SudokuSolver Forum

Here is another "onion" Hope you won't cry peeling this one !








3x3::k:2304:2304:3842:3842:4868:4868:4868:2055:2055:2304:5642:5642:5642:3085:3085:4623:5392:2055:4882:2579:2579:5642:3085:4623:4623:5392:2330:4882:2579:5917:2590:3359:3359:5392:5666:2330:4882:5917:5917:5159:2590:5392:5666:5666:5164:2093:5917:5159:2608:2608:2590:5666:3636:5164:2093:5159:3128:3128:2362:6203:3636:3636:5164:4927:5159:3128:2362:2362:6203:6203:6203:3399:4927:4927:4938:4938:4938:1869:1869:3399:3399:



Solution :





SSscore : 1.26

Thanks for the nice "onion"! To peel off the outer layer is not hard, but it's the 2nd layer which is tricky. I'm not a big fan of combo crunching, but I have to use a little here. Interested to see if there are easier ways (quite likely). Bottom line: no forcing chains used.




(Edited as the final version with correction, thanks Andrew! )

_________________
ADYFNC HJPLI BVSM GgK Oa m

A171 was quite fun since it's actually easier than it looks, so thanks manu! Step 7b seems to be crucial for an "easy" solving path because udosuk also found and used it.

A171 Walkthrough:

1. R123
a) Innies R1 = 11(4) = {1235} locked for R1
b) 9(3): R2C1 <> 2 since R1C12 <> 4,6
c) Outies R1 = 6(2) = [15/42/51]
d) 9(3) = 3{15/24} -> 3 locked for R1+N1

2. C789
a) Outies C9 = 5(2) = [14/23]
b) 8(3) = {125} locked for N3; 5 also locked for C9
c) 20(3) = 9{38/47} -> 9 locked for C9

3. C1+R9 !
a) Outies C1 = 10(2) = [19/28/37]
b) Outies R9 = 13(2) <> 1,2,3; R8C1 <> 4,8
c) ! Innies R9 = 19(4): R9C1 <> 3,4 since R9C8 = (34) and 5 only possible @ R9C1
d) 19(3) @ R8C1 = 8{29/56} -> 8 locked for R9+N7
e) 19(3) @ R9C3 = 9{37/46} -> 9 locked for R9
f) Outies C1 = 10(2) = {28} -> R1C2 = 2, R9C2 = 8
g) 9(3) = {234} -> R1C1 = 3, R2C1 = 4

4. C789
a) R1C8 = 1, R1C9 = 5, R2C9 = 2
b) Outie C9 = R9C8 = 4
c) 9(2) = [36/63/81]
d) 13(3) = 4{18/36}; R9C9 <> 6
e) 4 locked in 20(3) = {479} @ C9 for N6

5. R789
a) 19(3) @ R9C3 = {379} locked for R9
b) R9C9 = 1 -> R8C9 = 8
c) 7(2) = {25} locked for R9
d) R9C1 = 6 -> R8C1 = 5

6. C123
a) 19(3) @ N1 = {289} -> 2 locked for C1+N4
b) 10(3) = 1{36/45} -> R4C2 = (34); 1 locked for R3+N1
c) 2 locked in 12(3) @ C3 for 12(3) -> 12(3) <> 5,8
d) Hidden Single: R7C6 = 8 @ R7

7. C456 !
a) 24(4) = 8{169/349/367} <> 2
b) ! 9(3) = 2{16/34} since {135} blocked by Killer pair (13) of 24(4) -> 2 locked for N8
c) R9C6 = 5, R9C7 = 2

