help with the Min Max Quad Sudoku

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help with the Min Max Quad Sudoku

Postby katherine_china » Sun Aug 24, 2008 12:33 am

Min Max Quad Sudoku
Fill the grid with the digits 1 to 9. Each row, column and 3x3-box will have exactly one of each digit. The red points in the near of crosses where four cells meet each other show that the cell with the red points is greater then the three other ones. The blue rings in the near of crosses where four cells meet each other show that the cell with the blue ring is smaller then the three other ones.
Image
i play this sudoku variant with my friends,but after a hole afternoon discussion,we only find out five dight 9.
first in C8 only R9C8 can be 9,than R4C1=R5C5=R8C2=R7C6=9
in N4,find a pair{R5C3,R6C1}=12
we also find some messages,like 8 locked in C5 in N8.but it seem no use
how to continue?
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Postby tarek » Sun Aug 24, 2008 3:05 am

I haven't played this variant before....

However it should have the following qualities derived from the constraints.

Red marked cells can't have 1
Blue marked Cells can't have 9
any marked cell can't be equal to any of the neighbouring cells.

tarek
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Postby HATMAN » Sun Aug 24, 2008 5:27 pm

Phyrron (you skeptic - as an engineer I'm an amatuer Popperite - so perhaps not too far apart)

I've got this much further than Katherine on my second attempt:
C5: 8 Locked in R789
N2: r3c5<>6
R4c5 <>5 blue dot
R2c5<>4 conflict C5 -> r26 <>6
R5c2<>6 clash 789 r6c3
but still having difficulties?
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Postby Smythe Dakota » Sun Aug 24, 2008 8:50 pm

tarek wrote:.... it should have the following qualities ....

Red marked cells can't have 1 ....

Or a 2 either. Or a 3, except in cases where the four cells are in at least two different boxes (because then you could have two 2's and a 1, or vice versa).

tarek wrote:.... Blue marked Cells can't have 9 ....

Or an 8 either, or a 7 except when the four cells are in at least two different boxes.

Bill Smythe
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Postby Jean-Christophe » Mon Aug 25, 2008 3:51 am

I too got stuck with this one, so I added support for user defined GT/LT in my soft JSudoku.
I'm afraid we found yet another Uwe's puzzle with multiple solutions:!:

JSudoku wrote:42 solutions found. This grid is invalid!
Code: Select all
+----------------------+----------------------+----------------------+
| 1456   567    467    | 39     123    12     | 89     456    78     |
| 3467   58     34     | 49     56     78     | 129    246    12     |
| 128    12     9      | 18     45     67     | 56     3      47     |
+----------------------+----------------------+----------------------+
| 9      67     8      | 67     23     5      | 4      12     123    |
| 57     4      12     | 127    9      38     | 23     56     68     |
| 12     3      56     | 68     12     4      | 578    78     9      |
+----------------------+----------------------+----------------------+
| 3456   125    67     | 1245   4678   9      | 123    78     345    |
| 368    9      12     | 45     678    13     | 67     124    456    |
| 34568  12578  34567  | 234    678    126    | 1678   9      2345   |
+----------------------+----------------------+----------------------+
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Postby Glyn » Mon Aug 25, 2008 6:08 am

Thanks JC I tried this and ground to a halt. This has saved me from trying again.

EDIT But I did and out of all its solutions the one I like most by bifurcating on Box 4 is reachable with singles from where JC left off
Code: Select all
.------.------.------.
| 1 6 4| 9 3 2| 8 5 7|
| 7 5 3| 4 6 8| 9 2 1|
| 8 2 9| 1 5 7| 6 3 4|
:------+------+------:
| 9 7 8| 6 2 5| 4 1 3|
| 5 4 1| 7 9 3| 2 6 8|
| 2 3 6| 8 1 4| 5 7 9|
:------+------+------:
| 6 1 7| 2 4 9| 3 8 5|
| 3 9 2| 5 8 1| 7 4 6|
| 4 8 5| 3 7 6| 1 9 2|
'------'------'------'
Glyn
 
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Postby udosuk » Mon Aug 25, 2008 1:00 pm

If a blue ring is added to the top-left corner of r9c9 the puzzle will have a unique solution.:idea:

Now try and see if you guys can solve it logically.:!:
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Postby HATMAN » Mon Aug 25, 2008 1:31 pm

A red dot in the bottom right of r1c4 gives Glyn's solution from JC's position. This feels like a classic typo to me - and I've made enough of them myself.

Now I just need to try and solve it from where I left off.
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Postby Glyn » Mon Aug 25, 2008 2:32 pm

Exploring JC's other 41 solutions the only other one I reached 'satisfactorily' was :-

Code: Select all
.------.------.------.
| 5 7 4| 3 1 2| 9 6 8|
| 6 8 3| 9 5 7| 2 4 1|
| 2 1 9| 8 4 6| 5 3 7|
:------+------+------:
| 9 6 8| 7 3 5| 4 1 2|
| 7 4 2| 1 9 8| 3 5 6|
| 1 3 5| 6 2 4| 7 8 9|
:------+------+------:
| 4 2 6| 5 8 9| 1 7 3|
| 8 9 1| 4 7 3| 6 2 5|
| 3 5 7| 2 6 1| 8 9 4|
'------'------'------'
Glyn
 
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Postby HATMAN » Wed Aug 27, 2008 4:08 pm

Matt

Given we posted at almost the same time - I'm pretty sure my spot is human solvable (without necessarily including your level) but I've not had the oportunity to do it yet. So which one (or another spot) is most likely to be Uwe's typo?

Maurice
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