Atps sudoku

Etapa 1

Passo 1:

U = {y ∈ N|1 ≤ y ≤ 9} = {0,1,2,3,4,5,6,7,8,9}

c = complementar (Ex = cL1)

Linhas:

L1 = {8,6}        cL1 = {x ∈ N|x ∈ U ^ x ∉ L1} = {1,2,3,4,5,7,9}

L2 = {9}                cL2 = {x ∈ N|x ∈ U ^ x ∉ L2} = {1,2,3,4,5,6,7,8}

L3 = {6,4,2}        cL3 = {x ∈ N|x ∈ U ^ x ∉ L3} = {1,3,5,7,8,9}

…

Colunas:

C1 = {2}                cC1 = {x ∈ N|x ∈ U ^ x ∉ C1} = {1,3,4,5,6,7,8,9}

C2 = {8,1}        cC2 = {x ∈ N|x ∈ U ^ x ∉ C2} = {2,3,4,5,6,7,9}

C3 = {9,6,5}        cC3 = {x ∈ N|x ∈ U ^ x ∉ C3} = {1,2,3,4,6,7,8}

…

Subgrades:

S1 = {9,6}        cS1 = {x ∈ N|x ∈ U ^ x ∉ S1} = {1,2,3,4,5,7,8}

S2 = {4,2}        cS2 = {x ∈ N|x ∈ U ^ x ∉ S2} = {1,3,5,6,7,8,9}

S3 = {8,6}        cS3 = {x ∈ N|x ∈ U ^ x ∉ S3} = {1,2,3,4,5,7,9}

…

Passo 2:

SDKi,j  (i=linha, j=coluna)

SDK1,1 = {1,3,4,5,7}

SDK1,2 = {2,3,4,5,7}

SDK1,3 = {1,2,3,4,7}

SDK1,4 = {3,5,7,9}

...

SDK9,6 = {14,6,7}

SDK9,7 = {3,4,6,7}

SDK9,8 = {3,6,7,8}

SDK9,9 = {3,4,7,8}

Etapa 2

Passo 1:

U = {y ∈ N|1 ≤ y ≤ 9} = {0,1,2,3,4,5,6,7,8,9}

c = complementar (Ex = cL1)

Linhas:

L1 = {3,5,8}         cL1 = {x ∈ N|x ∈ U ^ x ∉ L1} = {1,2,4,6,7,9}

L2 = {1,2,6}         cL2 = {x ∈ N|x ∈ U ^ x ∉ L2} = {3,4,5,7,8,9}

L3 = {1,4,5,6}         cL3 = {x ∈ N|x ∈ U ^ x ∉ L3} = {2,3,7,8,9}

...

Colunas:

C1 = {3,4,6,8,9}         cC1 = {x ∈ N|x ∈ U ^ x ∉ C1} = {1,2,5,7}

C2 = ∅                 cC2 = {x ∈ N|x ∈ U ^ x ∉ C2} = {1,2,3,4,5,6,7,8,9}

C3 = {4,5}         cC3 = {x ∈ N|x ∈ U ^ x ∉ C3} = {1,2,3,6,7,8,9}

...

Subgrades:

S1 = {3,4,6,8}         cS1 = {x ∈ N|x ∈ U ^ x ∉ S1} = {1,2,5,7,9}

S2 = {1,2,5}         cS2 = {x ∈ N|x ∈ U ^ x ∉ S2} = {3,4,6,7,8,9}

S3 = {2,6}         cS3 = {x ∈ N|x ∈ U ^ x ∉ S3} = {1,3,4,5,7,8,9}

...