Can someone please tell me how you can solve this Sudoku without

There is no mathematical principle, sudoku is an NP problem there is no formula for it, you need to brute force. As the amount of squares increases it's solution time expands exponentially. Unless you think p=np in which case you're a brainlet

>>9036369
But with every other puzzle I've done (specifically this is the 'Hard' puzzle, from NYtimes) I have never had to guess before. So, I feel like there must be something I am missing, or some mathematical principle that I could use to solve one square.

There are mathematical rules that apply to Sudoku, for example: If in any row, column, or 3x3 box you have two smaller boxes where only 2 numbers can go, then none of the other boxes in that row, column, or 3x3 box can include those 2 numbers, so you can eliminate them from the other boxes.

I wanted to know if there is some principle like that I am missing.

>>9036369
t. brainlet who hasn't solved the p=np problem in his spare time

>>9036388
the fact that every sudoku you've found is piss easy doesn't mean that intracable sudokus don't exist. bruteforce it if stuck

>>9036392
Post proof then fggt

>>9036369
So you've never taken linear algebra, then?

>>9036454
you're an idiot

>>9036471
No, you are.

>>9036360
You can simplify it a bit atleast you have a quad in top left square 1,7,9 x2 and 1,2,9 x2 means that 1,2,7,9 cant be in the column below the three. from there you can conclude that the one must be in the left most column in the second row frist column 3x3 square and there some more stuff you can do from there.

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>>9036360
Eliminate the 5s in the lower right square.

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>>9036668
Good catch. Still doesn't allow me to solve the puzzle without making a guess though.

Anyone else have any clues? Or something else everyone has missed?

>>9036712
You're a millennial, aren't you?

>>9036712
You're just going to have to be more intelligent.

>>9036712
The two squares below the 7 top right must be 1 and 8 which means one of the squares below the 2 must be a 5, which means the the 5 in the bottom right must be the one next to the one highlighted. Easy.

>>9036761
Beautiful. Thank you.
>>9036727
I already admitted I'm a brainlet, and no I am not a millennial. You, though, are a faggot! PEACE, IM OUT THIS BITCH!

>>9036360
Are u asking for the mathematical word for lots of guessing?
Brute force it

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>>9036799
>>9036360

You need to learn how to find hidden doubles and triples

>>9036905
OP is a brainlet. anon saves the day with his genius

>>9036360

Most sudoku grids can be solved without guessing by using but the most difficult ones ever made require some form of guessing. Google "World's hardest sudoku" to find what I'm talking about

>>9036360
>no guessing
What do you mean by this?

There are 81 squares and each of them can take 9 possible values, so there are at most 81^9 possible Sudoku grids.
You can easily write a program (or, less easily, do it by hand) that generates and checks all possible grids iteratively, stopping and returning the first found grid such that:
- for every row and every number 1-9, that number appears exactly once among the 9 squares in that row
- for every column and every number 1-9, that number appears exactly once among the 9 squares in that column
- for every box and every number 1-9, that number appears exactly once among the 9 squares in that box
- for every square that is filled in the initial starting grid, the values agree
No guessing involved, guaranteed to find a solution if it exists, and if you want to find all solutions just keep going until you search all 81^9 grids.

This can be solved by Grobner basis. In a similar manner to a k-coloring problem. In this case it is a equivalent to a 9-color problem.