SudokuSolver Forum

Prelims

a) 35(5) cage at R1C7 = {56789}
b) 15(5) cage at R2C4 = {12345}
c) 15(5) cage at R2C6 = {12345}
d) 35(5) cage at R3C5 = {56789}
e) 34(5) cage at R6C2 = {46789}
f) 15(5) cage at R6C7 = {12345}
g) 35(5) cage at R7C8 = {56789}
h) 14(4) cage at R4C1 = {1238/1247/1256/1346/2345}, no 9

Steps resulting from Prelims
1a. 35(5) cage at R1C7 = {56789}, locked for N3
1b. 35(5) cage at R7C8 = {56789}, locked for N9
1c. 15(5) cage at R2C4 = {12345}, CPE no 5 in R4C4
1d. 15(5) cage at R2C6 = {12345}, CPE no 1,2,3,4,5 in R4C6
1e. 35(5) cage at R3C5 = {56789}, CPE no 5,6,7,8,9 in R5C5
1f. 34(5) cage at R6C2 = {46789}, CPE no 4,6,7,8,9 in R6C4
1g. 15(5) cage at R6C7 = {12345}, CPE no 1,2,3,4,5 in R6C6

2. Naked quad {1234} in R1289C9, locked for C9
2a. Naked quint {56789} in R4C456 + R5C4 + R6C6, locked for N5, 5 also locked for 35(5) cage at R3C5, no 5 in R3C5 + R5C3
2b. Naked quad {1234} in R1C9 + R3C7 + R5C5 + R6C4, locked for D/
2c. Naked quint {12345} in R23578C6, locked for C6
2d. 35(5) cage at R1C7, 15(5) cage at R2C6 = {12345}, 15(5) cage at R6C7 = {12345} and 35(5) cage at R7C8 = {56789} all contain 5, no other 5 in C6789
[4-way caged X-Wing; there’s probably a name for it.]
2e. 4 in N5 only in R5C56 + R6C5, CPE no 4 in R5C7 + R7C5
2f. 9 in N4 only in R5C3 + R6C23, CPE no 9 in R7C3

3. 24(4) cage at R1C4 = {1689/2679/3678} (cannot be {2589/3489/3579/4569/4578} which clash with R23C46), no 4,5, 6 locked for N2

4. 45 rule on N7 4 innies R7C3 + R8C1 + R9C12 = 20, min R7C3 + R9C1 = 11 -> max R8C1 + R9C2 = 9, no 9 in R8C1 + R9C2

5. 25(4) cage at R8C5 = {1789/2689/3589/3679/4579} (cannot be {4678} which clashes with R78C4), 9 locked for N8
5a. 34(5) cage at R6C2 = {46789}, 9 locked for R6 and N4

6. 14(4) cage at R4C1 = {1238/1247/1256/1346} (cannot be {2345} which clashes with R4C23), 1 locked for N4
6a. Hidden killer triple 6,7,8 in 14(4) cage, R5C3 and R6C23 for N4 -> R6C23 = {6789}
6b. 34(5) cage at R6C2 = {46789}, 4 locked for C4 and N8
6c. Naked quad {6789} in R6C2369, locked for R6
6d. 4 in N2 only in R23C6, locked for C6 and 15(5) cage at R2C6, no 4 in R3C7 + R4C78
6e. 4 in R4 only in R4C123, locked for N4

7. Consider placement for 5 in N5
R4C5 = 5 => both 15(5) cage at R2C4 and 15(5) cage at R2C6 require 5 => R3C3 = 5
or R5C4 = 5
-> no 5 in R23C4
7a. R23C6 = {45} (hidden pair in N2), locked for C6 and 15(5) cage at R2C6, no 5 in R4C78
7b. 5 in N6 only in R6C78, locked for R6
7c. Naked triple {123} in R236C4, locked for C4

