Task

Solve a partially filled-in normal   9x9   Sudoku grid   and display the result in a human-readable format.

references

 Algorithmics of Sudoku   may help implement this.
 Python Sudoku Solver Computerphile video.


solve[sudoku_] := 
 NestWhile[
  Join @@ Table[
     Table[ReplacePart[s, #1 -> n], {n, #2}] & @@ 
      First@SortBy[{#, 
           Complement[Range@9, s[[First@#]], s[[;; , Last@#]], 
            Catenate@
             Extract[Partition[s, {3, 3}], Quotient[#, 3, -2]]]} & /@ 
         Position[s, 0, {2}], 
        Length@Last@# &], {s, #}] &, {sudoku}, ! FreeQ[#, 0] &]