8. N45 !
a) 23(4) = 5{369/378/468} <> 1 since other combos blocked by R4C2 = (34), R6C1 = (17) and R45C1 = (289)
-> 5 locked for N4
b) Killer pair (89) locked in 23(4) + R45C1 for N4
c) Innies N5 = 12(2) <> 1,2,6; R5C4 <> 4,7
d) ! 20(4) <> 5 since 5,8 only possible @ R5C4
e) 1 locked in R6C13 @ N4 for R6
f) 13(2) <> 5,8
g) 1,5 locked in 10(3) @ N5 = {145} -> R6C6 = 4
h) Innies N5 = 12(2) = {39} locked for R5+N5
i) 13(2) = {67} locked for R4+N5
j) R4C9 = 3, R3C9 = 6
k) 21(4) = {1389} since R5C6 = (39) -> R4C7 = 1; 8 locked for C8+N3

9. C789
a) 22(4) = 25{69/78} -> 2,5 locked for N6
b) 14(3) = {356} -> R6C8 = 6; 3 locked for R7+N9
c) 18(3) = {279} -> R3C6 = 2; 7,9 locked for C7+N3
d) 21(4) = {1389} -> R5C6 = 9; 3 locked for C8
e) 19(3) = 4{69/78} -> R1C7 = 4; R1C5 = (89)
f) R4C4 = 5, R5C4 = 3

10. R123
a) 5 locked in 12(3) @ N2 = 5{16/34}
b) 12(3): R3C5 <> 3 since 4 only possible there
c) 10(3) = {145} -> R4C2 = 4; 5 locked for R3+N1
d) R3C5 = 4
e) 22(4) = {1678} -> R2C4 = 1; 6 locked for R2+N1

11. Rest is singles.

Rating: Hard 1.0. I used a Killer pair and placement analysis (can't come up with a better word ).

Thanks manu for another enjoyable "onion"! As udosuk commented, peeling the outer layer isn't hard. It's only after that has been done that the posted walkthroughs take different directions.

Here is my walkthrough. Thanks Afmob for your comments; I've done some minor editing including deleting step 36.

Prelims

a) R1C34 = {69/78}
b) R34C9 = {18/27/36/45}, no 9
c) R4C56 = {49/58/67}, no 1,2,3
d) R67C1 = {17/26/35}, no 4,8,9
e) R6C45 = {19/28/37/46}, no 5
f) R9C67 = {16/25/34}, no 7,8,9
g) 9(3) cage in N1 = {126/135/234}, no 7,8,9
h) R1C567 = {289/379/469/478/568}, no 1
i) 8(3) cage in N3 = {125/134}
j) R345C1 = {289/379/469/478/568}, no 1
k) 10(3) cage at R3C2 = {127/136/145/235}, no 8,9
l) 10(3) cage in N5 = {127/136/145/235}, no 8,9
m) R567C9 = {389/479/569/578}, no 1,2
n) 19(3) cage at R8C1 = {289/379/469/478/568}, no 1
o) R9C345 = {289/379/469/478/568}, no 1
p) 9(3) cage in N8 = {126/135/234}, no 7,8,9

1. 45 rule on R1 4 innies R1C1289 = 11 = {1235}, locked for R1

2. 45 rule on R1 2 outies R2C19 = 6 = {15/24}, no 3,6

3. 45 rule on R9 2 outies R8C19 = 13 = {49/58/67}, no 1,2,3

4. 45 rule on C1 2 outies R19C2 = 10 = [19/28/37], R1C2 = {123}, R9C2 = {789}

5. 45 rule on C9 2 outies R19C8 = 5 = [14/23/32], R1C8 = {123}, R9C8 = {234}

6. 45 rule on N5 2 innies R5C46 = 12 = {39/48/57}, no 1,2,6

7. 9(3) cage in N1 = {135/234}, 3 locked for R1 and N1, clean-up: no 2 in R9C8 (step 5)
7a. 4 of {234} must be in R2C1 -> no 2 in R2C1, clean-up: no 4 in R2C9 (step 2)
7b. R9C67 = {16/25} (cannot be {34} which clashes with R9C8), no 3,4

8. Naked triple {125} in 8(3) cage in N3, locked for N3, 5 locked for C9, clean-up: no 4 in R3C9, no 4,7,8 in R4C9, no 8 in R8C1 (step 3)
8a. R567C9 = {389/479}, no 6, 9 locked for C9, clean-up: no 4 in R8C1 (step 3)

