Named Intersections

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

Named Intersections

Postby kdub » Mon Jul 20, 2020 12:47 am

Hi All,
Has anyone coined a name for the Intersection(s) between a Line and a Block.
In each block there are 3 horizontal ( top, mid, btm) and 3 vertical (left, center, right) intersections
I currently think of them as Block 2 mid or block 7 right, etc.
... but would be nice to know if they have been previously named.
Regards,
Stay Well
Kerry
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Re: Named Intersections

Postby Pupp » Tue Jul 21, 2020 10:57 pm

None of the blocks are named. Generally a coordinate system is used. (9)R3C3 or (9)r3c3 would be broken down to this.

(9)= number of squares across the puzzle. (There are puzzles with less and more squares)

R3 = Row 3
C3 = Column 3

If your talking about cells within a specific box or block, the cells are usually identified as sub cells. The only difference between a "cell" and a "sub cell", is that sub cells imply that your talking about cells that share the same block.

Some techniques can only be used if all the cells are in the same block, so describing the technique has to imply that all the cells are in the same block, so "sub cells" are used. Other techniques might only apply if 2 cells are in one block, and 2 other cells are in a different block.

The reason nobody has names for blocks is because Sudoku is very symmetrical. You can rotate, flip, mirror image, swap numbers around, etc, and still have essentially the same puzzle.
There are 6,670,903,752,021,072,936,960 possible sudoku puzzles, but after your take out any sort of symmetry, rotating, number exchanges, etc, there is only 5,472,730,538 unique puzzles for a standard 9x9 sudoku, not including any variations.
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Re: Named Intersections

Postby kdub » Tue Jul 21, 2020 11:12 pm

Hi Pupp,
To my understanding the blocks are numbered 1 to 9 ( 3 in each chute )
https://www.screencast.com/t/FeznKeU4B
Image
The Cells I'm interested in are the 6 groups of 3 Cells in each Block ... For example the shaded cells in the attached piccy

Regards,
Kerry
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Re: Named Intersections

Postby SpAce » Wed Jul 22, 2020 2:28 am

Hi kdub,

kdub wrote:Has anyone coined a name for the Intersection(s) between a Line and a Block.

The generic term for those is 'mini-line', or more specifically 'mini-row" or 'mini-column'.

In each block there are 3 horizontal ( top, mid, btm) and 3 vertical (left, center, right) intersections
I currently think of them as Block 2 mid or block 7 right, etc.
... but would be nice to know if they have been previously named.

I don't know if there's any "official" name for them (StrmCkr or tarek might), but since they're box-line intersections, the obvious way to identify them is a combination of the box (=block) id and the line id. For example, if it's the intersection of box 5 and row 4, the mini-row could be specified as b5r4. A more accurate way is to use fish notation b5\r4 or r4\b5 depending on what you're doing. The first form would be used for pointing, and the latter for claiming. Rows are numbered from top to bottom, columns from left to right, and boxes from left to right and top to bottom. The cell positions within a box are identified using the same numbering as for the boxes themselves:

Code: Select all
     c1 c2 c3   c4 c5 c6   c7 c8 c9
   .----------.----------.----------.
r1 | p1 p2 p3 | p1 p2 p3 | p1 p2 p3 |
r2 | p4 p5 p6 | p4 p5 p6 | p4 p5 p6 | b1  b2  b3
r3 | p7 p8 p9 | p7 p8 p9 | p7 p8 p9 |
   '----------'----------'----------'
r4 | p1 p2 p3 | p1 p2 p3 | p1 p2 p3 |
r5 | p4 p5 p6 | p4 p5 p6 | p4 p5 p6 | b4  b5  b6
r6 | p7 p8 p9 | p7 p8 p9 | p7 p8 p9 |
   '----------'----------'----------'
r7 | p1 p2 p3 | p1 p2 p3 | p1 p2 p3 |
r8 | p4 p5 p6 | p4 p5 p6 | p4 p5 p6 | b7  b8  b9
r9 | p7 p8 p9 | p7 p8 p9 | p7 p8 p9 |
   '----------'----------'----------'
        b1         b2         b3

        b4         b5         b6

        b7         b8         b9

Thus there are two (*) coordinate systems in a vanilla sudoku: the row-column coordinates (r4c7) and the box-position coordinates (b6p1). A mini-line can also be identified using either one of those, just by listing the three cells in it. For example, the intersection (b8\c6) between box 8 and column 6 could be addressed as r789c6 or b8p369. (*) Software solvers may also use the one-dimensional cell numbering 1-81, but that's not very useful for human players).
-SpAce-: Show
Code: Select all
   *             |    |               |    |    *
        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."
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Re: Named Intersections

Postby Pupp » Wed Jul 22, 2020 5:02 am

Almost forgot to mention: some players and websites refer to the larger boxes as a house or houses. So a single house means it has to have one of each possible number.
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Re: Named Intersections

Postby kdub » Wed Jul 22, 2020 7:13 am

SpAce wrote:... A more accurate way is to use fish notation b5\r4 or r4\b5 depending on what you're doing. The first form would be used for pointing, and the latter for claiming.



Thanks, I'll investigate that notation. This is primarily just to get my own thinking straight but I'd like to use a recognisable syntax.


SpAce wrote:...
The cell positions within a box are identified using the same numbering as for the boxes themselves:
< .. >
Thus there are two (*) coordinate systems in a vanilla sudoku: the row-column coordinates (r4c7) and the box-position coordinates (b6p1). A mini-line can also be identified using either one of those, just by listing the three cells in it. For example, the intersection (b8\c6) between box 8 and column 6 could be addressed as r789c6 or b8p369. (*) Software solvers may also use the one-dimensional cell numbering 1-81, but that's not very useful for human players).


Thanks, I wasn't aware of the duality. That will be useful.

Regards,
Stay well
kdub
 
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Joined: 20 July 2020

Re: Named Intersections

Postby kdub » Wed Jul 22, 2020 7:18 am

Pupp wrote:Almost forgot to mention: some players and websites refer to the larger boxes as a house or houses. So a single house means it has to have one each of each possible number.


My understanding is that Rows, Columns and Blocks are Houses and that calling a Block a box was frowned upon due to possible confusion with a Cell.

Regards,
Stay Well.
kdub
 
Posts: 4
Joined: 20 July 2020

Re: Named Intersections

Postby Pupp » Sat Aug 01, 2020 4:22 pm

kdub wrote:Hi Pupp,
To my understanding the blocks are numbered 1 to 9 ( 3 in each chute )
https://www.screencast.com/t/FeznKeU4B
Image
The Cells I'm interested in are the 6 groups of 3 Cells in each Block ... For example the shaded cells in the attached piccy

Regards,
Kerry


That might be true, but since Sudoku puzzles have such variety in shape, most people and websites just don't bother naming the blocks individually.

Not just box shaped, but there are double sudokus, triple sudokus, samari, windmill, shaolin, etc., a bunch of sudokus much smaller than the traditional 9x9 that are found in sudoku websites geared for children. Then there are puzzles that basically just keep adding more and more overlapping squares... just to challenge people.

https://www.sudocue.net/special.php
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