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**MajikWaffle****Member**- Registered: 2005-12-14
- Posts: 11

Teacher gave that as a problem of the week, and from what I've done I figured it was unsolvable. Kind of messed up POW if it doesn't even work...

*Last edited by MajikWaffle (2006-11-02 11:56:22)*

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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

As far as I have tried for the past 40 minutes, it is impossible to solve with logic.

I'm going to try to solve it with a program, now.

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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

I managed to fill up quite a bit of it, but no luck yet. Sorry.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

I managed to solve it without too many problems. I made a mistake somewhere and so had to start again once, but apart from that it was fine. Maybe you just weren't being logical enough?

Why did the vector cross the road?

It wanted to be normal.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

A couple of much more interesting questions:

How can one tell if a sudoku puzzle is unsolvable?

What is the least amount of numbers one may have before any puzzle becomes unsolvable?

How many unsolvable puzzles are there?

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**MajikWaffle****Member**- Registered: 2005-12-14
- Posts: 11

Heh, the problem changed once he figured it was unsolvable including the linked image.

Now it's solvable...

Also, sudoku puzzles are impossible to solve based on the predefined numbers in boxes.

The old image was

_ 2 _ |1 5 _ |_ _ _

_ _ 5 |2 _ _ |_ _ 9

3 _ _ |_ _ 4 |_ 2 5

---------------------

_ 8 7 |_ _ 2 |5 _ _

_ 4 _ |_ 1 7 |_ _ _

_ _ _ |_ _ 3 |1 _ 7

----------------------

2 _ 4 |6 _ _ |_ _ _

6 _ _ |_ 9 _ |_ 3 _

_ 5 _ |_ _ _ |9 6 8

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,685

I had to code a solver before I could come up with a generator for my Sudoku Game.

Luckily there are plenty of resources for algorithms etc.

If you choose an Advanced puzzle you can watch it generating the puzzle. It tries solving it each time it adds a number - if it CAN solve it, then it gives you the puzzle.

In "Advanced Hard" mode, it actually removes clues until there is only ONE solution.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**Leren****Member**- Registered: 2017-04-19
- Posts: 3

The above puzzle is unsolvable. The following diagram shows the "solution" which has 0's in several cells where it is no possible to place a number.

*--------------------------*

| 4 2 6 | 1 5 9 | 3 7 0 |

| 7 0 5 | 2 3 6 | 4 1 9 |

| 3 1 9 | 8 7 4 | 6 2 5 |

|--------+-------+--------|

| 1 8 7 | 0 4 2 | 5 9 3 |

| 5 4 3 | 9 1 7 | 0 8 2 |

| 0 9 2 | 5 6 3 | 1 4 7 |

|--------+-------+--------|

| 2 3 4 | 6 0 8 | 7 5 1 |

| 6 7 1 | 4 9 5 | 2 3 0 |

| 0 5 0 | 3 2 1 | 9 6 8 |

*--------------------------*

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,600

Hi Leren;

Here are two options that, by making one change to the puzzle in post #6, converts it from unsolvable to one that has a unique solution:

```
Option 1: C1 empty Option 2: G1 empty
1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9
A | _ 2 _ | 1 5 _ | _ _ _ | A | _ 2 _ | 1 5 _ | _ _ _ |
B | _ _ 5 | 2 _ _ | _ _ 9 | B | _ _ 5 | 2 _ _ | _ _ 9 |
C | _ _ _ | _ _ 4 | _ 2 5 | C | 3 _ _ | _ _ 4 | _ 2 5 |
|-------+-------+-------| |-------+-------+-------|
D | _ 8 7 | _ _ 2 | 5 _ _ | D | _ 8 7 | _ _ 2 | 5 _ _ |
E | _ 4 _ | _ 1 7 | _ _ _ | E | _ 4 _ | _ 1 7 | _ _ _ |
F | _ _ _ | _ _ 3 | 1 _ 7 | F | _ _ _ | _ _ 3 | 1 _ 7 |
|-------+-------+-------| |-------+-------+-------|
G | 2 _ 4 | 6 _ _ | _ _ _ | G | _ _ 4 | 6 _ _ | _ _ _ |
H | 6 _ _ | _ 9 _ | _ 3 _ | H | 6 _ _ | _ 9 _ | _ 3 _ |
I | _ 5 _ | _ _ _ | 9 6 8 | I | _ 5 _ | _ _ _ | 9 6 8 |
```

Both solutions are easy to find, and are different from each other.

*Last edited by phrontister (2017-04-21 14:29:21)*

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**ericnumberking****Member**- From: Vancouver
- Registered: 2018-02-06
- Posts: 3

MajikWaffle wrote:

Teacher gave that as a problem of the week, and from what I've done I figured it was unsolvable. Kind of messed up POW if it doesn't even work...

This is tough one bud. I know someone that are always playing Sudoku but they are at work right now. When this person comes back, I'll get them to give it a shot.

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