The New Sudoku Players' Forum

[7b53]

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 .

[dobrichev]

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.

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

[dobrichev]

BTW, if our search is limited to a single band, we know there are only 416 possible different formations of all 9 values.

[Pat]

Code: Select all

E  E  .| .  .  .|E  E  .|
E  E  .| .  .  .|E  .  .|
.  .  .| .  .  .|.  .  .|


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

really??

[7b53]

otherwise there will be 6 odd numbers in row 3.

[Pat]

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