SudokuSolver Forum

3x3::k:4608:4608:4608:4865:4865:4865:5634:5634:5634:4608:4867:4867:4867:5636:4101:4101:4101:5634:4614:2823:2823:4867:5636:4101:1800:1800:6409:4614:4614:4106:4363:5636:2572:1293:6409:6409:4614:1806:4106:4363:5636:2572:1293:4879:6409:1806:1806:7696:4363:2321:2572:5906:4879:4879:3859:7696:7696:7696:2321:5906:5906:5906:1812:3859:3349:7696:4630:4630:4630:5906:4119:1812:3349:3349:1560:1560:4630:4377:4377:4119:4119:

Prelims

a) R3C23 = {29/38/47/56}, no 1
b) R3C78 = {16/25/34}, no 7,8,9
c) R45C3 = {79}
d) R45C7 = {14/23}
e) R67C5 = {18/27/36/45}, no 9
f) R78C1 = {69/78}
g) R78C9 = {16/25/34}, no 7,8,9
h) R9C34 = {15/24}
i) R9C67 = {89}
j) 19(3) cage at R1C4 = {289/379/469/478/568}, no 1
k) 10(3) cage at R4C6 = {127/136/145/235}, no 8,9
l) 7(3) cage at R5C2 = {124}
m) 19(3) cage at R5C8 = {289/379/469/478/568}, no 1

Steps resulting from Prelims
1a. Naked pair {79} in R45C3, locked for C3 and N4, clean-up: no 2,4 in R3C2
1b. Naked pair {89} in R9C67, locked for R9
1c. Naked triple {124} in 7(3) cage at R5C2, locked for N4

2. 45 rule on N4 1 innie R6C3 = 1 outie R3C1 + 4 -> R3C1 = {124}, R6C3 = {568}

3. 45 rule on N1 2 outies R23C4 = 1 innie R3C1 + 3, IOU no 3 in R2C4
3a. Max R3C1 = 4 -> max R23C4 = 7, no 7,8,9 in R23C4

4. 45 rule on R1 2 outies R2C19 = 14 = {59/68}

5. 45 rule on N6 1 outie R3C9 = 1 innie R6C7 + 4, R3C9 = {56789}, R6C7 = {12345}

6. 45 rule on N3 2 outies R23C6 = 1 innie R3C9
6a. Max R23C6 = 9, no 9 in R23C6

7. 45 rule on R789 3 outies R6C357 = 19 = {478/568} -> R6C7 = {45}, R6C3 = {68}, R6C5 = {678}, 8 locked for R6, clean-up: no 1 in R3C1 (step 2), no 5,6,7 in R3C9 (step 5), R7C5 = {123}

8. 45 rule on C1234 2 innies R18C4 = 10 = {28/37/46}/[91], no 5, no 9 in R8C4

9. 45 rule on C6789 2 innies R18C6 = 13 = {49/58/67}, no 1,2,3

10. 45 rule on R12 2 outies R3C46 = 1 innie R2C5 + 4, IOU no 4 in R3C46

11. 45 rule on N47 3(1+2) outies R3C1 + R79C4 = 15
11a. Max R3C1 + R7C4 = 13 -> min R9C4 = 2, clean-up: no 5 in R9C3
11b. Max R3C1 + R9C4 = 9 -> min R7C4 = 6

12. 45 rule on N69 3(1+2) outies R3C9 + R79C6 = 22
12a. Max R3C9 + R9C6 = 18 -> min R7C6 = 4
12b. Min R3C9 + R9C6 = 16 -> max R7C6 = 6

13. 10(3) cage at R4C6 = {127/136/235} (cannot be {145} which clashes with R18C6 + R7C6, ALS block), no 4

14. 45 rule on N9 2 outies R6C7 + R7C6 = 1 innie R9C7 + 1
14a. R9C7 = {89} -> R6C7 + R7C6 = 9,10 = {45/46}, 4 locked for 23(5) cage at R6C7, no 4 in R7C78 + R8C7

