5C5, R7C6 = 3, clean-up: no 5 in R1C4, no 3 in R2C4

12. R3C5 = 5, R4C56 = [31], R4C4 = 5, R5C34 = [53], R1C3 = 2, R8C23 = [17], R2C3 = 3, R2C4 = 6

and the rest is naked singles, without using the nonets.
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Andrew
PostPosted: Sun May 05, 2013 3:06 am 
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Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Texas Jigsaw Killer 5 by Ruud (July 2006)
Puzzle Diagrams:
ImageImage
Code: Select, Copy & Paste into solver:
SumoCueV1=18J0+0J0=12J1+2J1=16J1=8J1+5J1=23J2+7J2=19J0+0J0+0J0+4J1+4J1+4J1+7J2+7J2=23J2+9J3+9J0=15J0+20J0=24J1=9J2+23J2+17J2+17J4+9J3=20J3+20J0+22J5+22J5+22J5+23J2=23J4+17J4=20J6+28J3+28J3+28J5=9J5+34J5+34J4+34J4=28J7+36J6+36J6=20J3+47J3+40J5=15J4+50J4+44J7+44J7=13J6+36J6+36J6+47J3+40J5+50J4+44J7+44J7=7J7+54J6=19J6=10J8=22J3+66J5+66J4=21J8=11J7+62J7+64J6+64J8+65J8+65J8+66J8+69J8+69J8+70J8+70J7
Solution: 
+-------+-------+-------+
| 9 1 8 | 4 7 5 | 3 6 2 |
| 4 3 5 | 6 1 2 | 7 8 9 |
| 5 8 6 | 2 9 3 | 1 4 7 |
+-------+-------+-------+
| 2 4 7 | 1 8 6 | 5 9 3 |
| 8 6 1 | 9 3 7 | 2 5 4 |
| 1 2 9 | 3 4 8 | 6 7 5 |
+-------+-------+-------+
| 7 5 4 | 8 2 1 | 9 3 6 |
| 6 9 3 | 7 5 4 | 8 2 1 |
| 3 7 2 | 5 6 9 | 4 1 8 |
+-------+-------+-------+

Quote:
SSscore: 0.95

Andrew (in 2013):
Hint:
J comes before K and remember to keep looking at the Js.

Andrew's walkthrough:
Prelims

a) R1C34 = {39/48/57}, no 1,2,6
b) R1C67 = {17/26/35}, no 4,8,9
c) R78C1 = {49/58/67}, no 1,2,3
d) R89C9 = {16/25/34}, no 7,8,9
e) 9(3) cage at R3C6 = {126/135/234}, no 7,8,9
f) 9(3) cage at R5C5 = {126/135/234}, no 7,8,9
g) 20(3) cage at R6C3 = {389/479/569578}, no 1,2
h) 19(3) cage at R8C2 = {289/379/469/478/568}, no 1
i) 10(3) cage at R8C3 = {127/136/145/235}, no 8,9
j) 21(3) cage at R8C7 = {489/578/678}, no 1,2,3
k) 11(3) cage at R8C8 = {128/137/146/236/245}, no 9

1. 45 rule on NR1C3 1 innie R3C5 = 9, placed for NR1C3, clean-up: no 3 in R1C34

2. 9 in NR4C4 only in R5C46, locked for R5
2a. 45 rule on NR4C4 3 remaining innies R5C46 + R8C5 = 21 = {489/579}, no 1,2,3,6

3. 45 rule on NR5C1 1 outie R9C2 = 7, R8C2 + R9C1 = 12 = {39/48}, no 2,5,6
3a. R78C1 = {58/67} (cannot be {49} which clashes with R8C1 + R9C1), no 4,9

4. 45 rule on NR5C9 1 outie R9C8 = 1, R8C8 + R9C9 = 10 = {28/46}/[73], no 5, no 3 in R8C8

5. R9C2 = 7, R9C8 = 1, both placed for NR8C3 [Deliberately left until now, for simplicity.]
5a. 10(3) cage at R8C3 = {235} (only remaining combination), locked for NR8C3
5b. 21(3) cage at R8C7 = {489} (only remaining combination), locked for NR8C3 -> R9C5 = 6, clean-up: no 4 in R8C8 (step 4)

6. 9(3) cage at R5C5 = {135/234}, 3 locked for C5 and NR4C4
6a. Killer pair 4,5 in R5C46 + R8C5 and 9(3) cage, locked for NR4C4
6b. 6 in NR4C4 only in R4C46, locked for R4

7. 45 rule on NR1C1 2 outies R34C1 = 7 = {25/34}/[61], no 7,8,9, no 1 in R3C1
7a. 45 rule on NR1C1 2 innies R2C1 + R3C2 = 12 = [48/75/84/93], no 1,2,6, no 3,5 in R2C1

8. 45 rule on NR1C8 2 outies R34C9 = 10 = [19]/{28/37}[64], no 5, no 4 in R3C9, no 1 in R4C9
8a. 45 rule on NR1C8 2 innies R2C9 + R3C8 = 13 = {58/67}/[94], no 1,2,3, no 4 in R2C9

9. 45 rule on R89 2 outies R7C19 = 13 = [76/85], R8C1 = {56}, R8C9 = {12}

10. 45 rule on R12 2 innies R2C19 = 13 = [49/76/85], clean-up: no 3 in R3C2 (step 7a), no 5,6 in R3C8 (step 8a)

11. 45 rule on R1234 2 innies R4C28 = 13 = {49/58}, no 1,2,3,7

12. 45 rule on R6789 3 outies R5C159 = 15, max R5C5 = 5 -> min R5C19 = 10, no 1 in R5C19

13. 45 rule on NR1C1 + NR3C1 1 outie R5C4 = 1 remaining innie R8C4 + 2 -> R8C4 = {2357}, no 8 in R5C4

14. 45 rule on NR1C8 + NR3C9 1 outie R5C6 = 1 remaining innie R8C6 + 3 -> R8C6 = {1245}, no 9 in R5C6
14a. R5C4 = 9 (hidden single in R5), R8C4 = 7 (step 13), placed for NR3C1, clean-up: no 5 in R1C3, no 4 in R4C8 (step 11), no 3 in R9C9 (step 4)
14b. R8C4 + R9C5 = [76] = 13 -> R8C56 = 9 = [45/54/81], no 2, clean-up: no 5 in R5C6

15. R6C3 = 9 (hidden single in NR3C1), R67C4 = 11 = {38/56}, no 4
15a. 45 rule on C1234 2 remaining innies R24C4 = 7 = [16/52/61]
15b. R67C4 = {38} (cannot be {56} which clashes with R24C4), locked for C4 and NR3C1, clean-up: no 4 in R1C3, no 4 in R34C1 (step 7), no 5 in R4C8 (step11)
15c. R24C4 = {16} (cannot be [52] which clashes with R9C4), locked for C4
15d. Killer pair 5,6 in R34C1 and R8C1, locked for C1

16. 3,7,9 in NR5C9 only in 28(5) cage at R6C9 = {13789/34579}, no 2,6, 9 locked for R7

[Clean-ups omitted from here.]
17. 10(3) cage at R8C3 = {235}, 3 locked for C3
17a. 15(3) cage at R3C3 = {267} (only remaining combination, cannot be {168} because R3C4 only contains 2,4,5, cannot be {258/456} which clash with R2C1 + R3C2) -> R3C4 = 2, R34C3 = [67], all placed for NR1C1, R9C4 = 5, R1C34 = [84], both placed for NR1C3, R3C1 = 5, R4C1 = 2 (step 7), both placed for NR3C1, R4C2 = 4, R3C2 = 8, R2C1 = 4, R2C9 = 9 (step 10), placed for NR1C8, R3C8 = 4 (step 8a), R8C1 = 6, placed for NR5C1, R7C1 = 7, R7C9 = 6 (step 9), R8C9 = 1, placed for NR5C9
17a. Naked pair {23} in R89C3, locked for C3
17b. R5C23 = [61], R2C3 = 5, R7C3 = 4

18. Naked triple {168} in 24(4) cage at R3C5, locked for R4 and NR4C4 -> R4C8 = 9, R4C9 = 3, R3C9 = 7, all placed for NR3C9
18a. R4C7 = 5, placed for NR1C8 -> R1C9 = 2
18b. Naked pair {13} in R3C67, locked for NR1C8

19. R8C8 + R9C9 (step 4) = {28} (only remaining combination) -> R8C8 = 2, R9C9 = 8, placed for NR5C9, R89C3 = [32], R8C2 = 9, R9C1 = 3, placed for NR5C1, R5C1 = 8, R6C1 = 1

