## even & odd numbers formation

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

### even & odd numbers formation

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 .
7b53
2012 Supporter

Posts: 156
Joined: 01 January 2012
Location: New York

### Re: even & odd numbers formation

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
dobrichev
2016 Supporter

Posts: 1612
Joined: 24 May 2010

### Re: even & odd numbers formation

BTW, if our search is limited to a single band, we know there are only 416 possible different formations of all 9 values.
dobrichev
2016 Supporter

Posts: 1612
Joined: 24 May 2010

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

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

really??

Pat

Posts: 3627
Joined: 18 July 2005

### Re: even & odd numbers formation

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.
7b53
2012 Supporter

Posts: 156
Joined: 01 January 2012
Location: New York

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

Pat

Posts: 3627
Joined: 18 July 2005