# Sudoku: Puzzles have non-unique solutions

14 posts / 0 new
dave5252
Offline
Last seen: 15 years 2 days ago
Joined: 2009-07-28 10:38
Sudoku: Puzzles have non-unique solutions

Routinely, Sudoku Portable produces puzzles that have non-unique solutions. Here's an example:
3,,1,,,,5,2,7
7,2,4,5,1,,,,6
,9,,2,7,8,3,,
9,5,6,7,3,,,8,
8,4,,,,2,6,,3
1,2,3,6,8,,,4,
4,6,9,8,5,7,,,
,,,9,2,1,4,,8
2,1,,3,4,,9,7,

The '1' and the '2' in R4C7, R4C9 & R7C7, R7C9 can be interchanged.

Gizmokid2005
Offline
Last seen: 2 months 2 weeks ago
Joined: 2007-01-17 19:24
Forgive me

But isn't that one of the caveats of Sudoku? To have non-unique solutions?

dave5252
Offline
Last seen: 15 years 2 days ago
Joined: 2009-07-28 10:38
Hold it

Sudoku is a logic puzzle. No guessing, just rational thought. So, why would you want to be presented with a puzzle with no unique solution?

Gizmokid2005
Offline
Last seen: 2 months 2 weeks ago
Joined: 2007-01-17 19:24
Right...

But that's part of the logic...there is more than one possible solution to the puzzle.

dave5252
Offline
Last seen: 15 years 2 days ago
Joined: 2009-07-28 10:38
You're just having fun with me, but I'll play along

* BrainBashers say: Every Sudoku has to have a unique solution, we are not allowed to create a situation where this rule is violated.
* In “Complexity theory and Sudoku,” 0xDE (11011110) wrote: This is the Sudoku designer's problem: she must design a puzzle with a unique solution, and reject puzzles that have no or several solutions.
* The Lexicon of Sudoku: All published puzzles should only have one unique solution, that is one arrangement of the numbers in the grid that is correct. Some puzzles do have multiple solutions but you will rarely find a published puzzle that more than one solution, unless explicitly stated.
* Readmesoft sudoku for Windows description: The rules of Sudoku are simple. Enter digits from 1 to 9 into the blank spaces. Every row must contain one of each digit. So must every column, as must every 3x3 square. Each Sudoku has a unique solution that can be reached logically without guessing.
* How to Play Sudoku [Sudoku Dragon]: The process of solving a Sudoku puzzle is to fill in all the empty squares. However each square has only one solution as it must obey the Sudoku rule.
* Sudoku for Dummies: A Mathematician's Approach: The player is always given a grid with at least seventeen numbers filled in, and each valid Sudoku has only one unique solution that can be reached.
*Rational Sudoku: Sudoku is, fundamentally, a puzzle...not unlike the crossword puzzles that it often accompanies in papers and magazines. Like crosswords, Sudoku have (in most instances) a predetermined solution. It is possible to create Sudoku with non-Unique Solutions, but these are never knowingly used as puzzles.
* Super Sudoku: To answer this we need to understand that each Sudoku puzzle gives just one unique solution grid.
* What's wrong with most Sudoku games on the Internet (and even in newspapers)? [Sudoku Arena] Problem #1 - Bad algorithm (no unique puzzles and wrongly assigned level of difficulty)
Bad puzzles don't have a unique solution or they have miscalculated level of difficulty. True Sudoku puzzle has only one (unique) solution which a player can reach using a logic alone. If a puzzle doesn't have a unique solution players are leaved to guess, which is boring and the Sudoku suddenly becomes a game of luck which it isn't by its definition.
* Sudoku Wizard 1: … deceptively simple game of logic, Sudoku is puzzling players all over world. Each Sudoku has a unique solution that can be reached logically without guessing. Enter digits from 1 to 9 into the blank spaces. Every row must contain one of each digit.

Gizmokid2005
Offline
Last seen: 2 months 2 weeks ago
Joined: 2007-01-17 19:24
Hmmm.

Something you should take up with the creator You have more info on it than I do. I assumed it was normal, especially for the rarity that it occurred, but it's not something we can fix here.

ZachHudock
Offline
Last seen: 1 year 7 months ago
Joined: 2006-12-06 18:07
Most of the puzzles are

Most of the puzzles are unique, but there are several cases where the solution is not unique, in each of those cases, it's typically only 4 cells, 2 digits that can be somehow interchanged.

In my experience, non-unique solutions are few and far between, but they do happen.

The developer formerly known as ZGitRDun8705

jamcomm
Offline
Last seen: 14 years 10 months ago
Joined: 2009-07-24 14:51
Easier

Doesn't that make it easier to solve though?

dave5252
Offline
Last seen: 15 years 2 days ago
Joined: 2009-07-28 10:38
Way easier yet

Our friend Patti buys sudoku books at the store where she works. First, she completes the 'easy' numbers. Then, she enters a few numbers from the solutions section in the back of the book and goes on from there to solve the puzzle.

Bart.S
Offline
Last seen: 2 months 5 days ago
Joined: 2008-07-23 07:56
Try this

digitxp made a GameSuite Portable Dev Test. It contains Solo (Soduku game), which always has unique solutions (from my experience). Or you could download Solo only here. It's portable.

NathanJ79
Offline
Last seen: 4 years 5 months ago
Joined: 2007-07-31 15:07
Thanks!

I've seen that recommended before. It's got a lot of options, and you can customize the board.

As for unique vs. choice, by definition a Sudoku must be solvable by logic alone. If you must guess & test, the Sudoku (the puzzle itself) is broken. They are challenging to make, I'm sure, considering no two numbers on a grid of 81 (9x9) can be interchangeable.

The best Sudoku puzzle book I've done is something like Black Belt Sudoku. It comes in several volumes. I've only done White Belt, the first volume. There are also green and black, and either red or orange. These don't follow the traditional levels, usually they're all mid-level, but they're still challenging. I got mine at Barnes & Noble. I strongly recommend it. I got another Sudoku book and quickly lost interest. There's an art to making those puzzles, and the author/puzzlemaster of the Black Belt series is very good. Took me a right good 3 months to get through it, too.

dave5252
Offline
Last seen: 15 years 2 days ago
Joined: 2009-07-28 10:38
Other Good Books

NathanJ79: You're correct that the 'black belt' series of sudoku books by F. Longo and M. Rios are very good books. When you finish those, take-on the 'Absolutely Nasty' series by F. Longo.

capitalH
Offline
Last seen: 13 years 6 months ago
Joined: 2009-07-23 07:24
Guessing/non unique solutions

In theory if non unique solutions is allowed - you can start with a blank board, and have an insane amount of solutions...

I cannot say that I come close to enjoying the "Sudoku" problems that require guessing.

NathanJ79
Offline
Last seen: 4 years 5 months ago
Joined: 2007-07-31 15:07
Can't