# Solving Sudoku with logic?

1. Jun 1, 2015

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

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2. Jun 1, 2015

### 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 here. [I've done you the courtesy of typing out the sudoku.]

3. Jun 1, 2015

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?

4. Jun 1, 2015

### certainly

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

5. Jun 3, 2015

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

6. Jun 3, 2015

### HallsofIvy

Staff Emeritus
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.

Last edited: Jun 3, 2015
7. Jun 3, 2015

### 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.

8. Jun 4, 2015

What do you mean by redundant?

9. Jun 4, 2015

### TESL@

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

10. Jun 5, 2015

### certainly

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.

11. Jun 5, 2015