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clue=3 for 4*4 Sudoku puzzle

 
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Kiwy



Joined: 09 Oct 2006
Posts: 5
Location: Asia

PostPosted: Wed Oct 11, 2006 1:02 am    Post subject: clue=3 for 4*4 Sudoku puzzle Reply with quote

I find one of 4*4 Sudoku puzzle, which is the clue = 3.
It may be find by some one already, Smile

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

PostPosted: Wed Oct 11, 2006 9:43 am    Post subject: Reply with quote

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

PostPosted: Wed Oct 11, 2006 12:14 pm    Post subject: Reply with quote

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 Wink
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Ruud



Joined: 18 Jan 2006
Posts: 31

PostPosted: Wed Oct 11, 2006 2:21 pm    Post subject: Reply with quote

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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