def same_row(i,j): return (i/9 == j/9) def same_col(i,j): return (i-j) % 9 == 0 def same_block(i,j): return (i/27 == j/27 and i%9/3 == j%9/3) def r(a): i = a.find('0') if i == -1: print a excluded_numbers = set() for j in range(81): if same_row(i,j) or same_col(i,j) or same_block(i,j): excluded_numbers.add(a[j]) for m in '123456789': if m not in excluded_numbers: # At this point, m is not excluded by any row, column, or block, so let's place it and recurse r(a[:i]+m+a[i+1:]) r('530070000600195000098000060800060003400803001700020006060000280000419005000080079534678912672195348198342567859761423426853791713924856961537284287419635345286179')
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