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Kiwy
Joined: 09 Oct 2006 Posts: 5 Location: Asia

Posted: Wed Oct 11, 2006 1:02 am Post subject: clue=3 for 4*4 Sudoku puzzle 


I find one of 4*4 Sudoku puzzle, which is the clue = 3.
It may be find by some one already,
Code: 
01 00
00 02
00 00
03 00

Is any one know, do there exist clue=2 for 4*4 Sudoku puzzle?
[This puzzle is not vaild, more than one solution.
thanks Ravel's post. ]
KIWY
Last edited by Kiwy on Wed Oct 11, 2006 3:10 pm; edited 2 times in total 

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ravel
Joined: 21 Apr 2006 Posts: 536

Posted: Wed Oct 11, 2006 9:43 am Post subject: 


Hm, i see 3 solutions:
Code: 
21 34
34 12
12 43
43 21

21 43
34 12
12 34
43 21

21 43
34 12
42 31
13 24
 I thought the minimum is 4 (but cant find a proof). 

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Kiwy
Joined: 09 Oct 2006 Posts: 5 Location: Asia

Posted: Wed Oct 11, 2006 12:14 pm Post subject: 


Ravel, Thank you.
Code: 
21 00
34 12
02 00
03 20

The key point is T&R only can find a solution, but not proof the puzzle is a valid. Is that right?
Kiwy 

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Ruud
Joined: 18 Jan 2006 Posts: 31

Posted: Wed Oct 11, 2006 2:21 pm Post subject: 


ravel wrote:  I thought the minimum is 4 (but cant find a proof). 
There are 2 essentially different solution grids, which can be permutated into 288 different grids. Read more here
These are the 2 solution grids:
1234 1234
3412 3421
2143 2143
4321 4312
I've colored the 4 unavoidable sets in each grid. As you know, each unavoidable set must contain a given digit. 4 givens is therefore the minimum required for a 4x4.
Ruud 

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