20. R5C8 = 5, placed for NR3C9, R5C9 = 4, R5C7 = 2, R5C5 = 3, R6C9 = 5, R6C2 = 2, R6C5 = 4, R7C5 = 2 (cage sum)

and the rest is naked singles, without using the nonets.
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Andrew
PostPosted: Sun May 05, 2013 3:56 am 
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Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Texas Jigsaw Killer 6 by Ruud (July 2006)
Puzzle Diagrams:
ImageImage
Code: Select, Copy & Paste into solver:
SumoCueV1=20J0+0J0=11J0+2J0=13J1=6J1+5J1=12J1+7J1+0J0=11J0+10J2+10J2+4J2=19J2+14J2=14J1+7J1=5J0=7J2=9J2+20J3+4J3+14J3=15J3+16J3=15J1+18J0+19J2=6J4=9J4=20J4+31J4+24J4=15J3+26J1=15J0+36J2+29J4+30J5+31J5+31J5=12J4+34J3+34J6=10J7+45J8=18J4=19J5+48J5+48J5+42J4=9J3=8J6=9J7+47J8+47J8=16J5+57J5+57J5+42J8+52J3+53J6+54J7=15J7=13J8+65J8=8J8=8J8+68J8+52J6=17J6+64J7+64J7=11J7+74J7+67J7=10J6+77J6+71J6+71J6
Solution: 
+-------+-------+-------+
| 8 7 2 | 9 3 5 | 1 4 6 |
| 5 3 7 | 1 6 8 | 4 9 2 |
| 1 2 3 | 6 4 7 | 9 5 8 |
+-------+-------+-------+
| 4 5 1 | 2 8 9 | 6 3 7 |
| 6 9 5 | 7 2 1 | 3 8 4 |
| 9 1 4 | 8 5 6 | 7 2 3 |
+-------+-------+-------+
| 7 6 8 | 3 9 4 | 2 1 5 |
| 2 8 9 | 4 7 3 | 5 6 1 |
| 3 4 6 | 5 1 2 | 8 7 9 |
+-------+-------+-------+

SSscore: 0.90


Andrew's 2013 walkthrough:
Prelims

a) R1C34 = {29/38/47/56}, no 1
b) R1C67 = {15/24}
c) R23C8 = {59/68}
d) R34C1 = {14/23}
e) R34C2 = {16/25/34}, no 7,8,9
f) R3C34 = {18/27/36/45}, no 9
g) R34C7 = {69/78}
h) R34C9 = {69/78}
i) R45C3 = {15/24}
j) R45C4 = {18/27/36/45}, no 9
k) R5C12 = {69/78}
l) R6C12 = {19/28/37/46}, no 5
m) R67C9 = {17/26/35}, no 4,8,9
n) R78C1 = {18/27/36/45}, no 9
o) R8C34 = {49/58/67}, no 1,2,3
p) R89C5 = {17/26/35}, no 4,8,9
q) R8C67 = {17/26/35}, no 4,8,9
r) R9C34 = {29/38/47/56}, no 1
s) R9C67 = {19/28/37/46}, no 5
t) 20(3) cage at R1C1 = {389/479/569/578}, no 1,2
u) 11(3) cage at R2C2 = {128/137/146/236/245}, no 9
v) 19(3) cage at R2C6 = {289/379/469/478/568}, no 1
w) 19(3) cage at R6C4 = {289/379/469/478/568}, no 1
x) 9(3) cage at R6C8 = {126/135/234}, no 7,8,9

1. 45 rule on R6789 1 outie R5C7 = 3, placed for NR4C3, clean-up: no 6 in R45C4, no 5 in R8C6, no 7 in R9C6
1a. R5C7 = 3 -> R67C7 = 9 = {18/27/45}, no 6,9

2. 45 rule on R89 2 innies R8C18 = 8 = {26/35}/[71], no 4,8, no 1 in R8C1, clean-up: no 1,5,8 in R7C1

3. 45 rule on C12 2 innies R27C2 = 9 = {18/27/36/45}, no 9

4. 45 rule on NR5C4 3 innies R5C456 = 10 = {127/145}, no 6,8,9, 1 locked for R5 and NR5C4, clean-up: no 5 in R4C3, no 1 in R4C4

5. Hidden killer pair 6,8 in R5C12 and 15(3) cage at R4C8 for R5, R5C12 contains one of 6,8 -> 15(3) cage must contain one of 6,8 in R5 -> 15(3) cage = {258/267/348/456} (cannot be {168} which clashes with R5C12, other combinations don’t contain 6 or 8), no 1,9
5a. 9 in R5 only in R5C12 = {69}, locked for R5
5b. 8 in R5 only in 15(3) cage = {258/348}, no 6,7
5c. 7 in R5 only in R5C456 (step 4) = {127}, locked for R5 and NR5C4, clean-up: no 4 in R4C3, no 4,5 in R4C4
5d. 15(3) cage = {258/348}
5e. 2,3 only in R4C8 -> R4C8 = {23}
[As with an earlier TJK, I’m deliberately avoiding using CPEs for puzzles with low SSscores. These eliminations will probably come from easier steps.]

6. 9(3) cage at R6C8 = {126/135} (cannot be {234} which clashes with R4C8), no 4, 1 locked for C8
6a. Killer pair 2,3 in R4C8 and 9(3) cage, locked for C8
6b. Killer pair 5,6 in R23C8 and 9(3) cage, locked for C8

7. 15(3) cage at R4C8 (step 5b) = {258/348}
7a. R45C3 = [15] (cannot be [24] which clashes with 15(3) cage, combo blocker), both placed for NR4C3, clean-up: no 6 in R1C4, 4 in R3C1, no 6 in R3C2, no 4,8 in R3C4, no 4,8 in R7C7 (step 1a), no 8 in R8C4, no 6 in R9C4
7b. 15(3) cage = {348} -> R4C8 = 3, placed for NR3C4, clean-up: no 2 in R3C1, no 4 in R3C2, no 6 in R3C3, no 5 in R8C1 (step 2), no 4 in R7C1
7c. 9(3) cage at R6C8 (step 6) = {126} (only remaining combination), locked for C8, clean-up: no 8 in R23C8, no 3 in R8C1 (step 2a), no 6 in R7C1
7d. Naked pair {59} in R23C8, locked for C8

8. 19(3) cage at R6C4 = {469/568}, no 3, 6 locked for R6 and NR4C4, clean-up: no 4 in R6C12, no 2 in R7C9
8a. 16(3) cage at R7C4 = {349/358}, 3 locked for R7, clean-up: no 5 in R6C9, no 6 in R8C1, no 2 in R8C8 (step 2a)
8b. Naked triple {126} in 9(3) cage at R6C8, 2 locked for NR3C4, clean-up: no 7 in R3C3

9. Naked pair {27} in R78C1, locked for C1 and NR6C1, clean-up: no 3 in R3C1, no 3,8 in R6C2, no 4,9 in R9C34
9a. R34C1 = [14], both placed for NR1C1, clean-up: no 7 in R1C34, no 3 in R3C2, no 8 in R3C3, no 6 in R4C2, no 9 in R6C2

10. 4 in NR6C1 only in R89C2, locked for C2
10a. 15(3) cage at R8C2 = {348/456}, no 1,9
10b. R6C1 = 9, R9C5 = 1 (hidden singles in NR6C1), R6C2 = 1, R8C5 = 7, both placed for NR6C2, R5C1 = 6, placed for NR1C1, R5C2 = 9, placed for NR2C3, R5C5 = 2, R6C8 = 2, clean-up: no 5 in R1C4, no 7 in R4C4, no 7 in R7C7 (step 1a), no 6,7 in R7C9, no 6 in R8C34, no 9 in R9C67

11. R6C9 = 3 (hidden single in R6), placed for NR5C9, R7C9 = 5, clean-up: no 4 in R6C7 (step 1a), no 7 in R9C7
11a. 16(3) cage at R7C4 (step 8a) = {349} (only remaining combination), locked for R7 and NR5C4
11b. Naked triple {568} in 19(3) cage at R6C4, locked for R6 -> R6C7 = 7, placed for NR4C3, R7C7 = 2 (cage sum), R78C1 = [72], R6C3 = 4, clean-up: no 4 in R1C6, no 5 in R3C4, no 8 in R34C7, no 9 in R8C4, no 6 in R8C67

