Is it possible to do sudoku without guessing

In at least 3 cases over the last few years, I found a puzzle that had more than one solution. I had to choose which one of a pair of numbers was going to be the "solution" number. From there, I could solve the puzzle.

I actually saved one puzzle and ran it both ways. It checked out each way. Very,very rare, but it happens. I came across this result that claims that clue sudokus are not solvable without guessing as they have multiple solutions possible. While they have used brute-force to go over all the solutions, there is no mathematical proof yet.

I think. Guessing would be necessary only if solving the Sudoku puzzle means to get the puzzle creator's intended solution and there are multiple valid solutions available. Yes for example, the puzzle below cannot be solved by logic only guesswork and it only has one solution too. Ok, this thread has no clear answer. However, this example may prove that the answer is that some Sudoku puzzles require a guess as part of the technique.

See the three puzzles below. Plug the puzzles into a Sudoku solver website such as this and you will see that the solver reports back that it is stuck. There is no more logic to use to deduce the solution, therefore you must guess at one of the pairs. The simple answer is yes, but not in most cases.

A prime example is Arto Inkala's Worlds Hardest Sudoku it has been published with the point that it has a high number of required guesses. Another good example is SudokuWiki's Weekly Unsolvable Sudoku all of them have the property that they require guesses, although occasionally one of those turns out to be solvable by logical means.

The important thing to note here is these are published specifically as not solvable by standard logic. Most puzzle makers go through some effort to make sure their published puzzles are all solvable by logic, either by having a human solve it using only logic or having software solve it using logic based techniques humans would use.

This is usually incorporated in the grading of the puzzle as easy or extreme if it is found not to be solvable without guessing it won't usually be published. There are definitely a lot of Sudoku puzzles that require guessing.

By guessing I include selecting a box for which you have two potential numbers and using one of those numbers to see how far it will take you to solution. If you solve the puzzle you "guessed" correctly. If you get a conflict, you go back and use the other number to solve the puzzle. I have also seen puzzles where it did not matter.

You could chose either number and solve the puzzle. It is still guessing and I consider it a crappy puzzle. Sign up to join this community.

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That is, there was a choice to make, and either one would have been correct. Not the same as guessing. Sometimes Sudoku players will feel tempted to guess.

But unfortunately, guessing might ultimately bring you farther away from solving the Sudoku puzzle. If you guess wrong, and then that wrong number becomes the basis for additional faulty assumptions about the puzzle, you might end up creating a series of confusing errors that end up with you abandoning the puzzle in frustration.

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This means, we can eliminate 8 from the upper and lower rows in the middle-right column. Naked Subset The example shows that row number 1 and row number 5 both have a cell in the same column containing only the candidate numbers 4 and 7. These two numbers appear as candidates in all of the other open cells in that column too, but since they are the only two candidates in rows 1 and 5, these two numbers cannot appear anywhere else in the row, thus you can remove them.

In the example, the two candidate pairs circled in red, are the sole candidates. Since 4 and 7 must be placed in either of these two cells, all of the pairs circled in blue, can remove those numbers as candidates. In this puzzle, this means 1 becomes sole candidate in the second row; 2 becomes sole candidate in row 6; and thus, 6 is sole candidate for row number 4. You can also use this technique if you have more than two candidates. For example, let us say the pairs circled in red were instead triple candidates of the numbers 1, 4, 7.

This would mean those three numbers would have to be placed in either rows 1, 2 or 5. We could remove these three numbers as candidates in any of the remaining cells in the column. Hidden subset This is similar to Naked subset, but it affects the cells holding the candidates.

In this example, we see that the numbers 5, 6, 7 can only be placed in cells 5 or 6 in the first column marked in a red circle , and that the number 5 can only be inserted in cell number 8 marked in a blue circle. Since 6 and 7 must be placed in one of the cells with a red circle, it follows that the number 5 has to be placed in cell number 8, and thus we can remove any other candidates from the 8th cell; in this case, 2 and 3.

X-Wing This method can work when you look at cells comprising a rectangle, such as the cells marked in red. In this example, let's say that the red and blue cells all have the number 5 as candidate numbers.

Now, imagine if the red cells are the only cells in column 2 and 8 in which you can put 5. In this case you obviously need to put a 5 in two of the red cells, and you also know they cannot both be in the same row.

Well, now, this means you can eliminate 5 as the candidate for all the blue cells. This is because in the top row, either the first or the second red cell must have a 5, and the same can be said about the lower row.

Swordfish Swordfish is a more complicated version of X-Wing. In most cases, the technique might seem like much work for very little pay, but some puzzles can only be solved with it. So if you want to be a sudoku-solving master, read on!

Example A In example A, we've plotted in some candidate cells for the number 3. Now, assume that in column 2, 4, 7 and 9, the only cells that can contain the number 3 are the ones marked in red.