9. 10(3) cage at R3C2 = {127/136/145/235}
9a. 3 of {136} must be in R4C2 -> no 6 in R4C2

10. 5 in R1 locked in R1C19
10a. 45 rule on R19C19 4 corner cells R19C19 = 15
10b. Min R1C19 = 6 -> max R9C19 = 9, no 9 in R9C1, no 8 in R9C9

11. 13(3) cage in N9 = {148/238/247/346}
11a. 2 of {247} must be in R9C9 -> no 7 in R9C9

12. R9C345 = {289/379/469/478} (cannot be {568} which clashes with R9C67), no 5

13. 19(3) cage at R8C1 = {289/379/469/478/568}
13a. 3,4 of {379/478} must be in R9C1 -> no 7 in R9C1
13b. 2,4 of {289/478} must be in R9C1, 8 of {568} must be in R9C2 -> no 8 in R9C1
[Alternatively min R8C1 + R9C2 = 12 -> max R9C1 = 6 because 19(3) cage cannot be [577].]

14. Hidden killer triple 7,8,9 in R9C2 and R9C345 for R9 -> R9C345 must have two of 7,8,9 -> R9C345 (step 12) = {289/379/478}, no 6

15. 5 in C9 locked in R12C9
15a. 45 rule on C9 4 innies R1289C9 = 16 = {1258/1456/2356} (cannot be {1357} which clashes with R567C9), no 7, clean-up: no 6 in R8C1 (step 3)

16. 19(3) cage at R8C1 = {289/379/478/568} (cannot be {469} because 4,6 only in R9C1)
16a. 5 of {568} must be in R8C1 -> no 5 in R9C1

17. 5 in R9 locked in R9C67 -> R9C67 = {25}, locked for R9
17a. R9C345 (step 14) = {379/478}, 7 locked for R9, clean-up: no 3 in R1C2 (step 4)
17b. Killer pair 3,4 in R9C345 and R9C8, locked for R9 -> R9C1 = 6, R9C9 = 1, clean-up: no 5 in R2C1 (step 2), no 5 in R345C1 (prelim j), no 8 in R3C9, no 2 in R67C1
17c. Naked pair {25} in R12C9, locked for C9 and N3 -> R1C8 = 1, R9C8 = 4 (step 5), R8C9 = 8 (step 11), R8C1 = 5 (step 3), R9C2 = 8 (step 16), R1C2 = 2, R1C1 = 3, R12C9 = [52], R2C1 = 4 (step 2), clean-up: no 7 in R3C9

Wrapping up a few loose ends
18. Naked pair {17} in R67C1, locked for C1
18a. Naked pair {36} in R34C9, locked for C9
18b. 2 in C1 locked in R45C1, locked for N4
18c. 4 in C9 locked in R56C9, locked for N6

19. 10(3) cage at R3C2 = {136/145}, no 7
19a. 3,4 only in R4C2 -> R4C2 = {34}
19b. 1 locked in R3C23, locked for R3 and N1

20. 2 in N7 locked in R78C3, locked for 12(3) cage at R7C3, no 2 in R7C4
20a. 12(3) cage at R7C3 = {129/237/246}, no 5,8
20b. 6 of {246} must be in R7C4 -> no 4 in R7C4

21. Killer pair 2,5 in 9(3) cage and R9C6, locked for N8
[Just spotted this; it’s been there since step 17.]

22. 14(3) cage at R6C8 = {239/257/356}, no 8
22a. 7 of {257} must be in R7C78 (R7C78 cannot be {25} which clashes with R9C7), no 7 in R6C8

23. R56C9 = {47/49}
23a. 22(4) cage in N6 = {1678/2389/2569/2578} (cannot be {1579} which clashes with R56C9, cannot be {3568} which clashes with R4C9)
23b. Killer pair 7,9 in 22(4) cage and R56C9, locked for N6