8. Consider placements for R6C4
R6C4 = 1 => R23C4 = {23} => R4C23 = {45}
or R6C4 = 2, placed for D/ => R23C4 = {13}, locked for 15(5) cage at R2C4, 2 in 15(5) cage at R2C6 only in R4C78, locked for R4 => R4C23 = {45}
or R6C4 = 3, placed for D/ => R23C4 = {12}, locked for 15(5) cage at R2C4, 3 in 15(5) cage at R2C6 only in R4C78, locked for R4 => R4C23 = {45}
-> R4C23 = {45}, locked for R4, N4 and 15(5) cage at R2C4, no 4,5 in R3C3
8a. Naked triple {123} in R3C347, locked for R3
8b. Naked quad {6789} in R4C4569, locked for R4
8c. 1,2,3 in N4 only in 14(4) cage at R4C1 = {1238}, 8 locked for R5 and N4
8d. R5C4 = 5 (hidden single in R5)
8e. Naked triple {679} in R5C3 + R6C23, CPE no 6,7 in R7C3 -> R7C3 = 8, placed for D/
8f. Naked quad {1234} in R3C3 + R5C5 + R7C7 + R9C9, locked for D\
8g. 4 in C7 only in R67C7, locked for 15(5) cage at R6C6, no 4 in R6C8
8h. 9 in R5 only in R5C789, locked for N6

9. 25(4) cage at R8C5 (step 5) = {1789/2689/3589/3679}
9a. Killer triple 1,2,3 in R78C6 and 25(4) cage, locked for N8
9b. Min R6C6 + R7C5 = 11 -> max R5C67 + R6C5 = 10, no 9 in R5C7

10. Naked triple {123} in R3C7 + R4C78, CPE no 1,2,3 in R5C7

10. 21(5) cage at R5C6 = {12567} (only possible combination) -> R7C5 = 5, R5C6 + R6C5 = {12}, locked for N5, R6C4 = 3, placed for D/, R5C5 = 4 (hidden single in N5), placed for both diagonals
10a. Naked pair {12} in R23C4, locked for N2 and 15(5) cage at R2C4 -> R3C3 = 3, placed for D\
10b. R6C78 = [45] (hidden pair in R6)
10c. Naked pair {12} in R1C9 + R3C7, locked for N3
10d. Naked pair {12} in R7C7 + R9C9, locked for N9
10e. R4C7 = 3 (hidden single in C7)

11. 24(4) cage at R1C4 (step 3) = {3678} (only remaining combination), locked for N2, 3 also locked for C5 -> R3C5 = 9
11a. R4C6 = 9 (hidden single in N5), placed for D/
11b. 35(5) cage at R3C5 = {56789}, 8 locked for R4
11c. Naked pair {67} in R4C9 + R5C7, locked for N6 -> R56C9 = [98]
11d. R3C9 = 5 (hidden single in C9) -> R23C6 = [54]
11e. R9C4 = 9 (hidden single in C4)

12. 24(5) cage at R1C3 = {12678} (only possible combination), locked for N1, 1,2 also locked for C3

13. Naked pair {12} in R46C1, locked for C1 and N4
13a. R79C2 = {12} (hidden pair in N7)
13b. Naked pair {12} in R7C27, locked for R7 -> R7C6 = 3
13c. Naked pair {12} in R9C29, locked for R9
13d. R8C1 = 3 (hidden single in N7) -> R5C12 = [83], R28C9 = [34], R19C8 = [43]
13e. Naked triple {678} in R2C2 + R4C4 + R6C6, locked for D\ -> R8C8 = 9, placed for D\, R1C1 = 5, R1C2 = 9, R2C1 = 4
13f. Naked pair {67} in R7C89, locked for R7 and N9

14. 45 rule on N7 2 remaining innies R9C12 = 9 -> R9C1 = 7, placed for D/, R9C2 = 2, R2C8 = 6, placed for D/, R7C8 = 7, R3C8 = 8, R3C12 = [67], R2C2 = 8, placed for D\

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

I'll rate my walkthrough at 1.5. I used two short forcing chains, which would normally be Easy 1.5, but the second one makes eliminations from R4C23 in two different directions, so I feel it need the full 1.5.

