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HATMAN
PostPosted: Tue Feb 19, 2013 3:46 pm 
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Old Lace Ls triple large diagonals 1

So: Old Lace, two Ls and large triple diagonals.

The following six puzzles are in (sort of) increasing order of difficulty.

This one is fish free.
1A:

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One small fish
1B:

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One small fish
1C:

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16 fishes
1D:

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16 fishes
1E:

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18 fishes
1F:

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Last edited by HATMAN on Sat Feb 23, 2013 9:31 am, edited 1 time in total.

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Andrew
PostPosted: Wed Feb 20, 2013 11:58 pm 
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Thanks HATMAN for an interesting set of puzzles. I started with the first one because I'm a believer that even simpler puzzles deserve to have posted walkthrough.

I've just come back to this series of puzzles, to try some of the harder ones, and found that I'd made a few mistakes in my original walkthroughs; they've now been corrected for versions 1A, 1B and 1C.

Here is my walkthrough for version 1A:
There are L-shaped 45(9) cages at R1C1 and R9C9 (well, strictly speaking at R5C9 but R9C9 emphasises that it’s at the opposite corner), an Old Lace pattern in the centre of the grid and large diagonals D\ at R1C1, R1C3, R3C1 and D/ at R1C7, R1C9 and R3C9.

For the Old Lace pattern, the values in R37C5 must be in R5C46 and the values in R5C37 must be in R46C5.

Prelims

a) 8(3) cage at R1C1 = {125/134}
b) 19(3) cage at R1C9 = {289/379/469/478/568}, no 1
c) 10(3) cage at R3C1 = {127/136/145/235}, no 8,9
d) 9(3) cage at R3C5 = {126/135/234}, no 7,8,9
e) 20(3) cage at R3C5 = {389/479/569/578}, no 1,2
f) 10(3) cage at R5C3 = {127/136/145/235}, no 8,9
g) 21(3) cage at R5C7 = {489/579/678}, no 1,2,3
h) 19(3) cage at R6C1 = {289/379/469/478/568}, no 1
i) 8(3) cage at R9C5 = {125/134}

Steps resulting from Prelims
1a. 8(3) cage at R1C1 = {125/134}, 1 locked for N1 and D\ R1C1
1b. 8(3) cage at R9C5 = {125/134}, 1 locked for R9 and L R9C9

2. 9(3) cage at R3C5 = {126/135/234}
2a. 6 of {126} must be in R3C5 -> no 6 in R4C4 + R5C3
2b. 1 of {135} must be in R5C3 -> no 5 in R5C3

3. 20(3) cage at R3C5 = {389/479/569/578}
3a. 3,4 of {389/479} must be in R3C5 -> no 3,4 in R4C6 + R5C7

4. 21(3) cage at R5C7 = {489/579/678}
4a. 4 of {489} must be in R7C5 -> no 4 in R6C6

5. 10(3) cage at R5C3 = {127/136/145/235}
5a. 6,7 of {127/136} must be in R7C5 -> no 6,7 in R6C4

6. Old Lace R37C5 only contain 3,4,5,6,7 -> no 1,2,8,9 in R5C46
6a. Max R5C46 = 13 -> min R5C5 = 3

7. 1 in Old Lace only in R5C3 + R6C4, locked for D\ R3C1, CPE no 1 in R7C3 using D/ R1C9
7a. 10(3) cage at R5C3 contains 1 = {127/136/145}
7b. 8(3) cage at R9C5 = {125/134}, 1 locked for N8

8. 20(3) cage at R3C5, 21(3) cage at R5C7 and R5C5 are all part of Old Lace -> no 8,9 in R5C5 (because the 20(3) cage and 21(3) cage would clash with either of 8,9 in R5C5)

9. 16(3) cage at R5C4 = {367/457}, 7 locked for R5 and N5
9a. 20(3) cage at R3C5 = {389/569}, no 4, 9 locked for Old Lace and D\ R1C3, CPE no 9 in R4C789
9b. Old Lace R5C46 = R37C5 -> R357C5 = {367/457}, 7 locked for C5, CPE no 7 in R7C37 using D\ R1C1 and D/ R1C9
9c. 5 of {457} must be in R3C5 -> no 5 in R57C5

10. 21(3) cage at R5C7 = {489/579/678}
10a. 4,7 only in R7C5 -> R7C5 = {47}
10b. 9 of {579} must be in R5C7 -> no 5 in R5C7

11. 10(3) cage at R5C3 (step 7a) = {127/145}, no 3
11a. R7C5 = {47} -> no 4 in R5C3 + R6C4

My original steps 12 and 13 were incorrect, so I’ve re-worked from here and added a few bits, in blue, to earlier steps.

12. Old Lace R5C37 only contains 1,2,6,8,9 -> no 3,4,5 in R46C5

13. 10(3) cage at R5C3 (step 11) = {127/145} = {12}7/[154]
13a. 9(3) cage at R3C5 = {135/234} (cannot be {126} which clashes with 10(3) cage = {12}7 and with 10(3) cage = [154] because R357C5 (step 9b) cannot contain both of 4,6), no 6
13b. 9(3) cage at R3C5 = {135/234}, 3 locked for D/ R1C7 and Old Lace
13c. 3 of 9(3) cage in R3C5 + R4C4, CPE no 3 in R123C4, no 3 in R3C3 using D\ R1C1
13d. R5C3 = {12} -> no 2 in R4C4

14. Old Lace R37C5 only contains 3,4,5,7, -> no 6 in R5C46

15. R5C3 + R6C4 = {12} (hidden pair in Old Lace), locked for D\ R3C1, R7C5 = 7 (cage sum), placed for D\ R3C1 and D/ R3C9
15a. Naked pair {12} in R5C3 + R6C4, CPE no 2 in 19(3) cage at R6C1

16. Old Lace R37C5 only contains 3,5,7 -> no 4 in R5C46

17. 4 in Old Lace only in R4C4 + R5C5, locked for D\ R1C1, clean-up: no 3 in 8(3) cage at R1C1
17a. 8(3) cage = {125}, locked for N1 and D\ R1C1

18. R7C5 = 7 -> R5C7 + R6C6 = 14 = {68}, locked for Old Lace and D/ R3C9 -> R5C5 = 4, placed for D/ R1C9, R4C4 = 3, placed for D\ R1C1, R3C5 = 5, placed for D\ R1C3 and D/ R1C7, R4C6 = 9, placed for D/ R1C9, R5C7 = 6 (cage sum), placed for D\ R1C3, R6C6 = 8, placed for D\ R1C1, R7C7 = 9, R5C3 = 1 (cage sum), placed for D/ R1C7, R6C4 = 2, placed for D/ R1C9, R3C3 = 2
18a. Naked pair {57} in R5C46, locked for R5
18b. Naked pair {16} in R46C5, locked for C5
18c. Naked pair {67} in R8C8 + R9C9, locked for N9
18d. R9C6 = 1 (hidden single in R9)

19. 19(3) cage at R1C9 = {568} (only remaining combination) -> R3C7 = 8, placed for D/ R1C9, R1C9 + R2C8 = {56}, locked for N3 and D/ R1C9 -> R7C3 = 3, R9C1 = 7, R8C2 = 1, R2C2 = 5, R1C1 = 1, R2C8 = 6, R1C9 = 5, R8C8 = 7, R9C9 = 6

20. 10(3) cage at R3C1 = {235} (only remaining combination) -> R3C1 = 3, placed for D\ R3C1, R45C1 = [52], 2,3 placed for L R1C1

21. 19(3) cage at R6C1 = {469} (only remaining combination), locked for R6 and N4 -> R4C23 = [87], R5C2 = 3, R46C5 = [61], R6C789 = [537]

22. R9C7 = 4, placed for D\ R3C1, R9C5 = 3 (cage sum), placed for L R9C9

23. Naked pair {28} in R78C9, locked for C9 and N9 -> R5C9 = 9

24. Naked pair {14} in R34C9, CPE no 1,4 in R4C8 using D/ R3C9 -> R4C8 = 2, R4C7 = 1, R234C9 = [314]

25. R9C8 = 5, R9C3 = 9, placed for D/ R3C9, R9C24 = [28]
25a. Naked pair {48} in R12C3, locked for C3 and N1 -> R2C1 = 9, placed for L R1C1, R1C5 = 8

and the rest is naked singles, without using diagonals or the Ls.

