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The main difference between a classic sudoku and an outside sudoku is that the clues are outside the grid so the grid is totaly empty.  The numbers  outside the grid  must appear in the first three cells (in any order) of the column or the row.  This means that this numbers does not appear in the last 6 cells. With this particularity you coul deduct where the numer are placed or where they are not placed.

Look at the grid and the solution to better understand.

Outside Sudoku 0071 Outside Sudoku Solution 00071

 

 Some tips :

Start with the corners to find where to put numbers, by example in the upper left corner of the grid a 7 and a 4 are the clues for the third column and  7,6 and 3 are the clues for the second row,  this indicates that the common clue: 7 must be at the intersection (the cell in the second row and third colomn).