24. R45C1 = {28/29}
24a. 23(4) cage in N4 = {3569/3578/4568} (cannot be {1589} which clashes with R45C1, cannot be {1679} which clashes with R6C1, cannot be {3479} which clashes with R4C2), no 1, 5 locked for N4
24b. Killer pair 3,4 in R4C2 and 23(4) cage, locked for N4
24c. Killer pair 8,9 in R45C1 and 23(4) cage, locked for N4
24d. 1 in N4 locked in R6C13, locked for R6, clean-up: no 9 in R6C45

25. 20(4) cage at R5C4 = {1379/1469/1478/3467} (cannot be {1568/3458} because 5,8 only in R5C4), no 5, clean-up: no 7 in R5C6 (step 6)

26. R7C6 = 8 (hidden single in N8), clean-up: no 5 in R4C5, no 4 in R5C4 (step 6)
[Another one I spotted late, this has been there since step 20a.]
26a. 24(4) cage at R7C6 = {1689/3489/3678}, no 2
26b. 1,4 of {1689/3489} must be in R8C6 -> no 9 in R8C6

27. 9(3) cage in N8 = {126/234} (cannot be {135} because R8C45 = {13} clashes with R8C678), no 5, 2 locked for N8 -> R9C6 = 5, R9C7 = 2, clean-up: no 8 in R4C5, no 7 in R5C4 (step 6)

28. 5 in N9 locked in R7C78 for 14(3) cage at R6C8, no 5 in R6C8
28a. 14(3) cage at R6C8 (step 22) = {257/356}, no 9

29. 22(4) cage in N6 (step 23a) = {1678/2578} (cannot be {2389/2569} which clash with R4C9 + R6C8, ALS block), no 3,9, 7,8 locked for N6
29a. Naked pair {49} in R56C9, locked for C9 -> R7C9 = 7, R67C1 = [71], clean-up: no 3 in R6C45, no 9 in 12(3) cage at R7C3 (step 20a)

30. R6C3 = 1 (hidden single in R6), R3C2 = 1 (hidden single in R3)
30a. 9 in N8 locked in R9C45, locked for R9
30b. 9 in N7 locked in R78C2, locked for C2 and 20(4) cage at R5C4, no 9 in R5C4, clean-up: no 3 in R5C6 (step 6)

31. 1,9 locked in 20(4) cage at R5C4 (step 25) = {1379} (only remaining combination) -> R5C4 = 3, R78C2 = [97], R5C6 = 9 (step 6), R56C9 = [49], R7C4 = 6, R9C3 = 3, clean-up: no 9 in R1C3, no 4 in R4C56, no 4 in R6C5, no 1 in R8C45 (step 27)
31a. R8C6 = 1 (hidden single in N8)
31b. Naked pair {24} in R78C3, locked for C3

32. Naked pair {35} in R7C78, locked for R7 and N9, R6C8 = 6 (step 28a), R8C78 = [69], R34C9 = [63], R3C3 = 5, R24C2 = [64], R56C2 = [53], clean-up: no 9 in R1C4, no 4 in R6C4
32a. R8C5 = 3 (hidden single in N8)

33. Naked pair {28} in R6C45, locked for R6 and N5 -> R6C67 = [45], R7C78 = [35], R4C7 = 1
33a. Naked pair {67} in R4C56, locked for R4 and N5 -> R4C4 = 5, R5C5 = 1

34. 21(4) cage at R2C8 = {1389} (only remaining combination), no 7
34a. Naked pair {38} in R23C8, locked for C8 and N3 -> R45C8 = [27], R5C7 = 8, R5C13 = [26], R4C3 = 9 (step 24a), R34C1 = [98]

35. R2C4 = 1 (hidden single in C4) -> 22(4) cage at R2C2 = {1678} (only remaining combination), no 2,4
35a. Naked pair {78} in R13C4, locked for C4 and N2

and the rest is naked singles.

Hi,

thanks for your wts

this one is not really harder, but both cage pattern and solution are slightly different, which makes a really different solving path : you have not to peel this one !