15. 45 rule on N5 2 innies R45C5 = 1 outie R7C5 + 9, IOU no 9 in R45C5

16. 9 in N5 only in 17(3) cage at R4C4, locked for C4, clean-up: no 1 in R8C4 (step 8)
16a. 17(3) cage = {179/269/359}, no 4,8
16b. 4,8 in N5 only in R456C5
16c. 45 rule on N5 3 innies R456C5 = 18 = {468} (only possible combination), locked for C5 and N5, clean-up: no 2 in 17(3) cage, no 2 in R7C5
16d. 2 in N5 only in 10(3) cage at R4C6, locked for C6

17. Naked pair {68} in R6C35, locked for R6
17a. R6C357 (step 7) = {568} (only remaining combination) -> R6C7 = 5, R3C9 = 9 (step 5), clean-up: no 5 in R2C1 (step 4), no 2 in R3C3, no 2 in R3C8

18. R6C7 + R7C6 contains 4 (step 14a) -> R7C6 = 4, clean-up: no 6 in R1C4 (step 8), no 9 in R18C6 (step 9), no 3 in R8C9, no 2 in R9C3
18a. R6C7 + R7C6 = [54] -> 23(5) cage at R6C7 = {14567/23459}, no 8
18b. R9C6 = 9 (hidden single in C6), R9C7 = 8

19. 45 rule on N8 3 remaining innies R7C45 + R9C4 = 14 = {158/356} (cannot be {167} because 6,7 only in R7C4, cannot be {257} because 2,5 only in R9C4) -> R7C4 = {68}, R9C4 = 5, R9C3 = 1, clean-up: no 8 in R1C6 (step 9)

20. 17(3) cage at R4C4 (step 16a) = {179} (only remaining combination), locked for C4 and N5, clean-up: no 3 in R18C4 (step 8)
20a. Naked triple {235} in 10(3) cage at R4C6, locked for C5, clean-up: no 8 in R8C6 (step 9)
20b. Naked pair {67} in R18C6, locked for C6

21. Naked pair {18} in R23C6, locked for N2 and 16(4) cage at R2C6, no 1,8 in R2C78, clean-up: no 2 in R8C4 (step 8)
21a. R23C6 = {18} = 9 -> R2C78 = 7 = [25/34/43]

22. Naked pair {68} in R78C4, locked for C4 and N8 -> R18C6 = [67]
22a. 19(3) cage at R1C4 = {469} (only remaining combination) -> R1C45 = [49]

23. R23C4 = R3C1 + 3 (step 3)
23a. R23C4 = [23] = 5 -> R3C1 = 2, R6C3 = 6 (step 2), R7C4 = 8, R8C4 = 6, R6C5 = 8, R7C5 = 1, clean-up: no 4,5 in R3C78 (other clean-ups omitted)
23b. Naked pair {16} in R3C78, locked for R3 and N3 -> R23C6 = [18], R3C3 = 4 (hidden single in R3), R3C2 = 7, R23C5 = [75]
23c. R2C78 = {34} (hidden pair in R2), locked for N3
23d. R3C12 = {69} (hidden pair in R2)

24. R6C3 = 6, R7C4 = 8, 2 in C3 only in R78C3 -> 30(5) cage at R6C3 = {25689} (only remaining combination) -> R7C2 = 9, R78C3 = {25}, locked for C3 and N7, R8C1 = 8, R7C1 = 7
24a. Naked pair {35} in R45C1, locked for C1 and N4 -> R1C1 = 1, R4C2 = 8, R6C1 = 4, R9C1 = 6

25. R8C7 = 9 (hidden single in C7) -> 23(5) cage at R6C7 (step 18a) = {23459} -> R7C78 = {23}, locked for R7 and N9 -> R7C3 = 5, R7C9 = 6, R8C9 = 1
25a. R45C7 = {14} (cannot be {23} which clashes with R7C7), locked for C7 and N6 -> R2C78 = [34], R7C78 = [23], R9C8 = 7

26. 19(3) cage at R5C8 = {289} (only remaining combination, cannot be {379} because 3,7 only in R6C9) -> R5C8 = 8, R6C89 = [92]

and the rest is naked singles.

I'll rate my walkthrough for A272 at 1.25, and maybe that's a bit high. I don't understand the SS score of 1.55; I don't think I used any steps which SS wouldn't be able to find.

