Passo 1 mat. aplc. 4

Passo 1

Considerando uma casa fixa sem preencher. Ao eliminar os outros algarismos que aparecem na mesma coluna, na mesma linha ou na mesma subgrade, é possível que sobre uma única possibilidade, com a qual a casa deve ser preenchida.
L = Linha
C= Coluna
S= Subgrade
O primeiro valor entre chaves são os números já preenchidos pelo sudoku, o segundo são as possibilidades de números que podem ser introduzidos.
L1={6,8} L1’={1,2,3,4,5,7,9}
C1={2} C1’={1,3,4,5,6,7,8,9}
S1={6,9} S1’={1,2,3,4,5,7,8}

L2={9} L2’={1,2,3,4,5,6,7,8}
C2={1,8} C2’={2,3,4,5,6,7,9}
S2={2,4} S2’={1,3,5,6,7,8,9}

L3={2,4,6} L3’={1,3,5,7,8,9}
C3={5,6,9} C3’={1,2,3,4,7,8}
S3={6,8} S3’={1,2,3,4,5,7,9}

L4={1,8} L4’={2,3,4,5,6,7,9}
C4={1,8} C4’={2,3,4,5,6,7,9}
S4={1,8} S4’={2,3,4,5,6,7,9}

L5={1,2} L5’={3,4,5,6,7,8,9}
C5={3,4} C5’={1,2,5,6,7,8,9}
S5={1,9} S5’={2,3,4,5,6,7,8}

L6={4,9} L6’={1,2,3,5,6,7,8}
C6={2,9} C6’={1,3,4,5,6,7,8}
S6={2,4} S6’={1,3,5,6,7,8,9}

L7={1,3,8} L7’={2,4,5,6,7,9}
C7={1,8,9} C7’={2,3,4,5,6,7}
S7={2,5} S7’={1,3,4,6,7,8,9}

L8={9} L8’={1,2,3,4,5,6,7,8}
C8={2,4} C8’={1,3,5,6,7,8,9}
S8={3,8} S8’={1,2,4,5,6,7,9}

L9={2,5} L9’={1,3,4,6,7,8,9}
C9={6} C9’={1,2,3,4,5,7,8,9}
S9={1,9} S9’={2,3,4,5,6,7,8}
Passo 2
Considerando os conjuntos complementares encontrados no Passo anterior, vamos determinar os conjuntos de algarismos possíveis para cada casa sem preenchimento da Figura 1.

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}
SDK1,5={1,5,7,9}
SDK1,6={1,3,5,7}
SDK1,8={1,3,5,7,9}

SDK2,1={1,3,4,5,7,8}
SDK2,2={2,3,4,5,7}
SDK2,4={3,5,6,7}
SDK2,5={1,5,6,7,8}
SDK2,6={1,3,5,6,7,8}
SDK2,7={2,3,4,5,7}
SDK2,8={1,3,5,7}
SDK2,9={1,2,3,4,5,7}

SDK3,1={1,3,5,7,8}
SDK3,2={3,5,7}
SDK3,4={3,5,7,9}
SDK3,7={3,5,7}
SDK3,8={1,3,5,7,9}
SDK3,9={1,3,5,7,9}

SDK4,1={3,4,5,6,7,9}
SDK4,3={2,3,4,7}
SDK4,5={2,5,6,7}
SDK4,6={3,4,5,6,7}
SDK4,7={3,5,6,7}
SDK4,8={3,5,6,7,9}
SDK4,9={3,5,7,9}