# Trying all the alternatives to solve a Sudoku puzzle

Trial and Error - The Labyrinth [Game solving Strategies forum]

If all else seems to fail you may need to do a trial and error approach for very tough Sudoku puzzles. There is a full page describing this 'strategy' on the guessing page.

Yes, this basically means you have to make a 'guess' of which of equally likely alternatives and see if it leads to a solution. If it turns out to be incorrect you'll need to backtrack - clearing all allocations made using that assumption until reaching a branch point when the choice was made. SudokuDragon makes this very easy actually as you can add a note to the square when you make the 'guess' explaining which branch was taken, you can then use the 'Undo' feature to take you all the way back to the decision point.

It's really a strategy of last resort because it takes some time to undo it.

Guessing (re: Trial and Error - The Labyrinth) contributed by Jim Sheehan

How about placing a G after a puzzle that requires a guess?

Labyrinth Ban (re: Trial and Error - The Labyrinth) contributed by Prudence

I have heard and read that puzzles that require the use of a trial and error strategy are not considered genuine Sudoku puzzles.

Basically if a puzzle cant be solved by logical reasoning it shouldn't count as a Sudoku puzzle.

Does SudokuDragon make this distinction I wonder?

Labyrinth Policy (re: Labyrinth Ban) contributed by SudokuDragon

It's a subject we are actively reviewing.

With Release 2.7 (14) we have made sure none of our Moderate puzzles can ever require any backtracking.

Many of the more difficult puzzles are also solvable using the straightforward Sudoku strategies (only place, forced choice, excluded subgroups and excluded twins).

However some truly challenging puzzles although having a single solution may not be solvable using these techniques alone.

Let us know what you would like to see. We are thinking of introducing an extra hard level of difficulty rather than banning the backtrack/labyrinth altogether.

Labyrinth banned (re: Labyrinth Policy) contributed by SG

I prefer the puzzles to be able to be solved by logic. Using a trial and error method detracts from the game. I also owned a timed version of Sudoku and I spend considerable time on trying to find the logic to rationalize the answer. Having an extra hard category for logical puzzles without a stripe would be nice.

No backtracking (re: Labyrinth banned) contributed by Alexander

Yes, I agree it's most frustrating to find out that there was no proper solution after all and have to resort to guessing rather than using pure logic to solve the puzzle.

The vast majority of puzzles are now machine generated and perhaps that has something to do with it.

No Trial and Error (re: Labyrinth Policy) contributed by Drue

I personally do not want to spend time on puzzles that will require trial and error. Along with many sudoku fans, I don't consider those puzzles to be true sudoku.

1. Does Dragon still generate trial-and-error-only puzzles?

2. Are all puzzles generated one solution only?

If trial and error is still available, I would like to either see it removed, or isolated in some fashion so that those gamers that are ok with it can work with it.

Also, in my view, puzzles should have only one solution. If this is not the case with SD, I vote for unique solutions as a policy.

Current Policy (re: No Trial and Error) contributed by SudokuDragon

This is a tricky issue as there are some very complex solution strategies out there that may make most, even advanced, players reckon that a puzzle in 'unsolvable' without guessing.

SudokuDragon does not yet use all the advanced strategies (for example X-Y Wing) so there are puzzles with a unique solution that SudokuDragon needs to guess to be able to solve.

Currently (version 4.1) it may generate a 'trial and error' puzzle but at ONLY the topmost difficulty level. There are players who still find our puzzles too easy and like to do some trial and error, so this has been left in for them. If you want to guarantee no trial and error please select a difficulty level other than 'hardest'.

The second point is easier to answer, all our puzzles should have only one solution. Some people have been caught out by our 'stripe' if you select the 'stripe' or 'diagonal' generation option there may be other 'solutions' that do not obey the stripe or diagonal rule. If you do find an example of a SudokuDragon puzzle with two (or more) solutions please send it to us. So far no-one has found one.

Labyrinth Tip (re: Trial and Error - The Labyrinth) contributed by Alexander

If you are solving a puzzle using a bit of trial and error - by following one possibility and seeing if it gives a solution it is quite convenient to use SudokuDragon to mark the point where you made the guess. The easiest way to do this is use is to use CTRL key + number, so just click on the guessed number (say '4' if there is a choice between 4 and 6). If the route does not prove fruitful you can use the Undo feature to take you back to when you allocated the marked square (which conveniently has a 4 in the corner) and then you know to change the '4' into a '6' and try that alternative possibility.

Origins of Labyrinth (re: Labyrinth Tip) contributed by Nivlem

It might be worth mentioning the origins of the Labyrinth tip. It takes it's name from the ancient Greek tale of Theseus and the Minotaur. While trying to escape the Minotaur (a monster half bull and half man). Ariadne gave a ball of thread to Theseus to mark his way to the Minotaur through the Labyrinth and then back out again. Most people latch on to the use of the thread to find your way back as you just follow the thread and you can backtrack, however according to the myth the ball of thread helped find the Minotaur as well.

Stuck in a Hard place (re: Trial and Error - The Labyrinth) contributed by Lynne

Here's an example of a 'hard' puzzle that I can't find a way of solving without using backtracking

Unsolvable sudoku puzzles (re: Trial and Error - The Labyrinth) contributed by Vi Lee

Are there any sudoku puzzles that claim to be unsolvable? Do you know which websites post them? Thanks

How unsolvable? (re: Unsolvable sudoku puzzles) contributed by Rosina

I am not sure what you mean by 'unsolvable'.

Many people consider a puzzle that can not be solved with pure logic as 'unsolvable'.

If a puzzle needs 'trial and error' to solve it then it is not really unsovlable. Many of the Challenging class of puzzle on this site are in this class.

If you really mean unsolvable then this can be because the puzzle has multiple possible solutions (so it has no unique solution) or it is badly formed and has no solution at all.

On the theory page I think there are some examples of the puzzles considered to be the hardest of all.

Guessing and backtracking (re: How unsolvable?) contributed by Michael Teter

I think that calling a puzzle that requires guessing and backtracking one that cannot be solved by logic simply means that you haven't learned the logical step necessary to solve it There are probably more complex patterns that we haven't learned yet that make it obvious.

Naked singles are easy, just look and see than only one number can go in a square. Hidden singles are a little harder, you just have to look more I can go on and on but basically the harder the logic step the more analysis required. Puzzles are graded on difficulty based on how hard the logic steps are that are required to solve it. No one disagrees that using doubles to eliminate possibles is a valid logic step. They all are grounded in the concept that if you violate the logic, you get an illegal game. Seeing the result that a guess leads to an illegal game and eliminating the possibility is just carrying the logic one step further.

Most real objections to it are based on the fact that it is simply harder to do.

Give the games that require it a harder rating, but don't eliminate them, some of us like a challenge.

Mike