Enjoy

Alt version A 171





SS score : 1.35

3x3::k:6656:6656:3842:3842:4868:4868:4868:2055:2055:6656:3338:3338:1292:4109:4109:4879:3344:2055:6656:2579:2579:1292:4109:4879:4879:3344:5146:6656:2579:4637:2590:3359:3359:4879:3344:5146:3876:3876:4637:4637:2590:5673:5673:5146:5146:3876:4910:3375:2608:2608:2590:5673:3636:7477:3876:4910:3375:3375:2362:2363:3636:3636:7477:4927:4910:3375:2362:2362:2363:3909:3909:7477:4927:4927:4938:4938:4938:1869:1869:7477:7477:

solution :

Thanks for the alt version. In some sense this one is easier than the original because the critical move is immediately available from the very start:


Won't be bothered to write a walkthrough though, because people never give any feedback anyway (e.g. A170). Why waste the time?

_________________
ADYFNC HJPLI BVSM GgK Oa m

Thanks manu for the challenging alt version. I found it harder than the original but that was because I didn't spot udosuk's neat breakthrough move that's there in the initial position. One could say that this puzzle is a "one trick pony".


Here is my walkthrough for Alt 171. I've corrected a few typos.
Although I regret not spotting that breakthrough move, at the same time I'm sort of happy about it because it allowed me several interesting steps. With hindsight I don't understand how I saw step 19 but didn't spot the outies for N8.

Prelims

a) R1C34 = {69/78}
b) R2C23 = {49/58/67}, no 1,2,3
c) R23C4 = {14/23}
d) R4C56 = {49/58/67}, no 1,2,3
e) R6C45 = {19/28/37/46}, no 5
f) R78C6 = {18/27/36/45}, no 9
g) R8C78 = {69/78}
h) R9C67 = {16/25/34}, no 7,8,9
i) R1C567 = {289/379/469/478/568}, no 1
j) 8(3) cage in N3 = {125/134}, 1 locked for N3
k) 10(3) cage at R3C2 = {127/136/145/235}, no 8,9
l) 10(3) cage in N5 = {127/136/145/235}, no 8,9
m) 22(3) cage at R5C6 = {589/679}, CPE no 9 in R5C89
n) R678C2 = {289/379/469/478/568}, no 1
o) 19(3) cage at R8C1 = {289/379/469/478/568}, no 1
p) R9C345 = {289/379/469/478/568}, no 1
q) 9(3) cage in N8 = {126/135/234}, no 7,8,9
r) 13(4) cage at R6C3 = {1237/1246/1345}, no 8,9

1. 45 rule on R1 4 innies R1C1289 = 11 = {1235}, locked for R1
1a. 8(3) cage in N3 = {125/134}
1b. 4 of {134} must be in R2C9 -> no 3 in R2C9

2. 45 rule on C12 2 outies R23C3 = 12 = [57/75/84/93], clean-up: no 7,9 in R2C2
2a. Min R3C3 = 3 -> max R34C2 = 7, no 7

3. 45 rule on C89 2 outies R78C7 = 9 = [18/27/36], clean-up: no 6 in R8C8
3a. Max R7C7 = 3 -> min R67C8 = 11, no 1

4. 45 rule on N5 2 innies R5C46 = 12 = [39/48/57/75]
4a. Max R5C4 = 7 -> min R45C3 = 11, no 1

5. 1 in C3 locked in R678C3, locked for 13(4) cage at R6C3, no 1 in R7C4

6. 45 rule on N8 4 innies R7C4 + R9C456 = 27 = {3789/4689/5679}, no 1,2, clean-up: no 5,6 in R9C7
6a. 3 of {3789} must be in R9C6 -> no 3 in R7C4 + R9C45
6b. 4,6 of {4689} must be in R7C4 + R9C6 -> no 4 in R9C45
6c . R78C6 = {18/27/45} (cannot be {36} which clashes with R7C4 + R9C456), no 3,6

