Math Is Fun Forum

MajikWaffle

Member

Registered: 2005-12-14

Posts: 11

This Sudoku's unsolvable, correct?

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)

Devantè

Real Member

Registered: 2006-07-14

Posts: 6,400

Re: This Sudoku's unsolvable, correct?

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.

Devantè

Real Member

Registered: 2006-07-14

Posts: 6,400

Re: This Sudoku's unsolvable, correct?

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

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: This Sudoku's unsolvable, correct?

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?

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Why did the vector cross the road?
It wanted to be normal.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: This Sudoku's unsolvable, correct?

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?

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"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..."

MajikWaffle

Member

Registered: 2005-12-14

Posts: 11

Re: This Sudoku's unsolvable, correct?

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

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: This Sudoku's unsolvable, correct?

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.

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

Leren

Member

Registered: 2017-04-19

Posts: 3

Re: This Sudoku's unsolvable, correct?

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  |
*--------------------------*

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,882

Re: This Sudoku's unsolvable, correct?

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)

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