12. Naked triple {689} in R4C567, locked for R4 -> R4C4 = 2, R5C4 = 7, R5C6 = 1, R34C2 = [25], both placed for NR2C3, R4C9 = 7, R3C9 = 8, both placed for NR1C5, R1C8 = 4, R5C8 = 8, R5C9 = 4, placed for NR5C9, R9C8 = 7, R3C3 = 3, placed for NR2C3, R3C4 = 6, placed for NR3C4, R34C7 = [96], R9C7 = 8, R9C6 = 2, R9C3 = 6, R9C4 = 5, R78C3 = [89], R2C3 = 7, R1C3 = 2, R1C4 = 9

and the rest is naked singles, without using the nonets.
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Andrew
PostPosted: Mon May 06, 2013 1:04 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Texas Jigsaw Killer 7 by Ruud (July 2006)
Puzzle Diagrams:
ImageImage
Code: Select, Copy & Paste into solver:
SumoCueV1=15J0+0J0=12J0=25J0+3J0=21J1+5J1+5J1=9J2+0J0+0J0+2J3+3J0+3J0=6J1=18J1+15J1+8J2=8J4=15J3+2J3=24J3+21J5+14J1+15J1+15J1=7J2+18J4+19J4=18J3+21J5+21J5=20J5=18J6=16J2+26J2+18J4=8J3+29J3+32J3+32J5+32J6+33J6+34J6=19J2=14J4+37J4+29J3+32J5=18J5+49J5+33J6=4J2+44J2+45J4=18J7+55J7=6J7+49J5+49J6=9J6+52J6+44J2=13J4+55J7+55J7+57J7=20J8+67J8+60J6=23J8+70J8+63J4=21J7+73J7+73J7+67J8+67J8+60J8+70J8+70J8
Solution: 
+-------+-------+-------+
| 3 1 5 | 6 2 9 | 8 4 7 |
| 7 4 1 | 9 8 5 | 3 6 2 |
| 5 8 6 | 4 9 1 | 7 2 3 |
+-------+-------+-------+
| 1 7 2 | 8 3 6 | 5 9 4 |
| 2 5 9 | 3 1 8 | 4 7 6 |
| 6 3 7 | 2 5 4 | 9 1 8 |
+-------+-------+-------+
| 8 9 4 | 1 7 2 | 6 3 5 |
| 4 2 3 | 5 6 7 | 1 8 9 |
| 9 6 8 | 7 4 3 | 2 5 1 |
+-------+-------+-------+

Quote:
SSscore: 0.85

Andrew (in 2013): A simpler one. The jigsaw pattern was easy to use.

Andrew's walkthrough:
Prelims

a) R12C9 = {18/27/36/45}, no 9
b) R23C6 = {15/24}
c) R34C2 = {69/78}
d) R34C9 = {16/25/34}, no 7,8,9
e) R45C8 = {79}
f) R56C2 = {17/26/35}, no 4,8,9
g) R67C1 = {59/68}
h) R67C8 = {13}
i) R78C4 = {15/24}
j) R89C1 = {49/58/67}, no 1,2,3
k) 21(3) cage at R1C6 = {489/579/678}, no 1,2,3
l) 8(3) cage at R3C1 = {125/134}
m) 19(3) cage at R5C9 = {289/379/469/478/568}, no 1
n) 9(3) cage at R7C7 = {126/135/234}, no 7,8,9
o) 21(3) cage at R9C2 = {489/579/678}, no 1,2,3

Steps resulting from Prelims
1a. Naked pair {79} in R45C8, locked for C8
1b. Naked pair {13} in R67C8, locked for C8
1c. 8(3) cage at R3C1 = {125/134}, 1 locked for C1 and NR3C1, clean-up: no 7 in R5C2
1d. R89C1 = {49/67} (cannot be {58} which clashes with R67C1), no 5,8
1e. Killer pair 6,9 in R67C1 and R89C1, locked for C1

2. 45 rule on NR1 1 innie R1C3 = 5, placed for NR1C1, clean-up: no 4 in R2C9
2a. R1C3 = 5 -> R23C3 = 7 = {16/34}, no 2,7,8,9
2b. 21(3) cage at R1C6 = {489/678}, 8 locked for R1 and NR1C6, clean-up: no 1 in R2C9

3. 45 rule on NR8C5 1 innie R9C7 = 2, placed for NR8C5
3a. R9C7 = 2 -> R78C7 = 7 = {16/34}, no 5
3b. Killer pair 1,3 in R78C7 and R7C8, locked for NR4C7
3c. 18(3) cage at R4C7 = {459/567} (cannot be {468} which clashes with R78C7), no 8, 5 locked for C7 and NR4C7
3d. 2 in NR4C7 only in R57C6, locked for C6, clean-up: no 4 in R23C6
3e. Naked pair {15} in R23C6, locked for C6 and NR1C6

4. 45 rule on C123 1 outie R9C4 = 7, placed for NR7C2, clean-up: no 6 in R8C1
4a. R9C4 = 7 -> R9C23 = 14 = [59/68/86], no 4, no 9 in R9C2

5. R1C7 = 8 (hidden single in C7)
5a. 45 rule on C789 1 outie R1C6 = 9, R1C8 = 4 (cage sum), both placed for NR1C6, clean-up: no 5 in R2C9
5b. Naked pair {26} in R23C8, locked for C8 and 18(4) cage at R2C7
5c. Naked pair {37} in R23C7, locked for C7
5f. 18(3) cage at R4C7 (step 3c) = {459} (only remaining combination), locked for C7 and NR4C7 -> R5C8 = 7, placed for NR4C7
5g. Naked pair {16} in R78C7, locked for NR4C7 -> R7C8 = 3
5h. Naked pair {28} in R57C6, locked for C6

6. R46C8 = [91], both placed for NR1C9, clean-up: no 8 in R2C9, no 6 in R3C2, no 6 in R34C9
6a. Killer pair 2,3 in R12C9 and R34C9, locked for C9

7. Naked pair {58} in R89C8, locked for NR8C5
7a. R89C9 = {19} (hidden pair in C9), locked for NR8C5
7b. R9C9 = 1 (hidden single in R9), R8C9 = 9
7c. 20(4) cage at R8C5, 7 locked for R8 -> R8C1 = 4, R9C1 = 9, clean-up: no 3 in 8(3) cage at R3C1, no 5 in R67C1, no 2 in R7C4, no 5 in R9C2
7d. Naked pair {68} in R9C23, locked for R9 and NR7C2 -> R89C8 = [85]

8. Naked pair {34} in R9C56, locked for 20(4) cage at R8C5
8a. Naked pair {67} in R8C56, locked for R8 -> R67C7 = [61], R67C1 = [68], placed for NR3C1 -> R4C2 = 7, R3C2 = 8, placed for NR2C3, R9C23 = [68], R57C6 = [82], clean-up: no 1,2 in R5C2, no 2 in R6C2, no 5 in R7C4

9. Naked triple {125} in 8(3) cage at R3C1, locked for C1 and NR3C1 -> R6C2 = 3, R5C2 = 5, placed for NR2C3, R8C23 = [23], R8C4 = 5, R7C4 = 1, R1C2 = 1, placed for NR1C1
9a. Naked pair {37} in R12C1, locked for NR1C1, R1C2 = 1, R2C2 = 4 (cage sum), R7C23 = [94]
9b. Naked pair {16} in R23C3, locked for C3 and NR2C3
9c. 18(3) cage at R4C3 = [297], placed for NR2C3, R6C6 = 4, placed for NR3C5, R5C7 = 4

and the rest is naked singles, without using the nonets.
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Andrew
PostPosted: Mon May 06, 2013 2:06 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Texas Jigsaw Killer 8 by Ruud (July 2006)
Puzzle Diagrams:
ImageImage
Code: Select, Copy & Paste into solver:
SumoCueV1=15J0+0J0=10J1+2J1=23J1+4J2+4J2+4J2=10J2+0J0=18J0+10J0=5J1+12J1=16J1+14J1+8J2+8J2=19J3+10J0+10J0=17J0+21J4+21J1+14J5=14J2=7J2+18J3=13J3=13J0+29J4=24J4=15J1+32J5+25J5+26J2+18J3+28J3=12J3+31J4+31J4+31J4+32J5=13J5=17J5=6J6=5J3+38J3+38J7+31J4=10J4+50J8+43J5+44J5+45J6+46J6=11J3=20J7+57J4+57J8=14J8+60J8+44J5=20J6+63J6+56J7+56J7=15J7+67J7+60J8+60J8=18J8+63J6=19J6+73J6+73J6+73J7=6J7+77J7+71J8+71J8
Solution: 
+-------+-------+-------+
| 1 6 8 | 2 3 4 | 9 7 5 |
| 8 7 5 | 1 4 9 | 6 2 3 |
| 7 2 4 | 3 9 5 | 1 8 6 |
+-------+-------+-------+
| 3 8 9 | 4 2 7 | 5 6 1 |
| 9 5 6 | 7 8 1 | 3 4 2 |
| 2 4 1 | 5 6 3 | 7 9 8 |
+-------+-------+-------+
| 4 1 2 | 9 5 6 | 8 3 7 |
| 5 9 3 | 6 7 8 | 2 1 4 |
| 6 3 7 | 8 1 2 | 4 5 9 |
+-------+-------+-------+

Quote:
SSscore: 0.85

Andrew (in 2013): Not quite as easy as suggested by the SS score.

