Help! I want to see a REALLY HARD SuDoKu puzzle

Everything about Sudoku that doesn't fit in one of the other sections

Postby Wolfgang » Wed Jun 22, 2005 7:31 pm

scrose wrote:But is it an enjoyable technique? ...But I suppose you can say that you never claimed the puzzle would be enjoyable...:)
Well, yes, i just tried to produce hard puzzles. Now i have to decide, if it is enoyable for me to tell my program to produce (hard) "human" puzzles:D
Wolfgang
 
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Postby Wolfgang » Thu Jun 23, 2005 5:06 pm

As a beginning,
scrose, can you enjoy this one?

I added the numbers
4 in (1,6), 3 in (3,9), 4 in (6,2) and 8 in (6,3)
to make it manually solvable without t&e
(it would be unique without them also)

0 0 1 0 5 4 0 0 0
4 0 0 0 0 0 0 1 0
0 0 0 9 2 0 7 0 3
1 2 3 0 0 0 0 0 0
9 0 0 2 0 0 0 0 8
0 4 8 0 0 0 3 0 0
0 3 9 0 6 0 0 0 4
8 0 4 3 0 7 0 0 5
0 0 0 4 0 0 0 0 0
Wolfgang
 
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Postby scrose » Thu Jun 23, 2005 5:40 pm

I think your new puzzle still requires some trial-and-error. I was able to fill 9 cells before "getting stuck".

Update: Using the colouring technique, I managed to eliminate a candidate 1 from r9c5, but it hasn't let me get any further.
scrose
 
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Postby Hammerite » Thu Jun 23, 2005 9:19 pm

Code: Select all
+---+---------------------------+---+
| 7 | .   3   .   6   .   .   . | . |
|   |   +---+-------------------+   |
| . | 9 | . | .   .   4   .   .   2 |
|   |   |   |   +---+---+-----------+
| 8 | . | . | . | . | . | .   .   . |
|   +---+   |   |   |   +-------+   |
| . | .   . | 6 | . | .   .   2 | . |
|   |   +---+---+   +-------+   |   |
| 9 | . | .   2   .   8   . | . | 3 |
|   |   +-------+   +---+---+   |   |
| . | 2   .   . | . | 5 | .   . | . |
|   +-------+   |   |   |   +---+   |
| .   .   . | . | . | . | . | . | 4 |
+-----------+---+---+   |   |   |   |
| 1   .   .   4   .   . | . | 3 | . |
|   +-------------------+---+   |   |
| . | .   .   .   7   .   4   . | 6 |
+---+---------------------------+---+


This one comes from another user, tso. I got it from his topic on the Suggestions board. I found it pretty difficult... although it doesn't use very advanced reasoning, it's hard to get your head around when you're used to the regular box layout. (Each row, column, and enclosed area has to contain all of the digits 1 to 9.)
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Postby Wolfgang » Fri Jun 24, 2005 7:21 am

scrose wrote:I think your new puzzle still requires some trial-and-error. I was able to fill 9 cells before "getting stuck"...

I tried it myself and i am rather sure that you can solve it without trial-and-error, though you might need some tricky combinations. Please tell me where you got stuck.
Wolfgang
 
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Postby angusj » Fri Jun 24, 2005 8:50 am

Wolfgang wrote:Please tell me where you got stuck.


Code: Select all
3.1|.54|...
4.2|.3.|51.
.8.|921|743
-----------
123|...|...
9..|2.3|..8
.48|...|3..
-----------
.39|.6.|..4
8.4|3.7|..5
...|4..|.3.


[3]     [79]    [1]     [67]    [5]     [4]     [2689]  [2689]  [269]   
[4]     [79]    [2]     [678]   [3]     [68]    [5]     [1]     [69]   
[56]    [8]     [56]    [9]     [2]     [1]     [7]     [4]     [3]     
[1]     [2]     [3]     [568]   [4789]  [5689]  [469]   [5679]  [679]   
[9]     [56]    [567]   [2]     [14]    [3]     [14]    [567]   [8]     
[567]   [4]     [8]     [156]   [179]   [569]   [3]     [25679] [12679]
[257]   [3]     [9]     [158]   [6]     [258]   [18]    [78]    [4]     
[8]     [16]    [4]     [3]     [19]    [7]     [1269]  [269]   [5]     
[2567]  [156]   [567]   [4]     [89]    [2589]  [1689]  [3]     [1679] 
angusj
 
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Postby Wolfgang » Fri Jun 24, 2005 9:19 am

1 in box 8:
    If you have a 1 in (8,5) or (9,5),
    the 1s in (6,4), (5,7) and (9,9) directly follow.