Solution, which applies for all the versions: 
+-------+-------+-------+
| 1 7 4 | 6 8 3 | 2 9 5 |
| 9 5 8 | 1 2 4 | 7 6 3 |
| 3 6 2 | 9 5 7 | 8 4 1 |
+-------+-------+-------+
| 5 8 7 | 3 6 9 | 1 2 4 |
| 2 3 1 | 7 4 5 | 6 8 9 |
| 4 9 6 | 2 1 8 | 5 3 7 |
+-------+-------+-------+
| 6 4 3 | 5 7 2 | 9 1 8 |
| 8 1 5 | 4 9 6 | 3 7 2 |
| 7 2 9 | 8 3 1 | 4 5 6 |
+-------+-------+-------+

Rating Comment (Amended):
My original intention was that I wouldn't give a rating for my walkthrough because it would be too high. "For the Old Lace pattern, the values in R37C5 must be in R5C46 and the values in R5C37 must be in R46C5" is, technically, a "sees all except" or "clone" step so ought to be considered to be in the 1.5 range. However I'll accept that any solvers using Old Lace features wouldn't consider it that high. Considering the fact that SudokuSolver uses hidden windows to solve Windokus, such as the Paper Solvable 12 puzzles, and doesn't give them a high rating, I'll rate these puzzles as if this Old Lace step doesn't have a high rating.

I'll therefore rate version 1A at 1.0 based on step 8 and my re-worked step 13a, which I consider to be my hardest steps.


Last edited by Andrew on Thu Nov 07, 2013 8:27 pm, edited 4 times in total.

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Andrew
PostPosted: Thu Feb 21, 2013 4:28 am 
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Version 1B wasn't really any harder than 1A.

Slightly longer:
and I made more use of LR9C9

Here is my walkthrough for version 1B:
There are L-shaped 45(9) cages at R1C1 and R9C9 (well, strictly speaking at R5C9 but R9C9 emphasises that it’s at the opposite corner), an Old Lace pattern in the centre of the grid and large diagonals D\ at R1C1, R1C3, R3C1 and D/ at R1C7, R1C9 and R3C9.

For the Old Lace pattern, the values in R37C5 must be in R5C46 and the values in R5C37 must be in R46C5.

Prelims

a) 8(3) cage at R1C1 = {125/134}
b) 19(3) cage at R1C9 = {289/379/469/478/568}, no 1
c) 9(3) cage at R3C5 = {126/135/234}, no 7,8,9
d) 20(3) cage at R3C5 = {389/479/569/578}, no 1,2
e) 10(3) cage at R5C3 = {127/136/145/235}, no 8,9
f) 21(3) cage at R5C7 = {489/579/678}, no 1,2,3
g) 19(3) cage at R6C1 = {289/379/469/478/568}, no 1
h) 8(3) cage at R9C5 = {125/134}

Steps resulting from Prelims
1a. 8(3) cage at R1C1 = {125/134}, 1 locked for N1 and D\ R1C1
1b. 8(3) cage at R9C5 = {125/134}, 1 locked for R9 and L R9C9

2. 9(3) cage at R3C5 = {126/135/234}
2a. 6 of {126} must be in R3C5 -> no 6 in R4C4 + R5C3
2b. 1 of {135} must be in R5C3 -> no 5 in R5C3

3. 20(3) cage at R3C5 = {389/479/569/578}
3a. 3,4 of {389/479} must be in R3C5 -> no 3,4 in R4C6 + R5C7

4. 21(3) cage at R5C7 = {489/579/678}
4a. 4 of {489} must be in R7C5 -> no 4 in R6C6

5. 10(3) cage at R5C3 = {127/136/145/235}
5a. 6,7 of {127/136} must be in R7C5 -> no 6,7 in R6C4

6. Old Lace R37C5 only contain 3,4,5,6,7 -> no 1,2,8,9 in R5C46
6a. Max R5C46 = 13 -> min R5C5 = 3

7. 1 in Old Lace only in R5C3 + R6C4, locked for D\ R3C1, CPE no 1 in R7C3 using D/ R1C9
7a. 10(3) cage at R5C3 contains 1 = {127/136/145}
7b. 8(3) cage at R9C5 = {125/134}, 1 locked for N8

8. 20(3) cage at R3C5, 21(3) cage at R5C7 and R5C5 are all part of Old Lace -> no 8,9 in R5C5 (because the 20(3) cage and 21(3) cage would clash with either of 8,9 in R5C5)

9. 16(3) cage at R5C4 = {367/457}, 7 locked for R5 and N5
9a. 20(3) cage at R3C5 = {389/569}, no 4, 9 locked for Old Lace and D\ R1C3, CPE no 9 in R4C789
9b. Old Lace R5C46 = R37C5 -> R357C5 = {367/457}, 7 locked for C5, CPE no 7 in R7C37 using D\ R1C1 and D/ R1C9
9c. 5 of {457} must be in R3C5 -> no 5 in R57C5

10. 21(3) cage at R5C7 = {489/579/678}
10a. 4,7 only in R7C5 -> R7C5 = {47}
10b. 9 of {579} must be in R5C7 -> no 5 in R5C7

11. 10(3) cage at R5C3 (step 7a) = {127/145} (cannot be {136} because R7C5 only contains 4,7), no 3
11a. R7C5 = {47} -> no 4 in R5C3 + R6C4

My original steps 12 and 13 were incorrect, so I’ve re-worked from here and added a few bits, in blue, to earlier steps.

12. Old Lace R5C37 only contains 1,2,6,8,9 -> no 3,4,5 in R46C5

13. 10(3) cage at R5C3 (step 11) = {127/145} = {12}7/[154]
13a. 9(3) cage at R3C5 = {135/234} (cannot be {126} which clashes with 10(3) cage = {12}7 and with 10(3) cage = [154] because R357C5 (step 9b) cannot contain both of 4,6), no 6
13b. 9(3) cage at R3C5 = {135/234}, 3 locked for D/ R1C7 and Old Lace
13c. 3 of 9(3) cage in R3C5 + R4C4, CPE no 3 in R123C4, no 3 in R3C3 using D\ R1C1
13d. R5C3 = {12} -> no 2 in R4C4

14. Old Lace R37C5 only contains 3,4,5,7, -> no 6 in R5C46

15. R5C3 + R6C4 = {12} (hidden pair in Old Lace), locked for D\ R3C1, R7C5 = 7 (cage sum), placed for D\ R3C1 and D/ R3C9
15a. Naked pair {12} in R5C3 + R6C4, CPE no 2 in 19(3) cage at R6C1

16. Old Lace R37C5 only contains 3,5,7 -> no 4 in R5C46

17. 4 in Old Lace only in R4C4 + R5C5, locked for D\ R1C1, clean-up: no 3 in 8(3) cage at R1C1
17a. 8(3) cage = {125}, locked for N1 and D\ R1C1

18. R7C5 = 7 -> R5C7 + R6C6 = 14 = {68}, locked for Old Lace and D/ R3C9 -> R5C5 = 4, placed for D/ R1C9, R4C4 = 3, placed for D\ R1C1, R3C5 = 5, placed for D\ R1C3 and D/ R1C7, R4C6 = 9, placed for D/ R1C9, R5C7 = 6 (cage sum), placed for D\ R1C3, R6C6 = 8, placed for D\ R1C1, R7C7 = 9, R5C3 = 1 (cage sum), placed for D/ R1C7, R6C4 = 2, placed for D/ R1C9, R3C3 = 2
18a. Naked pair {57} in R5C46, locked for R5
18b. Naked pair {16} in R46C5, locked for C5
18c. Naked pair {67} in R8C8 + R9C9, locked for N9
18d. R9C6 = 1 (hidden single in R9)

19. 19(3) cage at R1C9 = {568} (only remaining combination) -> R3C7 = 8, placed for D/ R1C9, R1C9 + R2C8 = {56}, locked for N3 and D/ R1C9 -> R7C3 = 3, R9C1 = 7, R8C2 = 1, R2C2 = 5, R1C1 = 1, R2C8 = 6, R1C9 = 5, R8C8 = 7, R9C9 = 6