Andrew's walkthrough:
Prelims

a) R1C34 = {19/28/37/46}, no 5
b) R2C45 = {14/23}
c) R34C8 = {59/68}
d) R34C9 = {16/25/34}, no 7,8,9
e) R45C2 = {49/58/67}, no 1,2,3
f) R4C45 = {49/58/67}, no 1,2,3
g) R56C8 = {49/58/67}, no 1,2,3
h) R6C67 = {19/28/37/46}, no 5
i) R67C1 = {15/24}
j) R67C2 = {14/23}
k) R8C56 = {69/78}
l) R9C67 = {15/24}
m) 10(3) cage at R1C9 = {127/136/145/235}, no 8,9
n) 19(3) cage at R3C1 = {289/379/469/478/568}, no 1
o) 11(3) cage at R7C3 = {128/137/146/236/245}, no 9
p) 20(3) cage at R7C4 = {389/479/569/578}, no 1,2
q) 20(3) cage at R8C1 = {389/479/569/578}, no 1,2
r) 14(4) cage at R7C7 = {1238/1247/1256/1346/2345}, no 9

1. R56C8 = {49/67} (cannot be {58} which clashes with R34C8), no 5,8
1a. Killer pair 6,9 in R34C8 and R56C8, locked for C8

2. 45 rule on C1 2 outies R18C2 = 15 = {69/78}
2a. Min R1C2 = 6 -> max R12C1 = 9, no 9 in R12C1

3. 45 rule on C9 2 outies R29C8 = 7 = {25/34}, no 1,7,8,9
3a. Max R9C8 = 5 -> min R89C9 = 13, no 1,2,3 in R89C9

4. 45 rule on R9 3 innies R9C189 = 20 = {389/479/569/578}, no 2, clean-up: no 5 in R2C8 (step 3)

5. 45 rule on NR1C1 2 innies R3C4 + R4C3 = 12 = [39]/{48/57}, no 1,2,6, no 9 in R3C4, clean-up: no 7 in R4C4

6. 45 rule on NR6C7 2 innies R6C7 + R7C6 = 13 = {49/67}/[85], no 1,2,3, no 8 in R7C6, clean-up: no 7,8,9 in R6C6

7. 10(3) cage at R1C9 = {127/136/235} (cannot be {145} which clashes with R34C9), no 4, clean-up: no 3 in R9C8 (step 3)

8. 45 rule on NR1C6 4 innies R1C678 + R3C8 = 28 = {4789/5689}, no 1,2,3
8a. 1 in NR1C6 only in R1234C9, locked for C9

9. 45 rule on NR1C6 1 innie R3C8 = 1 outie R1C5 + 5, R1C5 = {134}, no 5 in R3C8, clean-up: no 9 in R4C8

10. Killer triple 4,5,6 in R34C8, R56C8 and R9C8, locked for C8
10a. Killer triple 7,8,9 in R1C8, R34C8 and R56C8, locked for C8

11. 18(3) cage at R8C9 = {459/567} (cannot be {468} which clashes with R6C7 + R7C6), no 8, 5 locked for NR6C7
11a. R6C7 + R7C6 (step 6) = {49/67}, no 8, clean-up: no 2 in R6C6

12. 14(4) cage at R7C7 = {1238} (hidden quad in NR6C7), 8 locked for C7
12a. 1 in NR3C7 only in R345C7, locked for C7, clean-up: no 5 in R9C6

13. 8 in C9 only in 17(3) cage at R5C9, locked for NR3C7, clean-up: no 6 in R3C8, no 1 in R1C5 (step 9)
13a. 17(3) cage = {278/368/458}, no 9

14. Hidden killer pair 2,3 in R1234C9 and R2C8 for NR1C6, R2C8 = {23} -> R1234C9 must contain one of 2,3
14a. Hidden killer pair 2,3 in R1234C9 and 17(3) cage at R5C9 for C9, R1234C9 contains one of 2,3 -> 17(3) cage must contain one of 2,3 -> 17(3) cage (step 13a) = {278/368}, no 4,5
14b. R56C8 = {49} (cannot be {67} which clashes with 17(3) cage), locked for C8 and NR3C7 -> R13C8 = [78], both placed for NR1C6, R9C8 = 5, R4C8 = 6, placed for NR3C7, R1C5 = 3 (step 9), placed for NR1C3, clean-up: no 2 in R2C45, no 1 in R3C9, no 7 in R4C3, no 7 in R5C2, no 3 in 17(3) cage at R5C9 (step 13a) , no 1 in R9C6
14c. Naked triple {278} in 17(3) cage at R5C9, locked for C9 and NR3C7, clean-up: no 5 in R34C9

15. Naked triple {135} in R345C7, locked for C7
15a. Naked pair {28} in R78C7, locked for C7 and 14(4) cage at R7C7 -> R9C67 = [24], placed for NR7C4, clean-up: no 6 in R6C6
15b. R2C8 = 2 (hidden single in C8), R12C9 = 8 = [53], clean-up: no 4 in R34C9
[With hindsight, I’d overlooked in step 14b that R2C8 follows from R9C8 using step 3)
15c. R34C9 = [61], placed for NR1C6 -> R1C67 = [49], clean-up: no 1,6 in R1C34, no 1 in R6C6, no 6 in R6C7
15d. R6C7 = 7, placed for NR6C7, R7C6 = 6 (hidden single in NR6C7), R2C7 = 6, clean-up: no 9 in R8C5

16. Naked pair {28} in R1C34, locked for R1 and NR1C1 -> R1C2 = 6, R1C1 = 1, R2C1 = 8 (cage sum), both placed for NR1C1, clean-up: no 7 in R4C2, no 5 in R4C4, no 5 in R67C1
16a. Naked pair {24} in R67C1, locked for C1 and NR6C1, clean-up: no 1,3 in R6C2
16b. Naked pair {24} in R6C12, locked for R6 -> R56C8 = [49], R6C9 = 8, clean-up: no 9 in R4C2
16c. Naked pair {13} in R7C28, locked for R7

17. 19(3) cage at R3C1 = {379} (only remaining combination), locked for C1 and NR3C1 -> R89C1 = [56], R8C2 = 9 (cage sum), placed for NR6C1, clean-up: no 4 in R4C2, no 6 in R8C5
17a. Naked pair {58} in R45C2, locked for C2 and NR3C1
17b. Naked pair {78} in R8C56, locked for R8 and NR6C4

18. R56C3 = {16} (hidden pair in NR3C1), locked for C3, R6C4 = 5 (cage sum), R8C3 = 3, R8C8 = 1, R7C8 = 3, R7C2 = 1, R6C2 = 4, R2C2 = 7, placed for NR1C1
18a. R3C4 + R4C3 = 12 (step 5) -> R3C4 = 3, R4C3 = 9, R4C4 = 4, R2C45 = [14], R2C3 = 5, R2C6 = 9

19. R3C4 = 3 -> R3C56 = 14 = [95]

and the rest is naked singles, without using the nonets.
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Andrew
PostPosted: Mon May 06, 2013 3:12 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Texas Jigsaw Killer 9 by Ruud (August 2006)
Puzzle Diagrams:
ImageImage
Code: Select, Copy & Paste into solver:
SumoCueV1=13J0=11J1=14J1=10J1+3J2+3J2=16J2=10J2+7J2+0J0+1J0+2J1+2J1=20J1+6J2+6J3=18J2=6J2=11J4+18J0=11J0+20J1+13J1+13J3+16J3+16J3+17J2=13J4+27J4=9J0+29J0=19J1+13J3=17J3+33J3+33J5+27J4=7J6+37J6+37J0+31J0=22J3=20J3+42J5+42J5=13J4+45J4=11J6+31J6+31J7+41J7+41J7=9J7+52J5=17J4+45J8+47J8=18J6+57J6+57J7+41J7+52J5=28J5+54J4=18J4+64J8=21J8=11J6+67J6+62J7+62J7+62J5+54J8+64J8+64J8+66J8+66J8+67J6=12J7+78J5+78J5
Solution: 
+-------+-------+-------+
| 9 8 1 | 5 3 2 | 7 6 4 |
| 4 3 5 | 7 2 8 | 1 9 5 |
| 6 5 8 | 3 9 4 | 2 7 1 |
+-------+-------+-------+
| 1 9 7 | 2 4 5 | 6 3 8 |
| 3 2 4 | 1 6 9 | 8 5 7 |
| 5 7 9 | 8 1 6 | 4 2 3 |
+-------+-------+-------+
| 8 1 2 | 6 5 7 | 3 4 9 |
| 2 4 3 | 9 7 1 | 5 8 6 |
| 7 6 5 | 4 8 3 | 9 1 2 |
+-------+-------+-------+

Quote:
SSscore: 0.90

Archive Note: Ruud’s website gave an inconsistent solution. I assume that the code string was for the correct puzzle.