7. 9 in N8 locked in R9C45, locked for R9
7a. R9C345 = {289/379/469}, no 5
7b. 2,3,4 only in R9C3 -> R9C3 = {234}
7c. Max R9C12 = 15 -> min R8C1 = 4
7d. 1 in R9 locked in R9C789, locked for N9, clean-up: no 8 in R8C7 (step 3), no 7 in R8C8

8. 45 rule on N9 2 outies R6C89 = 1 innie R9C7 + 13
8a. Min R6C89 = 14, no 1,2,3,4
8b. Min R6C8 + R7C7 = 7 -> max R7C8 = 7
8c. R7C78 cannot be 9 (CCC because R78C7 = 9, step 3) -> no 5 in R6C8
8d. Min R6C8 + R7C7 = 8 -> max R7C8 = 5 (14(3) cage cannot be [626])

9. 45 rule on N1 2 outies R4C12 = 1 innie R1C3 + 4
9a. Min R1C3 = 6 -> min R4C12 = 10, min R4C1 = 4

10. 45 rule on R9 4(3+1) outies R678C9 + R8C1 = 29
10a. Max R678C9 = 24 -> min R8C1 = 5
10b. Max R8C1 = 9 -> min R678C9 = 20, no 2

11. 29(5) cage at R6C9 = {14789/15689/24689/25679/34679/35678} (cannot be {23789} which clashes with R7C7, cannot be {34589} because one of 8,9 must be in R6C9 to stop clash with R8C8 and then 3,4,5 in N9 clashes with R7C78, ALS block)
11a. All combinations have three of 6,7,8,9 and only two of them can be in N9 -> R6C9 = {6789}

12. Min R6C89 = 14 (step 8a) -> R6C89 = {68/69/78/79/89}
12a. 22(3) cage at R5C6 = {589/679}
12b. 5 of {589} must be in R56C7 (R56C7 cannot be {89} which clashes with R6C89), no 5 in R5C6, clean-up: no 7 in R5C4 (step 4)
12c. 7 of {679} must be in R5C6 (R56C7 cannot be {67} which clashes with R8C7), no 7 in R56C7
12d. Max R5C4 = 5 -> min R45C3 = 13, no 2,3

13. 22(3) cage at R5C6 = {589/679}
13a. R5C6 = {789} -> R56C7 = {58/59/69}
13b. R6C89 (step 12) = {68/69/78/79} (cannot be {89} which clashes with R56C7)
13c. Killer pair 8,9 in R56C7 and R6C89, locked for N6
13d. Max R6C89 = 16 -> max R9C7 = 3 (step 8), clean-up: no 3 in R9C6

14. Killer triple 1,2,3 in 29(5) cage at R6C9, R7C7 and R9C7, locked for N9
14a. Min R7C78 = 6 -> max R6C8 = 8

15. 3 in N8 locked in 9(3) cage = {135/234}, no 6
15a. Killer pair 4,5 in R7C4 + R9C456 and 9(3) cage, locked for N8

16. 45 rule on N2 2 outies R1C37 = 1 innie R3C6 + 10
16a. Max R1C37 = 17 -> max R3C6 = 7

17. 45 rule on N2 4 innies R1C456 + R3C6 = 24 = {1689/2679/3678/4569/4578} (cannot be {2589/3579} because 2,3,5 only in R3C6, cannot be {3489} which clashes with R23C4)
17a. 1,2,3,5 only in R3C6 -> R3C6 = {1235}

18. R56C7 (step 13a) = {58/59/69}, R6C89 (step 13b) = {68/69/78/79} -> R4C789 + R5C89 must contain 1,2,3,4 and one of 5,6,7 = 15,16,17
18a. Max R4C9 + R5C89 = {347} = 14 -> min R3C9 = 6
18b. Max R4C789 + R5C89 = 17, min R4C9 + R5C89 = 11 (from 20(4) cage) -> max R4C78 = 6, no 6,7