20. 8(3) cage at R9C5 = {125/134}
20a. 4,5 only in R9C7 -> R9C7 = {45}

21. R6C9 = 7, then R5C9 = 9 (hidden singles in L R9C9)
21a. 5 in L R9C9 only in R9C78, locked for R9 and N9

22. 19(3) cage at R6C1 = {469} (only remaining combination), locked for R6 and N4 -> R4C2 = 8, R46C5 = [61], R6C78 = [53], R9C7 = 4, placed for D\ R3C9, R9C5 = 3 (cage sum), placed for L R9C9, R9C3 = 9, placed for D/ R3C9, R9C24 = [28], R5C12 = [23], 2 placed for L R1C1, R4C13 = [57], R9C8 = 5

23. Naked pair {28} in R78C9, locked for C9 and N9 -> R8C7 = 3

24. Naked pair {48} in R12C3, locked for C3 and N1 -> R6C3 = 6, R8C3 = 5, R8C4 = 4, placed for D/ R3C9, R8C6 = 6, placed for D\ R3C1, R8C1 = 8, R8C9 = 2, R7C9 = 8, placed for D\ R1C3, R1C3 = 4

and the rest is naked singles, without using diagonals or the Ls.

Rating Comment:
Having amended my rating comment for version 1A, I've now added this one for version 1B.

I'll rate my walkthrough for version 1B at 1.0. Step 8 and my re-worked step 13a still my hardest steps.


Last edited by Andrew on Thu Nov 07, 2013 8:28 pm, edited 4 times in total.

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Andrew
PostPosted: Thu Feb 21, 2013 5:30 am 
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Having finished version 1B, it didn't take me long to do version 1C.

Version 1C wasn't much harder:
Just more use of hidden singles and the two Ls.

Here is my walkthrough for version 1C:
There are L-shaped 45(9) cages at R1C1 and R9C9 (well, strictly speaking at R5C9 but R9C9 emphasises that it’s at the opposite corner), an Old Lace pattern in the centre of the grid and large diagonals D\ at R1C1, R1C3, R3C1 and D/ at R1C7, R1C9 and R3C9.

For the Old Lace pattern, the values in R37C5 must be in R5C46 and the values in R5C37 must be in R46C5.

Prelims

a) 8(3) cage at R1C1 = {125/134}
b) 19(3) cage at R1C9 = {289/379/469/478/568}, no 1
c) 9(3) cage at R3C5 = {126/135/234}, no 7,8,9
d) 20(3) cage at R3C5 = {389/479/569/578}, no 1,2
e) 10(3) cage at R5C3 = {127/136/145/235}, no 8,9
f) 21(3) cage at R5C7 = {489/579/678}, no 1,2,3
g) 19(3) cage at R6C1 = {289/379/469/478/568}, no 1
h) 8(3) cage at R9C5 = {125/134}

Steps resulting from Prelims
1a. 8(3) cage at R1C1 = {125/134}, 1 locked for N1 and D\ R1C1
1b. 8(3) cage at R9C5 = {125/134}, 1 locked for R9 and L R9C9

2. 9(3) cage at R3C5 = {126/135/234}
2a. 6 of {126} must be in R3C5 -> no 6 in R4C4 + R5C3
2b. 1 of {135} must be in R5C3 -> no 5 in R5C3

3. 20(3) cage at R3C5 = {389/479/569/578}
3a. 3,4 of {389/479} must be in R3C5 -> no 3,4 in R4C6 + R5C7

4. 21(3) cage at R5C7 = {489/579/678}
4a. 4 of {489} must be in R7C5 -> no 4 in R6C6

5. 10(3) cage at R5C3 = {127/136/145/235}
5a. 6,7 of {127/136} must be in R7C5 -> no 6,7 in R6C4

6. Old Lace R37C5 only contain 3,4,5,6,7 -> no 1,2,8,9 in R5C46
6a. Max R5C46 = 13 -> min R5C5 = 3

7. 1 in Old Lace only in R5C3 + R6C4, locked for D\ R3C1, CPE no 1 in R6C123, no 1 in R7C3 using D/ R1C9
7a. 10(3) cage at R5C3 contains 1 = {127/136/145}
7b. 8(3) cage at R9C5 = {125/134}, 1 locked for N8

8. 20(3) cage at R3C5, 21(3) cage at R5C7 and R5C5 are all part of Old Lace -> no 8,9 in R5C5 (because the 20(3) cage and 21(3) cage would clash with either of 8,9 in R5C5)

9. 16(3) cage at R5C4 = {367/457}, 7 locked for R5 and N5
9a. 20(3) cage at R3C5 = {389/569}, no 4, 9 locked for Old Lace and D\ R1C3, CPE no 9 in R4C789
9b. Old Lace R5C46 = R37C5 -> R357C5 = {367/457}, 7 locked for C5, CPE no 7 in R7C37 using D\ R1C1 and D/ R1C9
9c. 5 of {457} must be in R3C5 -> no 5 in R57C5


10. 21(3) cage at R5C7 = {489/579/678}
10a. 4,7 only in R7C5 -> R7C5 = {47}
10b. 9 of {579} must be in R5C7 -> no 5 in R5C7

11. 10(3) cage at R5C3 (step 7a) = {127/145} (cannot be {136} because R7C5 only contains 4,7), no 3
11a. R7C5 = {47} -> no 4 in R5C3 + R6C4

My original steps 12 and 13 were incorrect, so I’ve re-worked from here and added a few bits, in blue, to earlier steps.

12. Old Lace R5C37 only contains 1,2,6,8,9 -> no 3,4,5 in R46C5

13. 10(3) cage at R5C3 (step 11) = {127/145} = {12}7/[154]
13a. 9(3) cage at R3C5 = {135/234} (cannot be {126} which clashes with 10(3) cage = {12}7 and with 10(3) cage = [154] because R357C5 (step 9b) cannot contain both of 4,6), no 6
13b. 9(3) cage at R3C5 = {135/234}, 3 locked for D/ R1C7 and Old Lace
13c. 3 of 9(3) cage in R3C5 + R4C4, CPE no 3 in R123C4, no 3 in R3C3 using D\ R1C1
13d. R5C3 = {12} -> no 2 in R4C4

14. Old Lace R37C5 only contains 3,4,5,7, -> no 6 in R5C46

15. R5C3 + R6C4 = {12} (hidden pair in Old Lace), locked for D\ R3C1, R7C5 = 7 (cage sum), placed for D\ R3C1 and D/ R3C9
15a. Naked pair {12} in R5C3 + R6C4, CPE no 2 in 19(3) cage at R6C1

16. Old Lace R37C5 only contains 3,5,7 -> no 4 in R5C46

17. 4 in Old Lace only in R4C4 + R5C5, locked for D\ R1C1, clean-up: no 3 in 8(3) cage at R1C1
17a. 8(3) cage = {125}, locked for N1 and D\ R1C1

18. R7C5 = 7 -> R5C7 + R6C6 = 14 = {68}, locked for Old Lace and D/ R3C9 -> R5C5 = 4, placed for D/ R1C9, R4C4 = 3, placed for D\ R1C1, R3C5 = 5, placed for D\ R1C3 and D/ R1C7, R4C6 = 9, placed for D/ R1C9, R5C7 = 6 (cage sum), placed for D\ R1C3, R6C6 = 8, placed for D\ R1C1, R7C7 = 9, R5C3 = 1 (cage sum), placed for D/ R1C7, R6C4 = 2, placed for D/ R1C9, R3C3 = 2
18a. Naked pair {57} in R5C46, locked for R5
18b. Naked pair {16} in R46C5, locked for C5
18c. Naked pair {67} in R8C8 + R9C9, locked for N9
18d. R9C6 = 1 (hidden single in R9)

19. 19(3) cage at R1C9 = {568} (only remaining combination) -> R3C7 = 8, placed for D/ R1C9, R1C9 + R2C8 = {56}, locked for N3 and D/ R1C9 -> R7C3 = 3, R9C1 = 7, R8C2 = 1, R2C2 = 5, R1C1 = 1, R2C8 = 6, R1C9 = 5, R8C8 = 7, R9C9 = 6

20. 8(3) cage at R9C5 = {125/134}
20a. 4,5 only in R9C7 -> R9C7 = {45}

21. R6C9 = 7, then R5C9 = 9 (hidden singles in L R9C9)
21a. 5 in L R9C9 only in R9C78, locked for R9 and N9
21b. 3 in R9 only in R9C58, locked for L R9C9, no 3 in R8C9
21c. 3 in C9 only in R23C9, locked for N3

22. R4C3 = 7 (hidden single in N4)

23. 7 in L R1C1 only in R1C24, locked for R1
23a. R2C7 = 7 (hidden single in N3)

24. R4C1 = 5 (hidden single in L R1C1)
24a. R6C7 = 5 (hidden single in R6), R9C7 = 4, placed for D\ R3C1, R9C3 = 9, placed for D/ R3C9, R1C7 = 2, then R2C6 = 4, placed for D/ R1C7

and the rest is naked singles, without using diagonals or the Ls.