Andrew's 2013 walkthrough:
Prelims

a) R12C1 = {49/58/67}, no 1,2,3
b) R12C2 = {29/38/47/56}, no 1
c) R1C89 = {19/28/37/46}, no 5
d) R23C9 = {15/24}
e) R3C12 = {29/38/47/56}, no 1
f) R3C34 = {29/38/47/56}, no 1
g) R4C34 = {18/27/36/45}, no 9
h) R67C3 = {29/38/47/56}, no 1
i) 10(3) cage at R1C4 = {127/136/145/235}, no 8,9
j) 7(3) cage at R5C2 = {124}
k) 20(3) cage at R5C7 = {389/479/569/578}, no 1,2
l) 9(3) cage at R6C8 = {126/135/234}, no 7,8,9
m) 21(3) cage at R8C4 = {489/579/678}, no 1,2,3
n) 11(3) cage at R8C5 = {128/137/146/236/245}, no 9
o) 28(4) cage at R7C9 = {4789/5689}, no 1,2,3

1. Naked triple {124} in 7(3) cage at R5C2, locked for R5
[As with some earlier Texas Jigsaw Killers with low SS scores, I’m avoiding using CPEs unless they prove necessary.]

2. 45 rule on R123 1 outie R4C6 = 5, placed for NR2C7, clean-up: no 4 in R4C34

3. 45 rule on R89 2 outies R7C19 = 17 = {89}, locked for R7, clean-up: no 2,3 in R6C3
3a. 17(3) cage cannot contain both of 8,9 -> no 8,9 in R89C1

4. 18(3) cage at R7C4 = {567} (only remaining combination), locked for R7, 5 also locked for NR5C2, clean-up: no 4,6 in R6C3

5. 45 rule on R1234 1 innie R4C5 = 1 outie R5C1 + 1, no 1,2,3 in R4C5, no 9 in R5C1

6. 45 rule on R6789 1 outie R5C6 = 2 innies R6C45
6a. Max R6C45 = 9, no 9 in R6C45

7. R6C3 = 9 (hidden single in NR5C2), R7C3 = 2, placed for NR7C2, clean-up: no 2,9 in R3C4, no 7 in R4C4

8. 45 rule on C123 4 outies R2345C4 = 13 = {1237/1246/1345}, no 8,9, 1 locked for C4, clean-up: no 3 in R3C3, no 1 in R4C3

9. 9 in C4 only in R89C4, locked for NR7C2
9a. 21(3) cage at R8C4 = {489/579}, no 6

10. Hidden killer pair 3,8 in R6C4 and 11(3) cage at R8C5 for NR5C2, 11(3) cage cannot contain both of 3,8 -> R6C4 = {38}, 11(3) cage contains one of 3,8 = {128/137/236}, no 4
10a. Hidden killer pair 6,7 in R7C45 and 11(3) cage for NR5C2, R7C45 contains one of 6,7 -> 11(3) cage must contain one of 6,7 = {137/236}, no 8, 3 locked for NR5C2 -> R6C4 = 8
10b. 4 in NR5C2 only in R5C23, locked for R5

11. R5C6 = R6C45 (step 6)
11a. Max R6C45 = 9 -> R6C5 = 1, placed for NR6C5
11b. R6C45 = 9 -> R5C6 = 9, placed for NR2C7

12. 45 rule on R5 2 remaining innies R5C15 = 9 = {36}, locked for R5
12a. R6C45 = [81] = 9 -> R45C5 = 10 = [46/73]
12b. Naked triple {578} in 20(3) cage at R5C7, 5 locked for NR4C9

[At this stage Law of Leftovers (LoL) would be very helpful. Using the four nonets on the right-hand side, R16C5 must contain the same numbers as R89C6, which immediately places 1 in R89C6. However I’ll continue trying to solve without LoL, since Texas Jigsaw Killers 1 to 17 all have low SS scores.]

13. 22(4) cage at R5C6 contains 9 = {2479/3469} (cannot be {2569} because R7C7 only contains 3,4), no 5, 4 locked for NR6C5
13a. Killer pair 6,7 in 22(4) cage and R7C6, locked for NR6C5
13b. 9(3) cage at R6C8 = {135/234} (cannot be {126} which clashes with 22(4) cage), no 6

14. 9 in C5 only in R23C5, locked for NR1C2, clean-up: no 2 in R2C2
14a.20(4) cage at R2C5 contains 5,9 = {2459} (only remaining combination)

15. 1 in NR1C1 only in R45C4, locked for C4
15a. 1 in NR1C2 only in 14(3) cage at R1C3 = {158/167}, 1 locked for C3 -> R5C3 = 4, clean-up: no 7 in R3C4

16. R9C5 = 8 (hidden single in C5), placed for NR7C2, R89C4 = 13 = {49}, locked for C4, 4 placed for NR7C2, clean-up: no 7 in R3C3
16a. R2345C4 (step 8) = {1237} (only remaining combination) -> R2C4 = 7, R3C4 = 3, both placed for NR1C2, R45C4 = {12}, locked for C4 and NR1C1, R3C3 = 8, placed for NR1C1, clean-up: no 5,6 in R1C1, no 4 in R12C2, no 5 in R2C1, no 9 in R3C1, no 3 in R4C3
16b. R2C4 = 7 -> R12C3 = 7 = {16}, locked for C3 and NR1C2 -> R1C4 = 5, R4C3 = 7, placed for NR1C1, R4C4 = 2, R4C5 = 4, R5C5 = 6 (cage sum), placed for NR1C1, R5C4 = 1, R5C2 = 2, placed for NR5C2, R1C2 = 8, R2C2 = 3, clean-up: no 2 in R1C89

17. Naked pair {49} in R12C1, locked for C1 and NR1C1 -> R3C2 = 5, R3C1 = 6, placed for NR3C1, R7C1 = 8, R7C9 = 9, placed for NR4C9, clean-up: no 1 in R1C8, no 1 in R2C9

18. R7C2 = 1, placed for NR7C2, R6C12 = 12 = [57], 7 placed for NR3C1

19. Naked pair {29} in R23C5, locked for C5 and 20(4) cage at R2C5 -> R3C6 = 4, placed for NR2C7, clean-up: no 2 in R2C9

20. R1C4 = 5 -> R1C56 = 5 = [32], 2 placed for NR1C5 -> R3C9 = 1, placed for NR1C5, R2C9 = 5, clean-up: no 7,9 in R1C8, no 7 in R1C9

21. Naked pair {46} in R1C89, locked for R1 and NR1C5 -> R1C1 = 9, R1C7 = 7, R2C6 = 8, R12C3 = [16], R3C78 = [27], R25C7 = [18], both placed for NR2C7

22. Naked triple {346} in R6C67 + R7C7, locked for NR6C5 -> R8C78 = [58], R7C9 = 9, R8C9 = 6 (cage sum)

23. R9C7 = 9 -> R9C89 = 3 = [12]

and the rest is naked singles, without using the nonets.
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Andrew
PostPosted: Mon May 06, 2013 3:58 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Texas Jigsaw Killer 10 by Ruud (August 2006)
Puzzle Diagrams:
ImageImage
Code: Select, Copy & Paste into solver:
SumoCueV1=15J0+0J0=7J0+2J0=12J0=13J0+5J0=10J1+7J1+0J0=19J2+10J0+10J2+4J2=14J2+14J2+14J2+7J1=13J3=24J2+19J2=4J2=23J4=11J4=21J4+24J1=7J1+18J3+19J5+19J4+21J4+22J4+23J4+24J4+24J4+26J1=12J3+36J5=5J5+38J5+22J5+22J5+22J5=15J5+43J1=8J3=19J6+46J6=17J6=9J6=6J6=20J6+51J5=11J1+45J3+46J3+46J6+48J6+49J6+50J7+51J7+51J7+53J1=9J3=15J7+64J7+64J7=12J7=16J7+68J8+68J7=14J8+63J3+63J3=13J8+74J8+67J8=11J8+77J8+71J8+71J8
Solution: 
+-------+-------+-------+
| 8 6 2 | 5 7 9 | 4 1 3 |
| 1 9 3 | 7 5 8 | 2 4 6 |
| 4 3 6 | 1 9 7 | 5 8 2 |
+-------+-------+-------+
| 9 7 8 | 3 1 4 | 6 2 5 |
| 7 5 1 | 4 2 3 | 8 6 9 |
| 6 2 5 | 8 3 1 | 7 9 4 |
+-------+-------+-------+
| 2 8 4 | 9 6 5 | 1 3 7 |
| 5 4 9 | 2 8 6 | 3 7 1 |
| 3 1 7 | 6 4 2 | 9 5 8 |
+-------+-------+-------+

Quote:
SSscore: 0.85
Andrew (in 2013):
Probably the easiest one:
if you spot the early way in.

