Do You Ever Have to Guess in Sudoku?

Solving Sudoku puzzles involves making a series of logical deductions to arrive at a unique solution. 

But, after having played Sudoku puzzles, you likely have found yourself in situations where you feel like you have no choice other than to guess. 

Guessing however is hardly a logical solving technique. So it might seem strange that in a puzzle all about logical deduction, you’d have to make guesses. 

So let’s take a look at whether you ever have to guess to solve a Sudoku puzzle.

Can all Sudokus be solved without guessing?

The short answer is yes. Every proper Sudoku puzzle can be solved without ever having to make a guess. 

Another way of thinking about it is that every Sudoku puzzle can be solved logically. Even though it may require highly complicated solving techniques you’re not familiar with. 

Where the answer begins to get complicated is when you take into account bifurcation or solving a puzzle through brute force. 

Sudoku guessing vs bifurcation or brute force

There will be times with very challenging puzzles where there is only one remaining pair of numbers that are candidates for a particular cell. 

While it may be theoretically possible to reduce the two candidates down to a single number through some highly advanced (or even undiscovered) solving technique, most advanced Sudoku solvers will instead turn to bifurcation. 

Bifurcation is the process of choosing one of these two remaining candidates for the particular cell and seeing if it’s possible to complete the Sudoku without running into an issue. 

If they run into an issue (such as the same number appearing twice in the same row or column) then they know they must have picked the wrong number. And therefore the correct solution would be the other candidate. 

Because this process can be seen as ‘guessing’, it can have a bad reputation in the Sudoku community. Instead, many solvers attempt to find a logical process to find the answer so they don’t have to rely on bifurcation. 

Whether or not you consider bifurcation guessing or not, it is not the same as randomly picking numbers to place in cells. 

It’s instead a brute force method of systematically running through all the remaining possibilities to find the answer. 

No Sudoku puzzle that’s be properly constructed will require you to simply guess by placing random numbers in cells. 

All Sudokus can be solved without guessing.