Rating Comment:
Having amended my rating comment for version 1A, I've now added this one for version 1C.

I'll rate my walkthrough for version 1C at 1.0. Step 8 and my re-worked step 13a are still my hardest steps.


Last edited by Andrew on Thu Nov 07, 2013 8:28 pm, edited 3 times in total.

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HATMAN
PostPosted: Sat Feb 23, 2013 9:35 am 
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I agree about the old lace rating - the first time you do it it is hard to see and interesting - next time it is an obvious feature of the pattern.

I liked your move 8 I plodded much more on this.
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Andrew
PostPosted: Thu Nov 07, 2013 5:17 am 
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Wow! What a difference the removal of the 8(3) cage in R9 makes!

I'd got as far as step 27 in version 1D back in February. When I came back to this puzzle, it took a lot of thought to find the next step, which may be the equivalent of several fishes.

Here is my walkthrough for version 1D:
There are L-shaped 45(9) cages at R1C1 and R9C9 (well, strictly speaking at R5C9 but R9C9 emphasises that it’s at the opposite corner), an Old Lace pattern in the centre of the grid and large diagonals D\ at R1C1, R1C3, R3C1 and D/ at R1C7, R1C9 and R3C9.

For the Old Lace pattern, the values in R37C5 must be in R5C46 and the values in R5C37 must be in R46C5.

Prelims

a) 8(3) cage at R1C1 = {125/134}
b) 19(3) cage at R1C9 = {289/379/469/478/568}, no 1
c) 9(3) cage at R3C5 = {126/135/234}, no 7,8,9
d) 20(3) cage at R3C5 = {389/479/569/578}, no 1,2
e) 10(3) cage at R5C3 = {127/136/145/235}, no 8,9
f) 21(3) cage at R5C7 = {489/579/678}, no 1,2,3
g) 19(3) cage at R6C1 = {289/379/469/478/568}, no 1

1. 8(3) cage at R1C1 = {125/134}, 1 locked for N1 and D\ R1C1

2. 9(3) cage at R3C5 = {126/135/234}
2a. 6 of {126} must be in R3C5 -> no 6 in R4C4 + R5C3
2b. 1 of {135} must be in R5C3 -> no 5 in R5C3

3. 20(3) cage at R3C5 = {389/479/569/578}
3a. 3,4 of {389/479} must be in R3C5 -> no 3,4 in R4C6 + R5C7

4. 21(3) cage at R5C7 = {489/579/678}
4a. 4 of {489} must be in R7C5 -> no 4 in R6C6

5. 10(3) cage at R5C3 = {127/136/145/235}
5a. 6,7 of {127/136} must be in R7C5 -> no 6,7 in R6C4

6. Old Lace R37C5 only contain 3,4,5,6,7 -> no 1,2,8,9 in R5C46
6a. Max R5C46 = 13 -> min R5C5 = 3

7. 1 in Old Lace only in R5C3 + R6C4, locked for D\ R3C1, CPE no 1 in R7C3 using D/ R1C9
7a. 10(3) cage at R5C3 contains 1 = {127/136/145}

8. 20(3) cage at R3C5, 21(3) cage at R5C7 and R5C5 are all part of Old Lace -> no 8,9 in R5C5 (because the 20(3) cage and 21(3) cage would clash with either of 8,9 in R5C5)

9. 16(3) cage at R5C4 = {367/457}, 7 locked for R5 and N5
9a. 20(3) cage at R3C5 = {389/569}, no 4, 9 locked for Old Lace and D\ R1C3, CPE no 9 in R4C789
9b. Old Lace R5C46 = R37C5 -> R357C5 = {367/457}, 7 locked for C5, CPE no 7 in R7C37 using D\ R1C1 and D/ R1C9
9c. 5 of {457} must be in R3C5 -> no 5 in R57C5


10. 21(3) cage at R5C7 = {489/579/678}
10a. 4,7 only in R7C5 -> R7C5 = {47}
10b. 9 of {579} must be in R5C7 -> no 5 in R5C7

11. 10(3) cage at R5C3 (step 7a) = {127/145} (cannot be {136} because R7C5 only contains 4,7), no 3
11a. R7C5 = {47} -> no 4 in R5C3 + R6C4

My original steps 12 and 13 were incorrect, so I’ve re-worked from here and added a few bits, in blue, to earlier steps.

12. Old Lace R5C37 only contains 1,2,6,8,9 -> no 3,4,5 in R46C5

13. 10(3) cage at R5C3 (step 11) = {127/145} = {12}7/[154]
13a. 9(3) cage at R3C5 = {135/234} (cannot be {126} which clashes with 10(3) cage = {12}7 and with 10(3) cage = [154] because R357C5 (step 9b) cannot contain both of 4,6), no 6
13b. 9(3) cage at R3C5 = {135/234}, 3 locked for D/ R1C7 and Old Lace
13c. 3 of 9(3) cage in R3C5 + R4C4, CPE no 3 in R123C4, no 3 in R3C3 using D\ R1C1
13d. R5C3 = {12} -> no 2 in R4C4

14. Old Lace R37C5 only contains 3,4,5,7, -> no 6 in R5C46

15. R5C3 + R6C4 = {12} (hidden pair in Old Lace), locked for D\ R3C1, R7C5 = 7 (cage sum), placed for D\ R3C1 and D/ R3C9
15a. Naked pair {12} in R5C3 + R6C4, CPE no 2 in 19(3) cage at R6C1

16. Old Lace R37C5 only contains 3,5,7 -> no 4 in R5C46

17. 4 in Old Lace only in R4C4 + R5C5, locked for D\ R1C1, clean-up: no 3 in 8(3) cage at R1C1
17a. 8(3) cage = {125}, locked for N1 and D\ R1C1

18. R7C5 = 7 -> R5C7 + R6C6 = 14 = {68}, locked for Old Lace and D/ R3C9 -> R5C5 = 4, placed for D/ R1C9, R4C4 = 3, placed for D\ R1C1, R3C5 = 5, placed for D\ R1C3 and D/ R1C7, R4C6 = 9, placed for D/ R1C9, R5C7 = 6 (cage sum), placed for D\ R1C3, R6C6 = 8, placed for D\ R1C1, R7C7 = 9, R5C3 = 1 (cage sum), placed for D/ R1C7, R6C4 = 2, placed for D/ R1C9, R3C3 = 2
18a. Naked pair {57} in R5C46, locked for R5
18b. Naked pair {16} in R46C5, locked for C5
18c. Naked pair {67} in R8C8 + R9C9, locked for N9

19. 19(3) cage at R1C9 = {568} (only remaining combination) -> R3C7 = 8, placed for D/ R1C9, R1C9 + R2C8 = {56}, locked for N3 and D/ R1C9 -> R7C3 = 3, R8C2 + R9C1 = {17}, locked for N7

20. 19(3) cage at R6C1 = {379/469}, no 5, 9 locked for R6 and N4
20a. 3 of {379} must be in R6C1 -> no 7 in R6C1
20b. 5 in R6 only in R6C79, locked for N6
20c. 5 in R6C79, CPE no 5 in R9C7 using L R9C9

21. 1 in L R1C1 only in R1C14, locked for R1
21a. 5 in L R1C1 only in R14C1, locked for C1

22. 6 in L R9C9 only in R9C69, locked for R9
22a. 7 in L R9C9 only in R69C9, locked for C9

23. 8 in R1 only in R1C2345, locked for L R1C1, no 8 in R245C1
23a. 8 in C1 only in R78C1, locked for N7

24. 3 in R9 only in R9C5678, locked for L R9C9, no 3 in R568C9
24a. 3 in C9 only in R23C9, locked for N3

[The removal of the 8(3) cage from R9C5 makes so much difference that now I can only see forcing chains or contradiction moves as the way forward. That’s hardly surprising, since HATMAN said that JSudoku used 16 fishes.]