3 in r45c57 blocked by 3 in n4 only in r45 -> at least one of r45c57 must have 4 ->7 blocked from r6c5 since it blocks 4 from r45c5 (h18(3)r456c5={38}[7]) and puts 4 in r6c7 (h19(3)r6c357 = [874] only)

1. Innies - Outies n6 -> r3c9 = r6c7 + 4
-> Max r6c7 = 5
Max r6c5 = 8
Outies r789 -> r6c357 = +19
-> Min r6c3 = 6

16/2@r4c3 = {79}
-> r6c3 from (68)
-> r6c357 from [685], [865], [874]

2. Innies n5 -> r456c5 = +18
9/2@r6c5 prevents a 9 from being in r456c5
-> 9 in n5 in r456c4
-> 8 in n5 in r456c5
-> r456c5 = {378} or {468} - No (1259)

3. r6c3 from (68)
(Innies - outies n4) -> r3c1 from (24)
(Innies n1 = +16) -> r2c23 from (+14, +12)
-> r23c4 from (+5, +7) - no (78)
-> 8 in c4 in one of r178c4.

4. r6c7 from 5 or 4 and r9c6 from (89)
a) Either r6c7 = 5
-> Outies n9 = +18 -> r79c6 = [49]

b) or r6c7 = 4
-> r6c357 = [874]
-> r7c5 = 2
-> (Innies c1234 r18c4 = +10) -> 8 in c4 cannot be in r1c4 -> 8 in c4 in r78c4
-> r9c6 = 9

Either way r9c6 = 9
-> r9c7 = 8
Also -> r6c7,r7c6 = {45}

5. Outies n7 = +19
Max r6c3+r7c4 = +15 -> Min r9c4 = 4
-> r7c6,r9c4 = {45}
-> r7c45 = +9

6. (59) in c5 both in n2 in r123c5
r6c5 from (678) -> r45c5 from (+12,+11,+10)
-> r23c5 from (+10,+11,+12) - cannot contain both 5 and 9
-> r1c5 from (59)
-> r23c5 from {56}, {57}, {91}, {92}, {93} -> No 4!
-> 4 in c4 in n5
-> r456c5 = {468} with r6c5 from (68)

7. -> r6c357 = [{68}5]
-> r7c6 = 4
-> r9c34 = [15]
Also (Innies - Outies n6) -> r3c9 = 9
-> 9 in n6 in r56c8
-> 9 in n9 in r78c7
-> 23/5@r6c7 = [54{239}]
-> 7/2@r7c9 = {16}
-> 16/3@r8c8 = [5{47}]
-> 6 in r9 in r9c12
-> 13/3@r8c2 = [4{36}]
-> r9c5 = 2
-> 7 in n8 in r8c456
-> (Since 6 in r9c12) -> 15/2@r7c1 = [78]
-> HS 8 in r7 -> r7c4 = 8
-> r7c5 = 1 and r8c456 = {367}

8. Continuing
r6c35 = [68]
HS 9 in n7 -> r7c2 = 9
-> r78c3 = [52]
Also r8c7 = 9
-> r7c78 = {23}
-> 5/2@r4c7 = {14}
Also (innies - outies n4) r3c1 = 2

9. Etc.
HS 8 in n4 -> r4c2 = 8
7/3@r5c2 = {124}
-> r45c1 = {35}
-> r9c12 = [63]
-> Outies r1 r2c19 = +14 -> r2c19 = [95]
-> Innies n1 -> r2c23 = [68]
-> Innies n3 -> r2c78 = [34]
Also 11/2@r3c2 = [74]
-> 7/2@r3c7 = [61]

Simple from here

End of wellbeback's step 2 in collapse above.

3. h18(3)r456c5 = {378/468} = [3/4..], 5(2)r4c7 = {14/23} = [3/4..]: 3 in n4 only in r45 -> the h18(3) and 5(2) cannot both have 3 -> at least one of them must have 4 in r45c57
3a. also, r6c357 from [685], [865], [874](step 1)
3b. but [874] is blocked since it forces r45c57 to be {38/23} -> r6c357 from [685], [865] (no 7)
3c. -> r6c7 = 5

on from there.