Solving Sudoku: A Logical Approach

[Adel Makram]

How to solve the attached Sudoku without computer or a guess?

 

[certainly]

This sudoku does not have a unique solution, in-fact it has at-least 500 solutions, therefore it is not possible to solve it purely based on logic. (By this I mean you will have to make a choice.)
How do I know it has at-least 500 solutions ? Click the solution-count button http://www.sudokuwiki.org/sudoku.htm. [I've done you the courtesy of typing out the sudoku.]

 

[Adel Makram]

This sudoku does not have a unique solution, in-fact it has at-least 500 solutions, therefore it is not possible to solve it purely based on logic. (By this I mean you will have to make a choice.)
How do I know it has at-least 500 solutions ? Click the solution-count button http://www.sudokuwiki.org/sudoku.htm. [I've done you the courtesy of typing out the sudoku.]

I clicked the link and I filled up the entries then it gave me all numbers (1 to 9) in all blank cells!. So how many solutions?

 

[certainly]

I clicked the link and I filled up the entries then it gave me all numbers (1 to 9) in all blank cells!. So how many solutions?

But I'd already filled the necessary squares for you ?
Click the yellow "solution-count" button at the top right.

 

[Adel Makram]

yes I got it thanks. So what is the lowest number of clues that give a unique solution?

 

[HallsofIvy]

This sudoku does not have a unique solution, in-fact it has at-least 500 solutions, therefore it is not possible to solve it purely based on logic. (By this I mean you will have to make a choice.)
How do I know it has at-least 500 solutions ? Click the solution-count button http://www.sudokuwiki.org/sudoku.htm. [I've done you the courtesy of typing out the sudoku.]

If it has "at least 500 solutions" then it does not have a unique solution!

Oops! I misread your response- you did say it does NOT have a unique solution.

 

[willem2]

According to http://arxiv.org/abs/1201.0749, no solvable sudoko exists with less than 17 clues. Your sudoku is actually a 16 clue sudoku, because the 5 in the top right corner is redundant.

 

[Adel Makram]

According to http://arxiv.org/abs/1201.0749, no solvable sudoko exists with less than 17 clues. Your sudoku is actually a 16 clue sudoku, because the 5 in the top right corner is redundant.

What do you mean by redundant?

 

[TESL@]

He means you already know it is 5, it's not a useful information.

 

[certainly]

Note that 17 clues does not guarantee a unique solution, but you need at-least 17, as the paper quoted by willem2 shows.

According to http://arxiv.org/abs/1201.0749, no solvable sudoko exists with less than 17 clues. Your sudoku is actually a 16 clue sudoku, because the 5 in the top right corner is redundant.

It's actually only a 12 clue sudoku. You should be able to enter the remaining entries from this.

 

[Adel Makram]

Note that 17 clues does not guarantee a unique solution, but you need at-least 17, as the paper quoted by willem2 shows.

It's actually only a 12 clue sudoku. You should be able to enter the remaining entries from this.

Still, I don't understand why do you want to consider all entries on the right upper square redundant? Just because they are on 2 perpendicular lines?

 

[certainly]

Still, I don't understand why do you want to consider all entries on the right upper square redundant? Just because they are on 2 perpendicular lines?

No. They aren't clues because you can solve the empty entries in the link from the given ones.