25. Consider placements for 1 on D/
1 in R8C2
or 1 in R9C1 => R1C4 = 1 (hidden single in L R1C1)
-> no 1 in R8C4

26. Consider placements for 6 on D/
6 in R1C9 => R9C6 = 6 (hidden single in L R9C9)
or 6 in R2C8 = 6
-> no 6 in R2C6

27. 19(3) cage at R6C1 = {379/469}
19(3) cage = {379} => R9C9 = 7 (hidden single in C9), R9C1 = 1, R8C2 = 7 => no 7 in R6C2
or 19(3) cage = {469}
-> no 7 in R6C2

[This was how far I got when I first tried this puzzle.]

[First seen as a contradiction move, I managed to find nested forcing chains …
The contradiction move 19(3) cage at R6C1 cannot be {379} because … giving a clash between 1 in R2C2 and 1 in R2C7 is a bit shorter.]
28. Consider placements for 1 on D\
1 in R1C1 => R9C1 = 7, R6C9 = 7 (hidden single in L R9C9) => no 7 in R6C3
or 1 in R2C2 => R1C7 + R2C67 = {247}, which must be a naked triple because of D/ R1C7
and then consider placements for 7 in R1C7 + R2C67
7 in R2 => 7 in N1 in R13C2 => R9C1 = 7, R6C9 = 7 (hidden single in L R9C9) => no 7 in R6C3 or 7 in R1C3 => no 7 in R6C3
or 7 in C7 => 7 in N6 only in R6C89 => no 7 in R6C3
28a. 19(3) cage at R6C1 (step 27) = {469} (only remaining combination), locked for R6 and N4 -> R46C5 = [61]
28b. Naked triple {357} in R6C789, locked for N6
28c. Naked triple {567} in R169C9, locked for C9

29. 7 in R4 only in R4C13, CPE no 7 in R1C3 using L R1C1

30. 3 in C1 only in R235C1, locked for L R1C1, no 3 in R1C25
30a. R1C6 = 3 (hidden single in R1)

31. 6 in N2 only in R1C4 + R3C46, CPE no 6 in R3C1 using L R1C1

32. 8 in C9 only in R4C9 or in R578C9, locked for L R9C9 => R9C4 = 8 (hidden single in R9)
-> 8 must be in R4C9 or R9C4
32a. Consider placement for 8 in R4C9 + R9C4
R4C9 = 8 => R5C2 = 8 (hidden single in N4), 8 in R1 only in R1C345, CPE no 8 in R2C4 using D\ R1C3
or R9C4 = 8
-> no 8 in R2C4
32b. Consider placement for 8 in R4C9 + R9C4
R4C9 = 8 => R4C2 = 5, R2C2 = 1 => R1C4 = 1 (hidden single in L R1C1)
or R9C4 = 8
-> no 8 in R1C4, no 1 in R9C4
32c. 8 in C4 only in R79C4, locked for N8

33. 1 in N8 only in R7C46 + R9C6, CPE no 1 in R7C9 using L R9C9

34. Consider placements for 1 on D\
1 in R1C1 => R9C1 = 7 => R4C3 = 7 (hidden single in R4)
or 1 in R2C2 => naked triple {247} in R2C467, locked for R2 => R4C3 = 7 (hidden single in C3)
-> R4C3 = 7
34a. 8 in N4 only in R45C2, locked for C2

[Taking the previous step a bit further …]
35. Consider placements for 1 on D\
1 in R1C1 => R9C1 = 7
or 1 in R2C2 => naked triple {247} in R2C467, locked for R2 => R9C1 = 7 (hidden single in R9C1)
-> R9C1 = 7, R8C2 = 1, R2C2 = 5, R1C1 = 1, R2C8 = 6, R1C9 = 5, R8C8 = 7, R9C9 = 6, R4C2 = 8, R6C789 = [537]
35b. Naked pair {23} in R5C12, locked for R5 and N4 -> R4C1 = 5

36. R79C8 = {15} (hidden pair in N9), locked for C8
36a. R5C8 = 8 (hidden single in C8), R5C9 = 9, placed for L R9C9, no 9 in R9C5
36b. R9C4 = 8 (hidden single in R9)

37. 7 in L R1C1 only in R1C24, locked for R1
37a. R2C7 = 7, then R4C7 = 1 (hidden singles in C7)
37b. Naked triple {248} in R478C9, locked for C9
37c. Naked pair {24} in R1C7 + R2C6, locked for D/ R1C7
37d. Naked pair {24} in R1C7 + R2C6, CPE no 4 in R1C4, no 2 in R1C5
37e. R5C1 = 2 (hidden single in L R1C1), R5C2 = 3

38. R9C68 = {15} (hidden pair in L R9C9), locked for R9
38a. R8C3 = 5 (hidden single in C3)

39. 6 in N1 only in R13C2, locked for C2 -> R6C2 = 9
39a. Naked pair {24} in R79C2, locked for C2 and N7 -> R9C3 = 9, placed for D/ R3C9, R8C4 = 4, placed for D/ R3C9, R4C8 = 2, R2C4 = 1, R2C9 = 3, R8C6 = 6, R78C1 = [68], R6C1 = 4, R2C1 = 9, placed for L R1C1, R1C5 = 8

and the rest is naked singles, without using diagonals or the Ls.

Rating Comment:
I'll rate my walkthrough for version 1D at 1.75. I used several forcing chains, including nested chains for step 28, the most important breakthrough.

Now to see whether version 1E can be solved in a similar way.
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Andrew
PostPosted: Thu Nov 07, 2013 11:10 pm 
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I wrote:
Now to see whether version 1E can be solved in a similar way.
Indeed it can; in fact in exactly the same way. :roll: I only needed to make minor changes to steps 20, 27 and 28.

Here is my walkthrough for version 1E:
There are L-shaped 45(9) cages at R1C1 and R9C9 (well, strictly speaking at R5C9 but R9C9 emphasises that it’s at the opposite corner), an Old Lace pattern in the centre of the grid and large diagonals D\ at R1C1, R1C3, R3C1 and D/ at R1C7, R1C9 and R3C9.

For the Old Lace pattern, the values in R37C5 must be in R5C46 and the values in R5C37 must be in R46C5.

Prelims

a) 8(3) cage at R1C1 = {125/134}
b) 19(3) cage at R1C9 = {289/379/469/478/568}, no 1
c) 9(3) cage at R3C5 = {126/135/234}, no 7,8,9
d) 20(3) cage at R3C5 = {389/479/569/578}, no 1,2
e) 10(3) cage at R5C3 = {127/136/145/235}, no 8,9
f) 21(3) cage at R5C7 = {489/579/678}, no 1,2,3

1. 8(3) cage at R1C1 = {125/134}, 1 locked for N1 and D\ R1C1

2. 9(3) cage at R3C5 = {126/135/234}
2a. 6 of {126} must be in R3C5 -> no 6 in R4C4 + R5C3
2b. 1 of {135} must be in R5C3 -> no 5 in R5C3

3. 20(3) cage at R3C5 = {389/479/569/578}
3a. 3,4 of {389/479} must be in R3C5 -> no 3,4 in R4C6 + R5C7

4. 21(3) cage at R5C7 = {489/579/678}
4a. 4 of {489} must be in R7C5 -> no 4 in R6C6

5. 10(3) cage at R5C3 = {127/136/145/235}
5a. 6,7 of {127/136} must be in R7C5 -> no 6,7 in R6C4

