Sudoku Assistant - The Sudoku Trainer and Solver

"Anything that involves copying grids multiple times is likely to become a chore rather than a challenge!"

Trial and Error Solving

Known inside our program as Recursion, described by some as 'Ariadne's Thread'

The Trial and Error technique in solving Sudoku puzzles should not be confused with 'guessing'.

Imagine getting to a point in a puzzle where you could not see any logical advancement to the puzzle. You could pick a cell that had a number of known possible values, and literally copy the whole Sudoku puzzle, one copy for each possible value for that cell. Then, in your first copy you write in the lowest possible value for the cell, the second possible value in the second copy, and so on (which is why you would typically choose a cell with a relatively low number of possible values!).

You could then try and solve the first copy of the puzzle; if you get stuck because of an impossible situation (e.g. there is no cell on a particular row that can take a particular value) then you know that the cell value that started this process is incorrect.

If however, you manage to work through to a complete solution, then you know that the cell value you picked is correct - or at least is one of the correct values. Why? Because it is possible for puzzles to be badly-formed and have more than one solution... though we would hope that these are not common in puzzles set nowadays.

A structured approach to unknown cell values is logical to an extent, but we agree that it is not something that could be considered entertaining. Therefore, you can be sure that Sudoku Assistant will not generate puzzles that require this!

Interestingly, we hear that Michael Mepham, Sudoku setter for the Telegraph, thinks that a Trial-and-Error approach is OK and a reasonable experience in a Sudoku puzzle (though he refers to it as 'Ariadne's Thread'). Fun as we think Sudoku is, anything that involves copying grids multiple times is likely to become a chore rather than a challenge! One of the issues to our mind is that expecting that you might need to use this technique may lead you to use it before you have actually exhausted other possibilities - and in fact, it could encourage the use of Guessing which really ought to be 'bad practice' when solving Sudoku.

Sudoku Assistant does have the trial-and-error facility enabled however, to help check puzzles that are entered from other sources - although it uses it only after all other implemented tests have been exhausted.

As a side-note, it is also possible that a puzzle can be badly formed in having no solutions! Here's a reproduction of a puzzle we have seen in a Sudoku puzzle magazine (that we will not name, unless they would prefer us to for copyright reasons?):

6     8   9     4
  8 9   3   6 1  
              9  
    1 9   8 7    
      5   1      
    4 3   9 9    
  1              
  6 7   8   2 3  
9     2   5     7

This error is almost certainly a simple misprint - but nevertheless is does demonstrate a puzzle that is impossible to solve!

 

If you are unsure of any of the terminology we use, you may find it helpful to refer to our Glossary.

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