even & odd numbers formation

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even & odd numbers formation

Postby 7b53 » Thu Oct 04, 2012 4:11 am

it is rare to see four even numbers in a box in the formation below
Code: Select all
E  E  .|
E  E  .|
.  .  .|


if there is one, can it have another in other boxes ?
for sure, there will not be another within the same (2 rows or 2 columns).

example;
Code: Select all
E  E  .| .  .  .|E  E  .|
E  E  .| .  .  .|E  .  .|
.  .  .| .  .  .|.  .  .|

here, we can definitely say (r2c89<>E)

can we derive anything from this ?
or it's simply a waste of time .
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Re: even & odd numbers formation

Postby dobrichev » Thu Oct 04, 2012 5:50 am

7b53 wrote:it is rare to see four even numbers in a box in the formation below
Code: Select all
E  E  .|
E  E  .|
.  .  .|


if there is one, can it have another in other boxes ?
for sure, there will not be another within the same (2 rows or 2 columns).

example;
Code: Select all
E  E  .| .  .  .|E  E  .|
E  E  .| .  .  .|E  .  .|
.  .  .| .  .  .|.  .  .|

here, we can definitely say (r2c89<>E)

Hi 7b53,
Another perspective to this problem is examining 'k-templates". See Minimal clues to complete a grid examining k-templates for terminology.
Even/Odd distinction after relabeling means only 4 values can appear, i.e. a 4-template.
The validity of your statement can be easily verified by checking all valid 119503485 4-templates for the supposed patterns. The number is taken from the table which initial post points to.
7b53 wrote:can we derive anything from this ?
or it's simply a waste of time .

The only suggestion is the name of the thread where the table with k-template counts are listed, but hope I am wrong.
Cheers,
MD
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Re: even & odd numbers formation

Postby dobrichev » Thu Oct 04, 2012 6:01 am

BTW, if our search is limited to a single band, we know there are only 416 possible different formations of all 9 values.
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Postby Pat » Thu Oct 04, 2012 8:09 am

7b53 wrote:
Code: Select all
E  E  .| .  .  .|E  E  .|
E  E  .| .  .  .|E  .  .|
.  .  .| .  .  .|.  .  .|

here, we can definitely say (r2c89<>E)

really??
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Re: even & odd numbers formation

Postby 7b53 » Sat Oct 06, 2012 2:18 pm

otherwise there will be 6 odd numbers in row 3.
Last edited by 7b53 on Sat Oct 13, 2012 6:54 pm, edited 1 time in total.
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Location: New York

Postby Pat » Wed Oct 10, 2012 1:20 pm


    oops
    seems i wan't quite as awake as i had hoped
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