6. Old Lace R37C5 only contain 3,4,5,6,7 -> no 1,2,8,9 in R5C46
6a. Max R5C46 = 13 -> min R5C5 = 3

7. 1 in Old Lace only in R5C3 + R6C4, locked for D\ R3C1, CPE no 1 in R6C123, no 1 in R7C3 using D/ R1C9
7a. 10(3) cage at R5C3 contains 1 = {127/136/145}

8. 20(3) cage at R3C5, 21(3) cage at R5C7 and R5C5 are all part of Old Lace -> no 8,9 in R5C5 (because the 20(3) cage and 21(3) cage would clash with either of 8,9 in R5C5)

9. 16(3) cage at R5C4 = {367/457}, 7 locked for R5 and N5
9a. 20(3) cage at R3C5 = {389/569}, no 4, 9 locked for Old Lace and D\ R1C3, CPE no 9 in R4C789
9b. Old Lace R5C46 = R37C5 -> R357C5 = {367/457}, 7 locked for C5, CPE no 7 in R7C37 using D\ R1C1 and D/ R1C9
9c. 5 of {457} must be in R3C5 -> no 5 in R57C5

10. 21(3) cage at R5C7 = {489/579/678}
10a. 4,7 only in R7C5 -> R7C5 = {47}
10b. 9 of {579} must be in R5C7 -> no 5 in R5C7

11. 10(3) cage at R5C3 (step 7a) = {127/145} (cannot be {136} because R7C5 only contains 4,7), no 3
11a. R7C5 = {47} -> no 4 in R5C3 + R6C4

12. Old Lace R5C37 only contains 1,2,6,8,9 -> no 3,4,5 in R46C5

13. 10(3) cage at R5C3 (step 11) = {127/145} = {12}7/[154]
13a. 9(3) cage at R3C5 = {135/234} (cannot be {126} which clashes with 10(3) cage = {12}7 and with 10(3) cage = [154] because R357C5 (step 9b) cannot contain both of 4,6), no 6
13b. 9(3) cage at R3C5 = {135/234}, 3 locked for D/ R1C7 and Old Lace
13c. 3 of 9(3) cage in R3C5 + R4C4, CPE no 3 in R123C4, no 3 in R3C3 using D\ R1C1
13d. R5C3 = {12} -> no 2 in R4C4

14. Old Lace R37C5 only contains 3,4,5,7, -> no 6 in R5C46

15. R5C3 + R6C4 = {12} (hidden pair in Old Lace), locked for D\ R3C1, R7C5 = 7 (cage sum), placed for D\ R3C1 and D/ R3C9
15a. Naked pair {12} in R5C3 + R6C4, CPE no 2 in 19(3) cage at R6C1

16. Old Lace R37C5 only contains 3,5,7 -> no 4 in R5C46

17. 4 in Old Lace only in R4C4 + R5C5, locked for D\ R1C1, clean-up: no 3 in 8(3) cage at R1C1
17a. 8(3) cage = {125}, locked for N1 and D\ R1C1

18. R7C5 = 7 -> R5C7 + R6C6 = 14 = {68}, locked for Old Lace and D/ R3C9 -> R5C5 = 4, placed for D/ R1C9, R4C4 = 3, placed for D\ R1C1, R3C5 = 5, placed for D\ R1C3 and D/ R1C7, R4C6 = 9, placed for D/ R1C9, R5C7 = 6 (cage sum), placed for D\ R1C3, R6C6 = 8, placed for D\ R1C1, R7C7 = 9, R5C3 = 1 (cage sum), placed for D/ R1C7, R6C4 = 2, placed for D/ R1C9, R3C3 = 2
18a. Naked pair {57} in R5C46, locked for R5
18b. Naked pair {16} in R46C5, locked for C5
18c. Naked pair {67} in R8C8 + R9C9, locked for N9

19. 19(3) cage at R1C9 = {568} (only remaining combination) -> R3C7 = 8, placed for D/ R1C9, R1C9 + R2C8 = {56}, locked for N3 and D/ R1C9 -> R7C3 = 3, R8C2 + R9C1 = {17}, locked for N7

20. 15(3) cage at R6C7 = {159/357}, no 4, 5 locked for R6 and N6
20a. 1 of {159} must be in R6C8 -> no 1 in R6C79
20b. 4 in R6 only in R6C123, locked for N4
20c. 5 in R6C79, CPE no 5 in R9C7 using L R9C9

21. 1 in L R1C1 only in R1C14, locked for R1
21a. 5 in L R1C1 only in R14C1, locked for C1

22. 6 in L R9C9 only in R9C69, locked for R9
22a. 7 in L R9C9 only in R69C9, locked for C9

23. 8 in R1 only in R1C2345, locked for L R1C1, no 8 in R245C1
23a. 8 in C1 only in R78C1, locked for N7

24. 3 in R9 only in R9C5678, locked for L R9C9, no 3 in R568C9
24a. 3 in C9 only in R23C9, locked for N3

25. Consider placements for 1 on D/
1 in R8C2
or 1 in R9C1 => R1C4 = 1 (hidden single in L R1C1)
-> no 1 in R8C4

26. Consider placements for 6 on D/
6 in R1C9 => R9C6 = 6 (hidden single in L R9C9)
or 6 in R2C8 = 6
-> no 6 in R2C6

27. 15(3) cage at R6C7 (step 20) = {159/357}, R6C5 = {16} -> R6C123 = {347/469}
27a. 3 of {347} must be in R6C1 -> no 7 in R6C1
27b. Consider combinations for R6C123 = {347/469}
R6C123 = {347} => R9C9 = 7 (hidden single in C9), R9C1 = 1, R8C2 = 7 => no 7 in R6C2
or 19(3) cage = {469}
-> no 7 in R6C2

[First seen as a contradiction move, I managed to find nested forcing chains …
The contradiction move R6C123 cannot be {347} because … giving a clash between 1 in R2C2 and 1 in R2C7 is a bit shorter.]
28. Consider placements for 1 on D\
1 in R1C1 => R9C1 = 7, R6C9 = 7 (hidden single in L R9C9) => no 7 in R6C3
or 1 in R2C2 => R1C7 + R2C67 = {247}, which must be a naked triple because of D/ R1C7
and then consider placements for 7 in R1C7 + R2C67
7 in R2 => 7 in N1 in R13C2 => R9C1 = 7, R6C9 = 7 (hidden single in L R9C9) => no 7 in R6C3 or 7 in R1C3 => no 7 in R6C3
or 7 in C7 => 7 in N6 only in R6C89 => no 7 in R6C3
28a. R6C123 (step 27) = {469} (only remaining combination), locked for R6 and N4 -> R46C5 = [61]
28b. Naked triple {357} in R6C789, locked for N6
28c. Naked triple {567} in R169C9, locked for C9

29. 7 in R4 only in R4C13, CPE no 7 in R1C3 using L R1C1

30. 3 in C1 only in R235C1, locked for L R1C1, no 3 in R1C25
30a. R1C6 = 3 (hidden single in R1)

31. 6 in N2 only in R1C4 + R3C46, CPE no 6 in R3C1 using L R1C1

32. 8 in C9 only in R4C9 or in R578C9, locked for L R9C9 => R9C4 = 8 (hidden single in R9)
-> 8 must be in R4C9 or R9C4
[Looking at this step for R9 shows that 8 cannot be in both of R4C9 and R9C4.
32a. Consider placement for 8 in R4C9 + R9C4
R4C9 = 8 => R5C2 = 8 (hidden single in N4), 8 in R1 only in R1C345, CPE no 8 in R2C4 using D\ R1C3
or R9C4 = 8
-> no 8 in R2C4
32b. Consider placement for 8 in R4C9 + R9C4
R4C9 = 8 => R4C2 = 5, R2C2 = 1 => R1C4 = 1 (hidden single in L R1C1)
or R9C4 = 8
-> no 8 in R1C4, no 1 in R9C4
32c. 8 in C4 only in R79C4, locked for N8

33. 1 in N8 only in R7C46 + R9C6, CPE no 1 in R7C9 using L R9C9

34. Consider placements for 1 on D\
1 in R1C1 => R9C1 = 7 => R4C3 = 7 (hidden single in R4)
or 1 in R2C2 => naked triple {247} in R2C467, locked for R2 => R4C3 = 7 (hidden single in C3)
-> R4C3 = 7
34a. 8 in N4 only in R45C2, locked for C2

