# Is the 7-clue 6x6 Sudoku solvable?

So I was trying to find an 8-clue 6x6 Sudoku because I knew from this paper that only 8 clues were needed to create a 6x6 Sudoku with a unique solution.

However, I have managed to find one with 7 clues:

Or, if you're like me and prefer it with 2x3 boxes:

While I am aware that this is supposed to be played as a Sixy Sudoku, what I would like to know is if it is actually solvable as a normal 6x6 Sudoku or not.

This is the progress I have made so far:

What I have done to make progress on the Sudoku is if there is no real way to tell which number goes in which cell, I type the numbers that can go there, and then use process of elimination to remove possibilities until there is only one number left. (no guesswork involved)

However, my question is:

## Is the 7-clue 6x6 Sudoku solvable from here, or is it only possible to solve it as a Sixy Sudoku?

• You can remove a 5 from one of the cells (obvious, or a typo). Commented Feb 29 at 18:06
• @WeatherVane Sorry about that, that is a typo. Thanks for catching it though. :) Commented Feb 29 at 18:07
• It depends on what you mean by "solvable". Do you mean "there is at least one solution"? Or a unique solution? Or "it can it be solved by deduction alone, without guessing?" Commented Mar 1 at 6:13

It is...

...not uniquely solvable. There are 281 solutions.

Here are two:

 5 2 6 4 3 1    1 2 6 4 3 5
1 4 3 6 2 5    5 4 3 6 2 1
4 5 1 3 6 2    4 5 1 3 6 2
3 6 2 1 5 4    3 6 2 1 5 4
2 3 4 5 1 6    2 3 4 5 1 6
6 1 5 2 4 3    6 1 5 2 4 3

Notice that some of your progress is too strong. In fact, it turns out that...

...only the 7 given cell values are uniquely determined. That is, for all other cells, there is more than one possible value among the 281 solutions.