19. 45 rule on N3 6(5+1) outies R3C6 + R4C789 + R5C89 = 1 innie R1C7 + 15
19a. R4C789 + R5C89 (step 18) = 15,16,17 -> R1C7 = R3C6, R3C6 + 1 or R3C6 + 2, no 8,9 in R1C7, no 1 in R3C6
19b. R1C7 = {467} is not equal to R3C6 = {235} -> R4C789 + R5C89 is not equal to 15 -> no 5 in R4C789 + R5C89

20. 5 in N6 locked in R56C7, locked for C7
20a. 22(3) cage at R5C6 = {589}, no 6,7, clean-up: no 5 in R5C4 (step 4)
20b. Max R5C4 = 4 -> min R45C3 = 14, no 4

21. Killer pair 3,4 in R23C4 and R5C4, locked for C4, clean-up: no 6,7 in R6C5
21a. 9(3) cage in N8 (step 15) = {135/234}
21b. 2 of {234} must be in R8C4 -> no 2 in R78C5

22. R5C46 = [39/48]
22a. R4C56 = {58/67} (cannot be {49} which clashes with R5C46), no 4,9
22b. 9 in R4 locked in R4C13, locked for N4
22c. 9 in R5 locked in R5C67, locked for 22(3) cage at R5C6, no 9 in R6C7

23. R1C456 + R3C6 (step 17) = {2679/3678/4569/4578}
23a. 16(3) cage in N2 = {169/178/259/358} (cannot be {268/349/367/457} which clash with R1C456 + R3C6), no 4

24. 45 rule on C12 3 innies R234C2 = 11 = {128/146/236/245}
[I should have spotted these innies, and the ones in the next step, a lot earlier.]
24a. 5 of {245} must be in R34C2 (10(3) cage at R3C2 cannot be {244}), no 5 in R2C2, clean-up: no 8 in R2C3, no 4 in R3C3 (step 2)

25. 45 rule on C89 3 innies R678C8 = 20 = {479/569/578}
25a. R8C8 = {89} -> no 8 in R6C8
25b. R6C8 = {67} -> R6C9 = {89} (step 13b)

26. Killer quad 1,2,3,4 locked in R6789C3, locked for C3, clean-up: no 9 in R2C3 (step 2), no 4 in R2C2
26a. Naked pair {57} in R23C3, locked for C3 and N1, clean-up: no 8 in R1C4
26b. Naked triple {689} in R145C3, locked for C3
[With hindsight I should have spotted R7C4 = {567} -> no other 5,6,7 in 13(4) cage at R6C3 after step 21.]

27. 18(3) cage at R4C3 = {369/468}, 6 locked for C3 and N4, clean-up: no 9 in R1C4

28. R69C4 = {89} (hidden pair in C4), R6C5 = {12}
28a. Naked pair {89} in R6C49, locked for R6 -> R6C7 = 5
28b. Naked pair {89} in R5C67, locked for R5 -> R5C3 = 6

29. 10(3) cage in N5 = {136/145/235} (cannot be {127} which clashes with R6C5), no 7
29a. 7 in N5 locked in R4C56 = {67}, locked for R4 and N5

30. R6C8 = 6 (hidden single in N6), R7C78 = 8 = [35], R8C7 = 6 (step 3), R8C8 = 9, clean-up: no 4 in R9C6

31. R1C9 = 5 (hidden single in R1), R1C8 + R2C9 = {12}, 2 locked for N3

32. R3C9 = 6 (hidden single in C9), R4C9 + R5C89 = 14 = {347} (only remaining combination), locked for N6, 7 locked for R5
32a. Naked pair {12} in R4C78, locked for R4 -> R4C4 = 5
32b. Naked pair {12} in R14C8, locked for C8

33. R9C79 = {12} (hidden pair in N9), locked for R9, clean-up: no 8 in R9C45 (step 7a)
33a. R9C4 = 9, R6C4 = 8, R6C5 = 2, R5C67 = [98], R5C4 = 3 (step 4), R4C3 = 9 (step 27), R1C3 = 8, R1C4 = 7, R1C7 = 4, R1C56 = [96], R2C2 = 6, R2C3 = 7, R23C7 = [97], R3C3 = 5, R4C56 = [67], R6C9 = 9, R7C4 = 6, R9C5 = 7, R9C3 = 3 (step 7a), R9C6 = 5, R9C7 = 2, R9C9 = 1, R2C9 = 2, R1C8 = 1, R4C78 = [12], R3C6 = 2 (cage sum), clean-up: no 1 in 9(3) cage in N8 (step 15)
33b. R7C5 = 4, R8C45 = [23], R5C5 = 1, R6C6 = 4, R678C3 = [124], R9C12 = [68], R8C1 = 5 (cage sum)

and the rest is naked singles.