[Taking the previous step a bit further …]
35. Consider placements for 1 on D\
1 in R1C1 => R9C1 = 7
or 1 in R2C2 => naked triple {247} in R2C467, locked for R2 => R9C1 = 7 (hidden single in R9C1)
-> R9C1 = 7, R8C2 = 1, R2C2 = 5, R1C1 = 1, R2C8 = 6, R1C9 = 5, R8C8 = 7, R9C9 = 6, R4C2 = 8, R6C789 = [537]
35b. Naked pair {23} in R5C12, locked for R5 and N4 -> R4C1 = 5

36. R79C8 = {15} (hidden pair in N9), locked for C8
36a. R5C8 = 8 (hidden single in C8), R5C9 = 9, placed for L R9C9, no 9 in R9C5
36b. R9C4 = 8 (hidden single in R9)

37. 7 in L R1C1 only in R1C24, locked for R1
37a. R2C7 = 7, then R4C7 = 1 (hidden singles in C7)
37b. Naked triple {248} in R478C9, locked for C9
37c. Naked pair {24} in R1C7 + R2C6, locked for D/ R1C7
37d. Naked pair {24} in R1C7 + R2C6, CPE no 4 in R1C4, no 2 in R1C5
37e. R5C1 = 2 (hidden single in L R1C1), R5C2 = 3

38. R9C68 = {15} (hidden pair in L R9C9), locked for R9
38a. R8C3 = 5 (hidden single in C3)

39. 6 in N1 only in R13C2, locked for C2 -> R6C2 = 9
39a. Naked pair {24} in R79C2, locked for C2 and N7 -> R9C3 = 9, placed for D/ R3C9, R8C4 = 4, placed for D/ R3C9, R4C8 = 2, R2C4 = 1, R2C9 = 3, R8C6 = 6, R78C1 = [68], R6C1 = 4, R2C1 = 9, placed for L R1C1, R1C5 = 8

and the rest is naked singles, without using diagonals or the Ls.

Rating Comment:
I'll rate my walkthrough for version 1E at 1.75, the same as for version 1D.
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Andrew
PostPosted: Fri Nov 08, 2013 9:51 pm 
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I found this the most enjoyable of the three harder versions.

My solving path was slightly longer but technically less difficult than versions 1D and 1E.

Here is my walkthrough for version 1F:
There are L-shaped 45(9) cages at R1C1 and R9C9 (well, strictly speaking at R5C9 but R9C9 emphasises that it’s at the opposite corner), an Old Lace pattern in the centre of the grid and large diagonals D\ at R1C1, R1C3, R3C1 and D/ at R1C7, R1C9 and R3C9.

For the Old Lace pattern, the values in R37C5 must be in R5C46 and the values in R5C37 must be in R46C5.

Prelims

a) 11(2) cage at R3C1 = {29/38/47/56}, no 1
b) 8(3) cage at R1C1 = {125/134}
c) 19(3) cage at R1C9 = {289/379/469/478/568}, no 1
d) 9(3) cage at R3C5 = {126/135/234}, no 7,8,9
e) 20(3) cage at R3C5 = {389/479/569/578}, no 1,2
f) 10(3) cage at R5C3 = {127/136/145/235}, no 8,9
g) 21(3) cage at R5C7 = {489/579/678}, no 1,2,3

1. 8(3) cage at R1C1 = {125/134}, 1 locked for N1 and D\ R1C1

2. 9(3) cage at R3C5 = {126/135/234}
2a. 6 of {126} must be in R3C5 -> no 6 in R4C4 + R5C3
2b. 1 of {135} must be in R5C3 -> no 5 in R5C3

3. 20(3) cage at R3C5 = {389/479/569/578}
3a. 3,4 of {389/479} must be in R3C5 -> no 3,4 in R4C6 + R5C7

4. 21(3) cage at R5C7 = {489/579/678}
4a. 4 of {489} must be in R7C5 -> no 4 in R6C6

5. 10(3) cage at R5C3 = {127/136/145/235}
5a. 6,7 of {127/136} must be in R7C5 -> no 6,7 in R6C4

6. Old Lace R37C5 only contain 3,4,5,6,7 -> no 1,2,8,9 in R5C46
6a. Max R5C46 = 13 -> min R5C5 = 3

7. 1 in Old Lace only in R5C3 + R6C4, locked for D\ R3C1, CPE no 1 in R6C123, no 1 in R7C3 using D/ R1C9
7a. 10(3) cage at R5C3 contains 1 = {127/136/145}

8. 20(3) cage at R3C5, 21(3) cage at R5C7 and R5C5 are all part of Old Lace -> no 8,9 in R5C5 (because the 20(3) cage and 21(3) cage would clash with either of 8,9 in R5C5)

9. 16(3) cage at R5C4 = {367/457}, 7 locked for R5 and N5
9a. 20(3) cage at R3C5 = {389/569}, no 4, 9 locked for Old Lace and D\ R1C3, CPE no 9 in R4C789
9b. Old Lace R5C46 = R37C5 -> R357C5 = {367/457}, 7 locked for C5, CPE no 7 in R7C37 using D\ R1C1 and D/ R1C9
9c. 5 of {457} must be in R3C5 -> no 5 in R57C5

10. 21(3) cage at R5C7 = {489/579/678}
10a. 4,7 only in R7C5 -> R7C5 = {47}
10b. 9 of {579} must be in R5C7 -> no 5 in R5C7

11. 10(3) cage at R5C3 (step 7a) = {127/145} (cannot be {136} because R7C5 only contains 4,7), no 3
11a. R7C5 = {47} -> no 4 in R5C3 + R6C4

12. Old Lace R5C37 only contains 1,2,6,8,9 -> no 3,4,5 in R46C5

13. 10(3) cage at R5C3 (step 11) = {127/145} = {12}7/[154]
13a. 9(3) cage at R3C5 = {135/234} (cannot be {126} which clashes with 10(3) cage = {12}7 and with 10(3) cage = [154] because R357C5 (step 9b) cannot contain both of 4,6), no 6
13b. 9(3) cage at R3C5 = {135/234}, 3 locked for D/ R1C7 and Old Lace
13c. 3 of 9(3) cage in R3C5 + R4C4, CPE no 3 in R123C4, no 3 in R3C3 using D\ R1C1
13d. R5C3 = {12} -> no 2 in R4C4

14. Old Lace R37C5 only contains 3,4,5,7, -> no 6 in R5C46

15. R5C3 + R6C4 = {12} (hidden pair in Old Lace), locked for D\ R3C1, R7C5 = 7 (cage sum), placed for D\ R3C1 and D/ R3C9, clean-up: no 4,9 in 11(2) cage at R3C1
15a. Naked pair {12} in R5C3 + R6C4, CPE no 2 in 19(3) cage at R6C1

16. Old Lace R37C5 only contains 3,5,7 -> no 4 in R5C46

17. 4 in Old Lace only in R4C4 + R5C5, locked for D\ R1C1, clean-up: no 3 in 8(3) cage at R1C1
17a. 8(3) cage = {125}, locked for N1 and D\ R1C1, clean-up: no 6 in R4C2

18. R7C5 = 7 -> R5C7 + R6C6 = 14 = {68}, locked for Old Lace and D/ R3C9 -> R5C5 = 4, placed for D/ R1C9, R4C4 = 3, placed for D\ R1C1, R3C5 = 5, placed for D\ R1C3 and D/ R1C7, R4C6 = 9, placed for D/ R1C9, R5C7 = 6 (cage sum), placed for D\ R1C3, R6C6 = 8, placed for D\ R1C1, R7C7 = 9, R5C3 = 1 (cage sum), placed for D/ R1C7, R6C4 = 2, placed for D/ R1C9, R3C3 = 2, clean-up: no 8 in R3C1
18a. Naked pair {57} in R5C46, locked for R5
18b. Naked pair {16} in R46C5, locked for C5
18c. Naked pair {67} in R8C8 + R9C9, locked for N9

19. 19(3) cage at R1C9 = {568} (only remaining combination) -> R3C7 = 8, placed for D/ R1C9, R1C9 + R2C8 = {56}, locked for N3 and D/ R1C9 -> R7C3 = 3, R8C2 + R9C1 = {17}, locked for N7

20. 1 in L R1C1 only in R1C14, locked for R1
20a. 5 in L R1C1 only in R14C1, locked for C1

21. 6 in L R9C9 only in R9C69, locked for R9
21a. 7 in L R9C9 only in R69C9, locked for C9

22. 8 in R1 only in R1C2345, locked for L R1C1, no 8 in R245C1
22a. 8 in C1 only in R78C1, locked for N7

23. 3 in R9 only in R9C5678, locked for L R9C9, no 3 in R568C9
23a. 3 in C9 only in R23C9, locked for N3

[And now, as well as the 8(3) cage having been removed from R9, there aren’t any 3-cell cages in R6 which had made that row interesting and useful for versions 1D and 1E. HATMAN said that JSudoku used 18 fishes for this puzzle.]

