Step 1:

The left (10) parts of R123: max R1C12,R2C12,R3C12=10 --> min R123C3=45-10-10-10=15

Step 2:

C3 is (12)+(33) --> the (12) part is R12C3={39/48/57}

(Step 1) max R12C123=10+10+12=32 --> min R3C123=45-32=13

Step 3:

R3 is (10)+(5)+(30) --> the (10) part is R3C12 (<>[5]) --> the (5) part: max R3C3=5 (<>{6789})

(Step 1) max R13C123,R23C123=10+9+10+5=34 --> min R1C123,R2C123=45-34=11

(Step 1) the left (10) parts of R12 are R1C12,R2C12 (<>[5]) --> R3C3=45-10-10-10-12=[3] --> the (5) part is R3C34=[32]

(Step 2) [5] of N1 is locked in R12C3={57} (C3,N1)

Step 4:

R1 is (10)+(10)+(25) --> the middle (10) part: max R1C34=10 --> max R1C4=4 (<>{56789})

Step 5:

C4 is (8)+(15)+(22) --> the (8) part: R1C4<>[4], R2C4<>{134689} --> R2C34={57} (R2) --> R1C3=R2C4 --> R1C34=R12C4

(Step 4) R1C34<>8 --> R12C4<>8 -> the (8) part is R123C4=[152]

(Step 4) the middle (10) part of R1 is R1C345=[514], R2C3=[7]

(Step 4) the left (10) part of R1 is R1C12={28} (R1,N1)

Step 6:

C6 is (13)+(32) --> the (13) part is R12C6=[76] --> R3C56={89} (R3,N2) --> R2C5=3

(Step 3) R2C12={19}, R3C12={46} (R23)

Step 7:

C5 is (20)+(25) --> the (20) part is R1234C5=[4385] --> R3C6=[9]

Step 8:

R2 is (10)+(25)+(10) --> the right (10) part is R2C89={28} --> R2C7=[4]

Step 9:

C7 is (12)+(21)+(12) --> the top (12) part is R123C7=[345] --> the bottom (12) part is R789C7={129} (C7,N9) --> R456C7={678} (N6)

Step 10:

C9 is (35)+(10) --> the (10) part is R89C9={37/46} (<>{58})

Step 11:

C8 is (34)+(11) --> the (11) part is R89C8={38/56} (step 10: <>{47}) --> R7C89=45-12-11-10=12={48/57} (<>{36})

Step 12:

R7 is (14)+(17)+(14) --> the right (14) part: R7C7=[2]

Step 13:

R8 is (34)+(11) --> the (11) part must have length 2/3/4

(Step 11) R89C8=11 --> R8C89<>11 --> not length 2

(Step 10) R89C9=10 --> R8C789<>1+10 --> not length 3

--> the (11) part must have length 4, is R8C6789=[2153]

(Step 11) R7C89={48} (R7,N9) --> R9C789=[967] --> R1C89=[96], R3C89=[71], R9C5=[1]

(Step 12) the (17) part of R7: [3] is locked in R7C46 (R7,N8)

Step 14:

R9 is (15)+(30) --> the (30) part is R9C6789=[8967] --> R9C34=[24] --> (hidden singles N8) R7C46=[35]

(Step 12) the left (14) part of R7 is R7C123={167} (N7) --> R7C5=[9]

Step 15:

C2 is (15)+(13)+(17) --> the (17) part: R78C2<>[69/79]

R2C2: R78C2<>[19] --> R8C2<>[9]

the (15) part: max R123C2=15

Step 16:

C1 is (20)+(25) --> the (20) part: max R123C1=20 --> min R123C2=45-20-15=10

(Step 15) R123C2=11/13/15 (must be odd with 2 even and 1 odd values)

R13C2<>10 --> not 11

R8C2: R123C2<>[814] --> not 13

--> R123C2=15=[294/816] --> R123C1=45-15-15=15=[294/816]

the (20) part: R45C1=20-15=5={23} (C1,N4) (R123C1: <>{14})

--> R123C1=[816], R123C2=[294], R9C12=[53] --> R7C1=[7], R8C2=8

Step 17:

R6 is (13)+(32) --> the (13) part is R6C123=[418]

(Step 5) the (22) part of C4 is R6789C4=[9364]

Naked singles to finish.

- Code: Select all
` 20 15 12 8 20 13 12 34 35`

10 .. .. .. | .. .. .. | .. .. .. 25

10 .. .. .. | .. .. .. | .. .. .. 10

10 .. .. .. | .. .. .. | .. .. .. 30

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26 .. .. .. | .. .. .. | .. .. .. 19

27 .. .. .. | .. .. .. | .. .. .. 18

13 .. .. .. | .. .. .. | .. .. .. 32

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14 .. .. .. | .. .. .. | .. .. .. 14

34 .. .. .. | .. .. .. | .. .. .. 11

15 .. .. .. | .. .. .. | .. .. .. 30

25 17 33 22 25 32 12 11 10

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