Thanks for the walkthrough Andrew!

After my whining about no feedback I think I'm obliged to read through yours and give some to you. I really tried but for some reasons it's really hard as it took me nearly a full hour to go through it step by step. But it's a good experience as it makes me more understanding about other people reading mine (while my paths are often shorter because I only post optimised ones but I'm sure the way I shorten things up must make them tougher to digest). So I'll try to take this experience into consideration when I write my next one.

Back to your walkthrough. It's surely valid (barring a little bit minor typos here or there, sorry I haven't recorded them but I'm sure most reader won't have too much problems with them). But one of my impression is that you could have drilled a little deeper in some of the moves (i.e. you've found a good logic to produce some eliminations, but somehow you didn't apply that logic more thoroughly as it could give you a few more eliminations). I'll try to cite an example below:


There seem to be a few other similar examples where when I read it I think "umm, nice move but why didn't you just do a little bit extra for another elimination there?", but I can't do the extra eliminations myself because that might mess up the logic when I follow the latter steps of the walkthrough.

Also, one of a critical breakthrough move you just missed is this one:


Anyway, it is your style of solving puzzles so perhaps I shouldn't comment too much. I just think that you're smart enough to spot a lot of clever moves, but if you just try to be more persistent on drilling each move deeper you will find it a lot easier when solving puzzles.

Meanwhile, on my critical move, I think one of the reasons you guys find it hard to spot is because of the smaller and more applicable innie-outies R7C4=R9C37+1. Somehow it masks the availability of my critical move, which uses some common cells but looks much scarier to apply. In some sense it's similar to Ed's A167, where his ingenius critical move is masked by easier moves available in the same region.

And if it can make you feel better, the original creator also didn't spot that move, instead following a similar route as yours (but he does spot the move you missed above).

Lastly, can't help but I have to rant about the ratings a little bit:


End of ranting.

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ADYFNC HJPLI BVSM GgK Oa m

Thanks udosuk for your interesting comments.

I also find that some posted walkthroughs take me a long time to go through; not from any particular person, just some walkthroughs.

Step 11 was a particularly difficult one for me to put into words. I could have made it simpler by not eliminating the {34589} combination and still got the same result for R6C9 but, since I'd seen that combination could be eliminated I felt it ought to be part of that step.

Thanks particularly for "The Move You Missed". That was a nice CCC! Maybe 3 cell CCCs are harder to spot than 2 cells ones.

I definitely ought to have got a bit more out of step 18 since after Min R4C9 + R5C89 = 11 I ought to have spotted that these cells must contain one of 5,6,7. Even so I still needed step 19 to remove 5 from R4C9 + R5C89.

You commented that 5(4+1) outies for N8 may have been hard to spot because there was the more obvious 1 innie R7C4 = 2 outies R9C37 + 1. I also missed that one although I did find 4 innies for N8 fairly useful.

From these comments I guess one of your reasons for regarding these moves as difficult are their sheer sizes, even though the difference is only 1 cell.

Yet you guys (you and Afmob etc) have no problem listing 6-7 possibilities of a 5-cell combo and go all hazy about them. I myself would feel a headache seeing such a long string of digits (and no I don't use SudokuSolver so combo recording solving is not my thing).

Limitation is surely a curious thing. You draw a circle around yourself and convince yourself that there are flames running on it. (And it applies to everyone of us, including you and me.)

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ADYFNC HJPLI BVSM GgK Oa m