## I thought there was only 1 answer per puzzle?

Advanced methods and approaches for solving Sudoku puzzles

### I thought there was only 1 answer per puzzle?

Hi,

I've just got hooked on these puzzles and thought there was only 1 solution. However, the image below is how I solved it but when I click on Show Solution is shows at lot of my answers as incorrect??

Is it just me or can their be more than one solution per puzzle?

My Solution:

Programs Solution:
Guest

Posts: 312
Joined: 25 November 2005

these are the images:

Mine:

Programs Solution:
Lintz

Posts: 3
Joined: 22 May 2005

Please, host the images somewhere else since it is impossible to see them...

(Instead of the images it displays a stupid advertising message from tripod!)
Animator

Posts: 469
Joined: 08 April 2005

have uploaded images to another site
Lintz

Posts: 3
Joined: 22 May 2005

You are missing a very important rule:

Each grid is defided into 9 smaller boxes of 3 colums and 3 rows.

Box1 for example is: r1c1, r1c2, r1c3, r2c1, r2c2, r2c3, r3c1, r3c2, r3c3.

Each box has to have the numbers 1 to 9.

If you look at your solution for box 1 then you clearly see that is not the case... as in, you have the number 1 twice, you also have the number 4 twice and you are missing the numbers 6 and 8...
Animator

Posts: 469
Joined: 08 April 2005

that would explain why i haven't got the correct solutons!!

Thanks.
Lintz

Posts: 3
Joined: 22 May 2005

### There can be more than one solution

I was doing the Medium puzzle in Perth's Sunday Times (22/5) and made a mistake somewhere early on. I overwrote one of the pre-printed digits. The interesting thing is that I managed to come up with a solution based on that wrong digit. I also discovered that there was an alternative solution again based on that wrong digit. Both solutions conform fully to the rules of Sukodu, so I believe that it is possible to have more than one solution. These are the 2 alternative answers:

694 823 157 * 684 923 157
287 951 643 * 297 851 643
531 467 289 * 531 467 289

173 248 965 * 173 248 965
465 139 728 * 465 139 728
928 576 431 * 928 576 431

346 715 892 * 346 715 892
759 682 314 * 759 682 314
812 394 576 * 812 394 576

The difference between the two is that the 8s and 9s in r1c2, r2c2, r1c4 and r2c4 are transposed (8 becomes 9 and 9 becomes 8). It is obvious why both solutions are valid. The only items affected by the transposition are row 1, row 2, col 1, col2, mini-grid 1 and mini-grid 2. The transposition has the same affect on all of these, in that where there was an 8 there is a 9 and vice-versa. So by definition, each of these still contain all nine digits.

One way of making either of these a 'unique' solution is for the problem setter to pre-set any one of these 4 cells to either an 8 or a 9. But if all are empty to begin with (as was the case here), then more than one solution is possible.

In fact with careful planning I suspect that one could compose a problem with not just 2 but possibly many solutions, if it contains multiple cell-combos like that shown above.
Guest

Puzzles can indeed have multiple solutions, but the puzzles generates by the Pappocom software assures that there is 1 logical solution.

Changing clues almost always results either in multiple solutions or in no solutions, that because of the proces how the puzzles are created. The generating proces follows the same rules...
Animator

Posts: 469
Joined: 08 April 2005

### Re: I thought there was only 1 answer per puzzle?

[I solved a puzzle too and got a different solution to the one published)

I've just got hooked on these puzzles and thought there was only 1 solution. However, the image below is how I solved it but when I click on Show Solution is shows at lot of my answers as incorrect??

Is it just me or can their be more than one solution per puzzle?

My Solution:

Programs Solution:
[/quote]
s1yf0x1e

Posts: 1
Joined: 27 May 2005

These are exactly the same images... so what's your point?