Andrew's walkthrough:
Prelims

a) R1C34 = {16/25/34}, no 7,8,9
b) R12C5 = {39/48/57}, no 1,2,6
c) R1C67 = {49/58/67}, no 1,2,3
d) R34C1 = {49/58/67}, no 1,2,3
e) R34C4 = {13}
f) R34C6 = {29/38/47/56}, no 1
g) R34C9 = {16/25/34}, no 7,8,9
h) R5C12 = {39/48/57}, no 1,2,6
i) R5C34 = {14/23}
j) R5C89 = {69/78}
k) R67C1 = {17/26/35}, no 4,8,9
l) R67C4 = {89}
m) R67C5 = {18/27/36/45}, no 9
n) R67C6 = {15/24}
o) R67C9 = {29/38/47/56}, no 1
p) R89C5 = {39/48/57}, no 1,2,6
q) R9C34 = {49/58/67}, no 1,2,3
r) R9C67 = {29/38/47/56}, no 1
s) 10(3) cage at R1C8 = {127/136/145/235}, no 8,9
t) 19(3) cage at R2C2 = {289/379/469/478/568}, no 1
u) 9(3) cage at R8C1 = {126/135/234}, no 7,8,9

Steps resulting from Prelims
1a. Naked pair {13} in R34C4, locked for C4, clean-up: no 4,6 in R1C3, no 2,4 in R5C3
1b. Naked pair {89} in R67C4, locked for C4 and NR6C2, clean-up: no 1 in R67C5, no 4,5 in R9C3

2. 45 rule on R5 2 outies R34C5 = 10
2a. 45 rule on C5 2 outies R5C67 = 11
2b. R34C5 = 10, R5C67 = 11 -> R5C5 = 2, R5C4 = 4, R5C3 = 1, all placed for NR4C2, clean-up: no 3 in R1C3, no 6 in R1C4, no 8 in R5C12, no 7 in R67C5, no 9 in R9C3
2c. Naked pair {25} in R1C1, locked for NR1C1, clean-up: no 8 in R1C67, no 7 in R2C5
2d. 1 in C5 only R34C5 = 10 = {19}, locked for C5, NR3C5 and 23(5) cage at R3C5 -> R4C4 = 3, placed for NR3C5, R3C4 = 1, placed for NR2C2, R34C5 = [91], clean-up: no 3 in R12C5, no 2,8 in R34C6, no 4,6 in R3C9, no 4 in R4C1, no 6 in R4C9, no 3 in R89C5
2e. R5C67 = 11 = {38/56}, no 7
2f. R67C5 = {36} (hidden pair in C5), locked for NR6C2
2g. 1 in NR6C2 only in R6C267, locked for R6, clean-up: no 7 in R7C1

3. 2 in C1 only in R6789C1, locked for NR3C1
3a. Killer triple 1,2,3 in R67C1 and 9(3) cage at R8C1, locked for NR3C1, clean-up: no 9 in R5C2

4. 15(3) cage at R1C1 = {168/348}, no 7,9, 8 locked for NR1C1, clean-up: no 4 in R2C5
4a. 9 in R1 only in R1C67 = {49}, locked for R1 and NR1C1 -> R1C5 = 7, placed for NR1C1, R2C5 = 5, placed for NR2C2
4b. 15(3) cage = {168} (only remaining combination), locked for NR1C1
4c. R2C3 = 3, -> R2C24 = 16 = [97], 7 placed for NR2C2, clean-up: no 6 in R9C3

5. 14(3) cage at R2C6 = {248} (only remaining combination), locked for R2 and NR2C2 -> R3C23 = [36], clean-up: no 7 in R4C1, no 5 in R4C6, no 4 in R4C9, no 9 in R5C1
5a. R3C23 = [36] = 9 -> R4C23 = 15 = {78}, locked for R4, clean-up: no 4 in R3C1, no 4 in R3C6
5b. Naked pair {57} in R5C12, locked for R5, clean-up: no 8 in R5C89
5c. Naked pair {69} in R5C89, locked for R5
5d. Naked pair {38} in R5C67, locked for NR4C2 -> R4C2 = 7, R5C2 = 5, R4C3 = 8, placed for NR3C5, R5C1 = 7, R9C3 = 7, R9C4 = 6, clean-up: no 5 in R3C1, no 6 in R4C1, no 1 in R7C1, no 4,5 in R9C67

6. R4C1 = 9 (hidden single in C1), R3C1 = 4, R9C2 = 1
6a. R1C1 = 8 (hidden single in C1)

7. R7C2 = 8 (hidden single in NR3C1), R67C4 = [89], clean-up: no 2,3 in R6C9, no 3 in R7C9
7a. Naked triple {245} in R6C23 + R7C3, locked for NR6C2 -> R6C6 = 1, R6C7 = 7, R7C6 = 5, R3C6 = 7, R4C6 = 4, R1C67 = [94], clean-up: no 3 in R6C1, no 6 in R6C9, no 4 in R7C9, no 2 in R9C7

8. 19(4) cage at R6C2 = {2458} -> R6C3 = 5, R1C34 = [25], R7C3 = 4, R8C4 = 2, R8C3 = 9, R8C2 = 4 (cage sum), 2 placed for NR7C6, R6C2 = 2, R6C1 = 6, R7C1 = 2, R6C5 = 3, R6C8 = 9, R6C9 = 4, R7C9 = 7

9. R8C5 = 8, R8C8 = 7 (hidden single in R8) -> R8C67 = 9 = {36}, locked for R8

10. R9C2 = 1, R8C1 = 5, R9C1 = 3, clean-up: no 8 in R9C67
10a. R9C67 = [29]

and the rest is naked singles, without using the nonets.
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Andrew
PostPosted: Mon May 06, 2013 11:00 pm 
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Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Texas Jigsaw Killer 11 by Ruud (August 2006)
Puzzle Diagrams:
ImageImage
Code: Select, Copy & Paste into solver:
SumoCueV1=25J0+0J0=14J1+2J1=6J1=17J1+5J1=15J2+7J2+0J0+0J0=22J1+2J1+4J3+5J1=16J1+7J2+7J2=14J0=7J0+11J0=19J0+21J3+21J2+15J2=10J2=13J2+18J4+19J4+11J4+11J0=15J3+15J2+15J5+25J5+26J5=21J4+36J4+36J4+36J3+31J3=18J3+41J5+41J5+41J5=6J4=7J4=22J4+47J6+31J3=23J7+50J5=10J5=6J5+45J6+46J6+47J6=20J6+57J3+57J7+50J7+52J7+53J7=18J6+63J6+47J8=19J8=7J3=12J8+50J8=23J7+70J7+63J6+63J6+66J8+66J8+67J8+68J8+68J8+70J7+70J7
Solution: 
+-------+-------+-------+
| 6 9 3 | 5 1 7 | 8 4 2 |
| 3 7 9 | 6 5 2 | 4 1 8 |
| 5 4 1 | 2 8 9 | 6 3 7 |
+-------+-------+-------+
| 9 3 4 | 8 2 5 | 1 7 6 |
| 8 5 7 | 1 6 3 | 2 9 4 |
| 2 1 6 | 9 7 4 | 3 8 5 |
+-------+-------+-------+
| 4 6 5 | 3 9 8 | 7 2 1 |
| 1 8 2 | 7 4 6 | 9 5 3 |
| 7 2 8 | 4 3 1 | 5 6 9 |
+-------+-------+-------+

Quote:
SSscore: 0.90
Andrew (in 2013):
Because the early Texas Jigsaw Killers have low SS scores:
I’ll avoid going as far as using Law of Leftovers. However I’ll go part way …

Andrew's walkthrough:
Prelims

a) R12C5 = {15/24}
b) R34C1 = {59/68}
c) R34C2 = {16/25/34}, no 7,8,9
d) R34C8 = {19/28/37/46}, no 5
e) R34C9 = {49/58/67}, no 1,2,3
f) R67C1 = {15/24}
g) R67C2 = {16/25/34}, no 7,8,9
h) R67C8 = {19/28/37/46}, no 5
i) R67C9 = {15/24}
j) R89C5 = {16/25/34}, no 7,8,9
k) 19(3) cage at R3C4 = {289/379/469/478/568}, no 1
l) 20(3) cage at R7C4 = {389/479/569/578}, no 1,2
m) 19(3) cage at R8C4 = {289/379/469/478/568}, no 1

1. 45 rule on R5 1 innie R5C5 = 6, clean-up: no 1 in R89C5
1a. R89C5 = {34} (cannot be {25} which clashes with R12C5), locked for C5, clean-up: no 2 in R12C5
1b. Naked pair {15} in R12C5, locked for C5
[I’ve deliberately avoided using several CPEs, based on naked pairs, because they aren’t necessary in this puzzle.]