24. Consider placements for 1 on D/
1 in R8C2
or 1 in R9C1 => R1C4 = 1 (hidden single in L R1C1)
-> no 1 in R8C4

25. Consider placements for 6 on D/
6 in R1C9 => R9C6 = 6 (hidden single in L R9C9)
or 6 in R2C8 = 6
-> no 6 in R2C6

26. Consider placements for 7 on D/
7 in R8C2
or 7 in R9C1 => R6C9 = 7 (hidden single in L R9C9)
-> no 7 in R6C2

27. Consider placements for 5 on D/
5 in R1C9 => R4C1 = 5 (hidden single in L R1C1)
or 5 in R2C8
-> no 5 in R4C8

28. 8 in C9 only in R4C9 or in R578C9, locked for L R9C9 => R9C4 = 8 (hidden single in R9)
-> 8 must be in R4C9 or R9C4
28a. Consider placement for 8 in R4C9 + R9C4
R4C9 = 8 => R5C2 = 8 (hidden single in N4), 8 in R1 only in R1C345, CPE no 8 in R2C4 using D\ R1C3
or R9C4 = 8
-> no 8 in R2C4
28b. Consider placement for 8 in R4C9 + R9C4
R4C9 = 8 => R4C2 = 5, R2C2 = 1 => R1C4 = 1 (hidden single in L R1C1)
or R9C4 = 8
-> no 8 in R1C4, no 1 in R9C4
28c. 8 in C4 only in R79C4, locked for N8

29. 3 in C1 only in R235C1, locked for L R1C1 => R1C6 = 3 (hidden single in R1) or in R6C1 -> 3 must be in R1C6 or R6C1
29a. Consider placements for 3 in R1C6 + R6C1
R1C6 = 3
or R6C1 = 3 => R5C8 = 3 (hidden single in R5), 3 in R9 only in R9C567, CPE no 3 in R8C6 using D\ R3C1
-> no 3 in R8C6
29b. Consider placements for 3 in R1C6 + R6C1
R1C6 = 3
or R6C1 = 3 => R3C1 = 6, R4C2 = 5, both placed for D\ R3C1 => R8C6 = 4, placed for D\ R3C1, R9C7 = 3
-> no 3 in R9C6
29c. 3 in C6 only in R13C6, locked for N2

30. 3 must be in R1C6 or R6C1 (step 29)
30a. Consider placements for 3 in R1C6 + R6C1
R1C6 = 3
or R6C1 = 3 => R3C1 = 6, R4C2 = 5, R2C2 = 1, R1C1 = 5, R1C9 = 6
-> no 6 in R1C6
30b. 6 in N2 only in R13C4 + R3C6, CPE no 6 in R3C1 using L R1C1

31. R3C1 = 3, placed for D\ R3C1, R4C2 = 8, R1C6 = 3 (hidden single in R1), R2C9 = 3 (hidden single in R2), R5C2 = 3 (hidden single in C2)
31a. 8 in R5 only in R5C89, CPE no 8 in R9C8 using L R9C9
31b. R9C4 = 8 (hidden single in R9)
[Or use step 28, no 8 in R4C9 -> 8 in R9C4.]

32. Consider placements for 1 on D\
1 in R1C1 => R9C1 = 7
or 1 in R2C2 => naked triple {247} in R2C467, locked for R2, no 7 in R2C1
-> no 7 in R2C1
32a. 1 in R1C1 => R9C1 = 7
or 1 in R2C2 => naked triple {247} in R2C467, locked for R2, R8C2 = 7, R1C3 = 7 (hidden single in N1), placed for L R1C1, no 7 in R4C1
-> no 7 in R4C1
32b. 7 in L R1C1 only in R1C234, locked for R1

33. Consider placements for 7 in C1
R6C1 = 7
or R9C1 = 7 => R6C9 = 7 (hidden single in L R9C9)
-> 7 in R6C19, locked for R6

34. Consider placements for 7 on D/
R8C2 = 7 => R2C2 = 1 (hidden single in C2) => naked triple {247} in R2C467, locked for R2, no 7 in R2C3
or R9C1 = 7 => 7 in C2 only in R13C2, locked for N1
-> no 7 in R2C3

35. Consider placements for 7 in C1
R6C1 = 7 => R9C1 = 1, R8C2 = 7, R1C3 = 7 (hidden single in N1), placed for D\ R1C3, no 7 in R2C4, R4C7 = 7 (hidden single in R4) => R2C6 = 7 (hidden single in R2)
or R9C1 = 7 => R8C8 = 7 (hidden single in R8) => R2C7 = 7 (hidden single in N3)
-> 7 in R2C67, locked for R2

36. Consider placements for 1 on D\
1 in R1C1 => R9C1 = 7 => R6C9 = 7 (hidden single in C9) => R2C7 = 7 (hidden single in C7)
or 1 in R2C2 => R2C4 = 4
-> no 1,4 in R2C7
36a. 1 in N3 only in R3C89, locked for R3
36b. 1 in R3C89, CPE no 1 in R4C8 using D/ R3C9
36c. 1 in N2 only in R12C4, locked for C4
36d. 1 in N8 only in R79C6, CPE no 1 in R7C9 using L R9C9

37. Consider placements for 1 on D\
1 in R1C1 => R9C1 = 7 => R6C9 = 7 (hidden single in C9) => R2C7 = 7 (hidden single in C7) => R1C7 + R2C6 = {24}, locked for D/ R1C7
or 1 in R2C2 => R2C4 = 4, R2C67 = {27}, no 2 in R1C7 using D/ R1C7 => R1C7 = 4
-> 4 in R1C7 + R2C6, locked for D/ R1C7, no 4 in R6C2 + R7C1
37a. 4 in R1C7 + R2C6, CPE no 4 in R1C4

38. 2 in N4 only in R45C1, locked for C1 and L R1C1, no 2 in R1C5
38a. 2 in R1 only in R1C78, locked for N3 -> R2C7 = 7
38b. R6C9 = 7 (hidden single in N6), R9C9 = 6, R8C8 = 7, R1C9 = 5, R2C8 = 6, R1C1 = 1, R2C2 = 5, R8C2 = 1, R9C1 = 7
38c. R2C4 = 1 (hidden single in C4), placed for D\ R1C3
38d. 1 in N9 only in R79C8, locked for C8
38e. Naked triple {249} in R134C8, locked for C8 -> R56C8 = [83]
38f. Naked pair {15} in R79C8, locked for N9 -> R9C7 = 4, placed for D\ R3C1, R1C7 = 2, placed for D/ R1C7, R8C7 = 3, R2C6 = 4

39. Naked pair {49} in R13C8, locked for C8 and N3 -> R3C9 = 1, R4C89 = [24]

40. Naked pair {28} in R78C9, locked for L R9C9 -> R5C9 = 9, placed for L R9C9, R9C5 = 3
40a. Naked pair {15} in R9C68, locked for R9 -> R9C3 = 9, placed for D/ R3C9

41. Naked triple {456} in R7C4 + R8C46, locked for N8 -> R79C6 = [21]

and the rest is naked singles, without using diagonals or the Ls.

Rating Comment:
I'll rate my walkthrough for version 1F at Easy 1.75; I used a lot of forcing chains but no nested ones.
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HATMAN
PostPosted: Sat Nov 09, 2013 9:12 am 
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Joined: Wed Apr 30, 2008 9:45 pm
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Location: Saudi Arabia
Well done Andrew
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