title: Formulate sudoku puzzle given the solutions
body: <p>I just recently did a sudoku solver in java using backtracking.</p>
  
  <p>Is it possible, given the solutions, to formulate a problem or puzzle?</p>
  
  <p><strong>EDIT</strong></p>
  
  <p>to formulate the original puzzle, is there some way to achieve this?</p>
  
  <p>and an additional question,</p>
  
  <p>given the puzzle and the solutions.</p>
  
  <p>If I am able to solve the puzzle using the solutions (result is puzzles)</p>
  
  <p>and at the same time able to solve the solutions using the puzzle (result is solutions)</p>
  
  <p>Which has the greater number?</p>
  
  <p>the puzzles? or the solutions?</p>