2. 45 rule on R1234 1 innie R4C5 = 2, R6C5 = 7 (cage sum), both placed for NR3C5, clean-up: no 5 in R3C2, no 8 in R3C8, no 3 in R7C8
2a. Naked pair {89} in R37C5, locked for NR3C5

3. 45 rule on R12 2 innies R2C37 = 13 = {49/58/67}, no 1,2,3

4. 45 rule on R89 2 innies R8C37 = 11 = {29/38/47/56}, no 1

5. 45 rule on C12 2 innies R5C12 = 13 = {49/58}
5a. 45 rule on C89 2 innies R5C89 = 13 = {49/58}
5b. Naked quad {4589} in R5C1289, locked for R5
5c. 45 rule on C12 2 outies R5C34 = 8 = {17} -> R5C3 = 7, R5C46 = [13], both placed for NR3C5, R5C7 = 2, placed for NR4C7, R2C5 = 5, R1C5 = 1, placed for NR1C3, R8C5 = 4, R9C5 = 3, placed for R8C3, clean-up: no 8 in R2C3, no 6,8 in R2C7 (both step 3), no 8 in R7C8, no 4 in R7C9, no 8,9 in R8C3, no 7,8 in R8C7 (both step 4)
5d. 5 in NR1C3 only in R1C3467, locked for R1
5e. 4 in NR8C3 only in R9C3467, locked for R9

6. 1 in NR8C3 only in 12(3) cage at R8C6 = {129/147/156}, no 8

7. 20(3) cage at R7C4 = {389/479/569/578}
7a. 3 of {389} must be in R7C4, 8,9 of {479/569/578} must be in R7C5 -> no 8,9 in R7C4

8. 17(3) cage at R1C6 = {278/359/368/458} (cannot be {269/467} which clash with R2C37)
8a. 9 of {359} must be in R2C6 -> no 9 in R1C67

9. 16(4) cage at R2C7 = {1348/1357/1456}, no 9, clean-up: no 4 in R2C3 (step 3)
9a. R2C7 = {47} -> no 4,7 in R3C7 + R4C67

10. 7 in C12 only in 25(4) cage at R1C1 and 18(4) cage at R8C1 -> both cages must contain 7
10a. 25(4) cage = {1789/3679/4678}, no 2
10b. 18(4) cage = {1278/2367}, no 5,9, 2 locked for NR6C4, clean-up: no 4 in R6C1, no 5 in R6C2

11. 2 in R7 only in R7C89, locked for NR6C6

[Because the early Texas Jigsaw Killers have low SS scores, I’ll avoid going as far as using Law of Leftovers. However I’ll go part way …]
12. NR6C4 and NR6C6 must both contain 4 in R67 -> 4 in R6C46, locked for R6, clean-up: no 3 in R7C2, no 6 in R7C8, no 2 in R7C9

13. R7C8 = 2 (hidden single in R7), R6C8 = 8, placed for NR4C7, clean-up: no 5 in R3C9, no 5 in R5C89
13a. Naked pair {49} in R5C89, locked for R5 and NR4C7, clean-up: no 1,6 in R3C8, no 4,9 in R3C9
13b. Naked pair {58} in R5C12, locked for NR4C1, clean-up: no 6,9 in R3C1, no 2 in R3C2, no 1 in R7C1
13c. 4 in NR4C1 only in R4C23, locked for R4

14. Naked pair {58} in R35C1, locked for C1 -> R7C1 = 4, placed for NR6C4, R6C1 = 2, clean-up: no 3 in R6C2, no 5 in R7C2
14a. Naked pair {16} in R67C2, locked for C2
14b. Naked pair {34} in R34C2, locked for C2

15. 9 in C2 only in R12C2, locked for NR1C1

16. R4C1 = 9 (hidden single in C1), placed for NR4C1, R3C1 = 5, placed for NR1C1, R5C12 = [85]

17. R4C6 = 5 (hidden single in NR1C7), clean-up: no 8 in R3C9
17a. 16(4) cage at R2C7 (step 9) = {1357/1456}, no 8, 1 locked for C7

18. R4C4 = 8 (hidden single in R4), placed for NR1C1, R9C3 = 8 (hidden single in NR8C3)
18a. Naked pair {79} in R12C2, locked for C2 and NR1C1 -> R89C2 = [82]
18b. R12C2 = {79} = 16 -> R12C1 = 9 = {36}, locked for C1 and NR1C1 -> R3C234 = [412], R4C2 = 3, placed for NR4C1, R6C3 = 6, R2C3 = 9, placed for NR1C3, R2C2 = 7, R2C7 = 4, placed for NR1C3, clean-up: no 5 in R8C7 (step 4)

19. R6C2 = 1, R6C79 = [35] , R6C4 = 9
19a. R6C67 = [43] = 7 -> R78C7 = 16 = {79} -> R7C7 = 7, placed for NR6C6, R8C7 = 9, placed for NR8C3, R8C3 = 2 (step 4), R7C3 = 5 (cage sum)

20. R3C7 = 6, R3C9 = 7, both placed for NR1C8, R4C9 = 6, R7C9 = 1, R9C9 = 9, both placed for NR6C6, R7C2 = 6, R7C6 = 8

and the rest is naked singles, without using the nonets.
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Andrew
PostPosted: Mon May 06, 2013 11:37 pm 
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Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Texas Jigsaw Killer 12 by Ruud (August 2006)
Puzzle Diagrams:
ImageImage
Code: Select, Copy & Paste into solver:
SumoCueV1=9J0+0J0=8J1=18J1+3J1+3J1=14J1=12J2+7J2+0J0=16J0+2J3=9J1=15J4=4J1+6J5=22J2+7J2=16J0+10J0+10J3+12J1+13J4+14J1+16J5+16J2=13J2+18J0+18J0=21J3=15J3=10J4=23J5=11J5+26J2+26J2=16J6+36J0+29J3+30J4+31J4+32J4+33J5=7J2+43J7=15J6+45J6+29J3+30J3+31J4+32J5+33J5=10J7+52J7+45J6=14J6+55J3=9J8=12J4=6J8=14J5+60J7+52J7=12J6+55J6=8J3+57J8+58J4+59J8=13J5+60J7=19J7+63J6+63J6+65J8=14J8+75J8+75J8+69J8+71J7+71J7
Solution: 
+-------+-------+-------+
| 3 5 6 | 9 2 7 | 8 4 1 |
| 1 4 2 | 5 8 3 | 6 9 7 |
| 6 9 3 | 4 7 1 | 5 8 2 |
+-------+-------+-------+
| 2 8 4 | 7 1 9 | 3 6 5 |
| 9 7 8 | 2 5 6 | 1 3 4 |
| 5 2 9 | 6 4 8 | 7 1 3 |
+-------+-------+-------+
| 8 3 5 | 1 9 4 | 2 7 6 |
| 7 6 1 | 8 3 2 | 4 5 9 |
| 4 1 7 | 3 6 5 | 9 2 8 |
+-------+-------+-------+

Quote:
SSscore: 0.80

Andrew (in 2013): Another easy one.

Andrew's walkthrough:
Prelims

a) R12C3 = {17/26/35}, no 4,8,9
b) R12C7 = {59/68}
c) R23C4 = {18/27/36/45}, no 9
d) R23C5 = {69/78}
e) R23C6 = {13}
f) R5C12 = {79}
g) R5C89 = {16/25/34}, no 7,8,9
h) R78C4 = {18/27/36/45}, no 9
i) R78C5 = {39/48/57}, no 1,2,6
j) R78C6 = {15/24}
k) R89C3 = {17/26/35}, no 4,8,9
l) R89C7 = {49/58/67}, no 1,2,3
m) 9(3) cage at R1C1 = {126/135/234}, no 7,8,9
n) 22(3) cage at R2C8 = {589/679}
o) 21(3) cage at R4C3 = {489/579/678}, no 1,2,3
p) 10(3) cage at R4C5 = {127/136/145/235}, no 8,9
q) 23(3) cage at R4C6 = {689}
r) 11(3) cage at R4C7 = {128/137/146/236/245}, no 9
s) 10(3) cage at R6C8 = {127/136/145/235}, no 8,9
t) 19(3) cage at R8C9 = {289/379/469/478/568}, no 1

1. Naked pair {79} in R5C12, locked for R5
[I’ve deliberately avoided using several CPEs, based on naked pairs, because they aren’t necessary in this puzzle.]