    But then you would have 3 1s in the rows 8 and 9,
    which is not possible.

    So the 1 of box 8 must be in (7,4).
You can continue then with the 1 in box 7.
Wolfgang
 
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Postby angusj » Fri Jun 24, 2005 9:36 am

Wolfgang wrote:1 in box 8:

I agree with your logic.
However, I would argue that this is (to me) still a case of trial and error - try 1 in r8c5 and low and behold it doesn't work.
angusj
 
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Joined: 12 June 2005

Postby Wolfgang » Fri Jun 24, 2005 10:33 am

angusj wrote:However, I would argue that this is (to me) still a case of trial and error ...

Well, this step and the next one below is clearly in the grey zone between
logically derived and using trial&error. But it is far away of the problems
you run into, if the 4 redundant numbers are not given. Then you really have
no chance than guessing.
And the title of the thread is "really hard". I would maintain that a puzzle
that is solvable with the standard techniques cannot be really hard but it
is "mechanically solvable".
So here is the next step for those who dont like such complex derivations:

If 1 is in (8,7), (8,2) becomes 6 and (8,8) is 2. But then only
(6,9) is left for both 1 and 2. So (8,2) has to be 1.
Wolfgang
 
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Re: Help! I want to see a REALLY HARD SuDoKu puzzle

Postby puzzleman » Sat Jun 25, 2005 9:30 pm

bking43 wrote:I have tried Sudoku puzzles that rated themselves as easy, medium and hard. I didn't find the "hard" at all hard; they just took a little longer. Can anyone steer me to some really hard puzzles? The ones I have looked at so far have easily fallen to the 3 or 4 step process I developeded in solving the two "easy" ones.

I would love to find something solvable but hard.

TIA,

B. King


Here is a hard puzzle containing some xwings, swordfish and nishios. Enjoy:)

4-----2--
9-3---1--
----14---
2----1---
-4--75---
-------3-
-5-6----4
-9------7
-1-4-86-5
puzzleman
 
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Re: Help! I want to see a REALLY HARD SuDoKu puzzle

Postby angusj » Sat Jun 25, 2005 10:47 pm

puzzleman wrote:
Code: Select all
4-----2--
9-3---1--
----14---
2----1---
-4--75---
-------3-
-5-6----4
-9------7
-1-4-86-5

I like that one because it can be solved using colors (filtering on 9s) without having to resort to Nishio.
angusj
 
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Re: Help! I want to see a REALLY HARD SuDoKu puzzle

Postby Wolfgang » Mon Jun 27, 2005 9:31 am

puzzleman wrote:Here is a hard puzzle containing some xwings, swordfish and nishios. Enjoy:)

hi, i cannot find any difficulty in this puzzle. If you see that (3,4) has to be 9 because of the 5/8-pair in (3,1) and (3,3) (the only other possibilty left would be 8 for this cell), everything is straightforward without using xwings etc.
Wolfgang
 
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Joined: 22 June 2005

Postby simes » Mon Jun 27, 2005 10:07 am

I don't see a 5/8 pair in (3,1) (3,3). According to my pencil marks, (3,3) has candidates 5, 6 and 8. Or were you able to eliminate the 6 somehow?
Last edited by simes on Sun Dec 11, 2011 9:45 am, edited 1 time in total.
simes
 
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Postby Wolfgang » Mon Jun 27, 2005 10:45 am

simes wrote:I don't see a 5/8 pair in (3,1) (3,3). According to my pencil marks, (3,3) has candidates 5, 6 and 8. Or were you able to eliminate the 6 somehow?

Ah yes, excuse me, i oversaw that my program eliminated the 6 in (3,3) before which was not trivial at all.
Wolfgang
 
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Postby scrose » Mon Jun 27, 2005 1:03 pm

angusj wrote:I like that one because it can be solved using colors (filtering on 9s) without having to resort to Nishio.
Wolfgang wrote: ...everything is straightforward without using xwings etc.

I agree with Wolfgang's opinion that the x-wing technique does not necessarily need to be applied. By applying angusj's recommendation of colours on the 9's, you can bypass the use of the x-wing technique; by eliminating one candidate 9, you will be able to place a 9 in r3c4 in two moves.
scrose
 
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