0. All 15(5)s are {12345}
All 35(5)s are {56789}
34(5) is {46789}

1. Since puzzle is an 'X' -> r4c6 from (6789)
Also -> r6c6 from (6789)
-> r4c6 and r6c6 are the same as r3c5 and r5c3
-> 5 in 35(5)r3c5 in r4c5 or r5c4
Also -> r5c56 + r6c45 in n5 are {1234}

2. -> (1234) in D/ locked in r1356
-> r7c3 not 4
Consider (6789) in n4
At most one of them is in the 14(4) and none in r4c23
-> r5c3 and r6c23 from (6789)
-> 4 in 34(5) in r78c4

3. Consider (789) in n2
None in the 15(5)s and at most two in 24(4)
-> r3c5 from (789) and two of them are in the 24(4)
-> 6 in 24(4)
-> 24(4) from {1689}, {2679}, {3678}
-> 5 in n2 in r23c46
Also 4 in n2 in r23c6
-> 4 in n5 in r56c5

4. 5 in 15(5)r2c6 in r23c6 or r4c78
But the latter implies 5 in r23c4 which leaves no place for 5 in 35(5)r3c5
-> r23c6 = {45}
-> 5 in r6c78

5! Since 4 in r78c4 and 5 in r6c78 -> r78c6 is two of (123)
-> Also since 4 in r78c6 -> 25(4)n8 must contain one of numbers (123)
-> r7c5 is min 5.
Since r3c7,r4c78 = {123}
and 4 in r56c5
and 5 in r6c78
-> r5c7 is min 6.
and since r6c6 is also min 6
-> 21(5)r5c6 = {12567} with r5c6,r6c5 = {12} and r7c5 = 5 and r5c7,r6c6 = {67}
-> r5c4 = 5, r5c5 = 4, r6c4 = 3
Also 4 in r6c78 -> r6c78 = {45}

6. HS 5 in c9 -> r3c9 = 5
-> r23c6 = [54]
-> r4c23 = {45}
-> 14(4)n4 = {1238}
-> Remaining cells n4 = {679}
-> r7c3 = 8

7. HS 3 in 15(5)r2c4 -> r3c3 = 3
-> r23c4 = {12}
-> 24(4)n2 = {3678}
-> r3c5 = 9
-> r4c6 = 9
-> r6c6 (from 67) = r5c3
-> 9 in r6c23
-> HS 9 in c4 -> r9c4 = 9

8. 3 in 15(5)r2c6 in r4c78
-> 3 in 15(5)r6c7 in r78c6
In D/ r1c9,r3c7 = {12}
In c7 r37c7 = {12}
-> Whichever of (12) is in r1c9 goes in r7c7 and -> in r4c8
-> r4c7 = 3
Also -> Whichever of (12) is in r3c7 goes in r9c9 and -> in r5c8
-> r46c1 = {12}
-> r5c12 = {38}

9. r1c8,r2c9 = {34}
and r8c9,r9c8 = {34}
-> r6c78 = [45]
-> 5 in n9 in r89c7
-> HS 5 in D\ -> r1c1 = 5
-> HS 5 in D/ -> r8c2 = 5
-> r9c7 = 5
Also r4c23 = [45]

10. r3c47 = {12}
-> r3c128 = {678}
Since remaining innies n1 = r1c2,r2c1 = +13(2)
-> r2c1 = 4, r1c2 = 9
-> 4 in n7 in r89c3
Remaining cells in D/ r2c8,r9c1 = {67}
Remaining Innies n7 = r8c1,r9c12 = +12(3)
Can only be [372]
-> Innies n9 = r7c7,r8c9,r9c89 = [2431]
etc.

Hard 1.0