2. Naked pair {13} in R23C6, locked for C6 and NR1C3, clean-up: no 5,7 in R2C3, no 6,8 in R23C4, no 5 in R78C6
2a. Naked pair {24} in R78C6, locked for C6 and NR7C4, clean-up: no 5,7 in R78C4, no 6 in R8C3, no 9 in R8C7

3. R89C7 = [49/67/76] (cannot be {58} which clashes with R12C7), no 5,8
3a. Killer pair 6,9 in R12C7 and R89C7, locked for C7

4. 45 rule on C89 2 outies R37C7 = 7 = [52], R78C6 = [42], clean-up: no 9 in R12C7, no 4 in R2C4, no 8 in R8C5, no 6 in R9C3
4a. Naked pair {68} in R12C7, locked for C7, clean-up: no 7 in R89C7
4b. R89C7 = [49], clean-up: no 8 in R7C5
4c. Killer pair 7,9 in R23C5 and R78C5

5. R3C7 = 5 -> R23C8 = 17 = {89}, locked for C8 and NR1C8
5a. R7C7 = 2 -> R78C8 = 12 = {57}, locked for C8 and NR5C9, clean-up: no 2 in R6C89
5b. 10(3) cage at R6C8 = {136} (only remaining combination), locked for NR5C9 -> R5C9 = 4, placed for NR5C9, R5C8 = 3, placed for NR1C8, R5C7 = 1

6. 45 rule on C5 2 innies R19C5 = 8 = [26/53]
6a. 4 in C5 only in 10(3) cage at R4C5 = {145} (only remaining combination) -> R5C5 = 5, R1C5 = 2, placed for NR1C3, R9C6 = 6, placed for NR7C4, clean-up: no 6 in R2C3, no 7 in R23C4, no 9 in R23C5, no 3 in R78C4, no 7 in R78C5
6b. Naked pair {78} in R23C5, locked for NR2C5 -> R5C46 = [26]
6c. R2C4 = 5, placed for NR1C3, R3C4 = 4, clean-up: no 3 in R2C3

7. Naked pair {89} in R46C6, locked for C6 and NR2C7 -> R1C6 = 7, R1C3 = 6, R2C3 = 2, R12C7 = [86], R1C4 = 9, R9C6 = 5, R9C4 = 3 (cage sum), clean-up: no 3,5 in R8C3
7a. Naked pair {18} in R78C4, locked for C4 and NR7C4 -> R9C3 = 7, R8C3 = 1, R78C4 = [18], R8C9 = 9, R78C5 = [93]

8. 45 rule on C12 2 outies R37C3 = 8 = [35], R23C6 = [31], R78C8 = [75]
8a. R7C3 = 5 -> R78C2 = 9 = [36], both placed for NR5C1, R78C1 = [87], both placed for NR5C1, R5C1 = 9, placed for NR5C1, R5C2 = 7
8b. R7C1 = 8 -> R6C12 = 7 = {25}, 2 locked for NR5C1

9. R3C3 = 3 -> R23C2 = 13 = [49], 4 placed for NR1C1

10. R4C2 = 8 (hidden single in C2) -> R34C1 = 8 = {26}, locked for C1

and the rest is naked singles, without using the nonets.
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Andrew
PostPosted: Tue May 07, 2013 1:15 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Texas Jigsaw Killer 13 by Ruud (August 2006)
Puzzle Diagrams:
ImageImage
Code: Select, Copy & Paste into solver:
SumoCueV1=6J0+0J0=19J0+2J0=9J1=6J1+5J1=15J1+7J2=8J0=14J3+10J0+2J0+4J1+5J1=22J2+15J1=12J2+9J0+10J3+10J3=24J0+21J1+21J2+15J2+15J1+17J2=25J3=15J3+28J3=18J3+30J4+30J4=7J2+33J2=17J2+27J3+27J3=25J4+38J4+38J4+38J4+38J4+35J5+35J5+27J6=6J6+46J6=11J4+48J4+48J5=11J5+51J5+35J5=12J6=21J7+55J6=11J6+57J7+57J8=17J5+60J5=12J8+54J6+55J7+55J6=17J7=8J7=18J8+60J8+60J5+62J8=10J6+72J7+66J7+66J7+67J7+68J8+68J8=9J8+79J8
Solution: 
+-------+-------+-------+
| 5 1 8 | 7 4 2 | 3 9 6 |
| 6 2 3 | 4 5 1 | 8 7 9 |
| 2 4 5 | 9 8 7 | 1 6 3 |
+-------+-------+-------+
| 1 6 9 | 3 7 8 | 5 2 4 |
| 7 8 6 | 1 9 5 | 4 3 2 |
| 9 5 1 | 2 3 6 | 7 4 8 |
+-------+-------+-------+
| 8 3 2 | 6 1 4 | 9 5 7 |
| 4 9 7 | 8 6 3 | 2 1 5 |
| 3 7 4 | 5 2 9 | 6 8 1 |
+-------+-------+-------+

Quote:
SSscore: 0.85

Andrew (in 2013): As easy as the previous one.

Andrew's walkthrough:
Prelims

a) R1C12 = {15/24}
b) R12C5 = {18/27/36/45}, no 9
c) R1C89 = {69/78}
d) R23C1 = {17/26/35}, no 4,8,9
e) R23C9 = {39/48/57}, no 1,2,6
f) R4C23 = {69/78}
g) R4C78 = {16/25/34}, no 7,8,9
h) R6C23 = {15/24}
i) R6C78 = {29/38/47/56}, no 1
j) R78C1 = {39/48/57}, no 1,2,6
k) R78C9 = {39/48/57}, no 1,2,6
l) R89C5 = {17/26/35}, no 4,8,9
m) R9C12 = {19/28/37/46}, no 5
n) R9C89 = {18/27/36/45}, no 9
o) 19(3) cage at R1C3 = {289/379/469/478/568}, no 1
p) 6(3) cage at R1C6 = {123}
q) 24(3) cage at R3C4 = {789}
r) 11(3) cage at R6C4 = {128/137/146/236/245}, no 9
s) 11(3) cage at R7C4 = {128/137/146/236/245}, no 9
t) 14(4) cage at R2C2 = {1238/1247/1256/1346/2345}, no 9

1. Naked triple {123} in 6(3) cage at R1C6, locked for NR1C5, clean-up: no 6,7,8 in R12C5
1a. Naked pair {45} in R12C5, locked for C5 and NR1C5, clean-up: no 3 in R89C5
1b. Naked triple {789} in 24(3) cage at R3C4, locked for R3 -> R3C8 = 6, clean-up: no 9 in R1C9, no 1,2 in R2C1, no 3,4,5 in R2C9, no 1 in R4C7, no 5 in R6C7, no 3 in R9C9

2. 45 rule on R4 2 innies R4C19 = 5 = {14/23}
2a. R4C78 = [25/52/61] (cannot be {34} which clashes with R4C19
2b. Killer pair 1,2 in R4C19 and R4C78, locked for R4

3. 45 rule on R6 2 innies R6C19 = 17 = {89}, locked for R6, clean-up: no 2,3 in R6C78
3a. Killer pair 4,5 in R6C23 and R6C78, locked for R6
3b. Killer triple 7,8,9 in R2C9, R6C9 and R78C9, locked for C9 -> R1C9 = 6, placed for NR1C9, R1C8 = 9, placed for NR1C5, clean-up: no 1 in R4C8, no 1,2,3 in R9C8

4. Naked pair {25} in R4C78, locked for R4 and NR1C9, clean-up: no 7 in R2C9, no 3 in R4C19 (step 2)
4a. Naked pair {14} in R4C19, locked for R4
4b. Naked triple {134} in R3C79 + R4C9, locked for NR1C9, 3 also locked for R3, clean-up: no 5 in R2C1
4c. Naked triple {789} in R2C789, locked for R2, clean-up: no 1 in R3C1

5. R1C34 = {78} (hidden pair in R1), locked for NR1C1, R2C4 = 4 (cage sum), placed for NR1C1, R3C4 = 9, clean-up: no 2 in R1C12
5a. Naked pair {15} in R1C12, locked for R1 and NR1C1 -> R3C1 = 2, placed for NR1C1, R2C1 = 6, R2C3 = 3, clean-up: no 4,8 in R9C2

6. 7 in R2 only in 22(4) cage at R2C7 = {1678} (only remaining combination) -> R3C7 = 1, placed for NR1C9, R4C9 = 4, R3C9 = 3, R2C9 = 9, R6C9 = 8, placed for NR5C8, R4C1 = 1, placed for NR2C2, R6C1 = 9, placed for NR6C1, R1C12 = [51], clean-up: no 5 in R6C3, no 3,7 in R78C1, no 9 in R9C2, no 5 in R9C8
6a. Naked pair {57} in R78C9, locked for C9 and NR7C6, clean-up: no 4 in R9C8, no 2 in R9C9
6b. Naked pair {48} in R78C1, locked for C1 and NR6C1, clean-up: no 2 in R6C23, no 2,6 in R9C2
6c. R9C89 = [81], both placed for NR7C6, R2C8 = 7, R2C7 = 8, placed for NR1C9, clean-up: no 4 in R6C7, no 7 in R8C5
6d. Naked pair {37} in R9C12, locked for R9, clean-up: no 1 in R8C5

7. R6C23 = [51], both placed for NR6C1, R6C8 = 4, placed for NR5C8, R6C7 = 7

8. R46C9 = [48] = 12, R5C9 = 2, -> R5C8 = 3 (cage sum), both placed for NR5C8 -> R6C6 = 6, placed for NR5C8
8a. Naked pair {15} in R78C8, locked for C8 and 17(4) cage at R7C7 -> R7C7 = 9, R8C7 = 2 (cage sum), R1C67 = [23], R2C6 = 1, R89C5 = [62], both placed for NR7C2, R9C4 = 5, R6C5 = 3, placed for NR4C5, R6C4 = 2

9. R7C34 = [26] (hidden pair in R7), R7C56 = 5 = [14], 1 placed for NR7C2, 4 placed for NR7C6

10. R46C1 = [19] = 10 -> R5C12 = 15 = [78], both placed for NR2C2 -> R4C4 = 3

and the rest is naked singles, without using the nonets.
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