The vast majority of puzzles don’t require the trickier techniques, but there are some which just aren’t solvable by simple logic alone, and require various forms of guessing to solve. Going on from this, it is possible to solve entire Sudoku puzzles from guesses alone, but it can take a long time!
Is there only one solution to Sudoku?
A Sudoku puzzle can have more than one solution, but in this case the kind of logical reasoning we described while discussing solving strategies may fall short. It is important to note that this is not the same as stating that if a Sudoku of rank n has n2-1 distinct digits in the givens, then it is well-formed.
Do nonograms have unique solutions?
These puzzles will always have a unique solution. Clearly, the fact that solving Nonograms is NP-hard indicates that not all puzzles can be solved using simple logic reasoning.
How to check if an instance of 8 puzzle is solvable?
The second example cannot. Following is simple rule to check if a 8 puzzle is solvable. It is not possible to solve an instance of 8 puzzle if number of inversions is odd in the input state. In the examples given in above figure, the first example has 10 inversions, therefore solvable. The second example has 11 inversions, therefore unsolvable.
Is it possible to get an insolvable puzzle?
Maybe it can help you to exclude some configurations. Yes, it will always have a solution as long as you start with a good solution and then make legal moves to randomize the tiles. BUT if you, for example, pop two pieces out and switch them, then you can get an insolvable puzzle. 😉 As you discovered.
Is it possible to make a puzzle that always has a solution?
Yes, it will always have a solution as long as you start with a good solution and then make legal moves to randomize the tiles. BUT if you, for example, pop two pieces out and switch them, then you can get an insolvable puzzle. 😉 As you discovered.
Is it possible for a random shuffle to result in no solution?
If it is possible that a random shuffle could result in no-solution, then I’d have to figure out how to verify that there exists a solution, which is a completely different beast. Martin Gardner had a very good writeup on the 14-15 puzzle in one of his Mathematical Games books. Sam Loyd invented the puzzle.
