The New Sudoku Players' Forum

[daj95376]

BTW: Am I the only one whose/who's bothered by the illogic of using stte in one instance and using lclste in another???

I have never quite understood how or why the only objective in these threads has become the aim to achieve a single-stepper along with the apparent exclusion of any attempts at increasing one's skillset by solving more difficult puzzles.

Still, if the challenge is a single-stepper, then one is kidding one's self if they think an lclste solution is equivalent to a stte solution (assuming that the acronym's are being used correctly).

I'm sorry. I now see how my point could be interpreted differently. I was harping on the point that STTE was used in one context for Singles To The End ... and that STE was used for Singles To End in the context of LCLSTE.

As for myself, everything is Basics before the single-step grid ... and everything is Basics after the single-step grid.

_

[daj95376]

Congratulations bat999, your chain uses a pattern that's caused considerable discussion in the past -- especially on notation.

An Empty Rectangle Pattern occurs in a box for a single value. It is the basis for the Empty Rectangle solving technique. The commonality in the names has caused considerable misunderstanding. Here are three examples of the Empty Rectangle Pattern.

Code: Select all

 +-----------------------------------+
 |  9  9  9  |  .  .  .  |  .  .  .  |
 |  /  /  /  |  .  .  .  |  .  .  .  |
 |  /  9  /  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  3  /  3  |  .  .  .  |
 |  .  .  .  |  /  3  /  |  .  .  .  |
 |  .  .  .  |  /  3  /  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  .  |  4  4  4  |
 |  .  .  .  |  .  .  .  |  /  4  /  |
 |  .  .  .  |  .  .  .  |  /  4  /  |
 +-----------------------------------+


In [b5], I hope you don't have a problem with the notation 3r4c46 = 3r56c5. There is no overlap of the value in cell r4c5, and the value is partitioned into two disjoint sets of cells in the box.

In [b9], there is the complication that <4> exists in r7c8. In the past, the purists wrote 4r7c789 = 4r789c8 to indicate that r7c8 was present when you read from l-to-r and when you read from r-to-l. This distinction was only necessary to support bidirectional logic and when eliminations were considered for loops. Note: r7c8 is called the Empty Rectangle Intersection cell (ERI). The candidate <4> would be eliminated in r7c8 if this pattern was present in an AIC loop.

People like David P Bird convinced me that the Empty Rectangle Pattern was sufficiently represented in an AIC by two disjoint sets of cells for a value. This meant that <4> in [b9] could be represented by 4r7c789 = 4r89c8. The two disjoint sets concept works in l-to-r and r-to-l logic. If the value is not in one set of cells, then the value must be in the other set of cells. Note: the four empty cells (/) give the Empty Rectangle Pattern its name. Other empty cells (/) for the value may also be present in the box. See [b1] and [b5].

Now, [b1] represents the cells for <9> in your grid. Using the two disjoint sets of cells approach, it's okay to say 9r13c2 = 9r1c13 and it be meaningful read l-to-r or r-to-l.

_

[bat999]

... I hope you don't have a problem with the notation...

Code: Select all

9r1c1 = (59-7)r46c1 = r5c2 - r5c8 = r4c7 - (7=5)r7c7 - (5=9)r7c2 - r13c2 = 9r1c13 => -9 r1c8; stte

"If the value is not in one set of cells, then the value must be in the other set of cells"
I don't know how to apply this to the AIC above.

From l-to-r the chain says "If r1c1 is not 9 then r1c3 is 9".
If it's a bidirectional AIC I would expect it to say from r-to-l "If r1c3 is not 9 then r1c1 is 9".
Saying "If the value is not in one set of cells, then the value must be in the other set of cells (in box 1) then r1c1 is 9" doesn't sound good to me.
Maybe you can word it differently?
If not, let's put it to bed.

[daj95376]

... I hope you don't have a problem with the notation...

Code: Select all

9r1c1 = (59-7)r46c1 = r5c2 - r5c8 = r4c7 - (7=5)r7c7 - (5=9)r7c2 - r13c2 = 9r1c13 => -9 r1c8; stte

"If the value is not in one set of cells, then the value must be in the other set of cells"
I don't know how to apply this to the AIC above.

From l-to-r the chain says "If r1c1 is not 9 then r1c3 is 9".
If it's a bidirectional AIC I would expect it to say from r-to-l "If r1c3 is not 9 then r1c1 is 9".
Saying "If the value is not in one set of cells, then the value must be in the other set of cells (in box 1) then r1c1 is 9" doesn't sound good to me.
Maybe you can word it differently?
If not, let's put it to bed.

To me, you seem fixated on network logic and unable to accept chain/AIC logic.

In a network: 1) branching is allowed, 2) previous states of the logic can be remembered, and 3) secondary eliminations can be remembered.

In a chain/AIC: 1) branching is not allowed, 2) previous states of the logic may not be remembered, and 3) secondary eliminations may not be remembered. All that exists is eliminations for candidates that force both ends of the chain to be false concurrently.

For your chain, r1c8=9 forces -9r1c1 ... and it forces -9r1c13. These cells and candidates represent both ends of the chain above.

_

[bat999]

... I can't see how this works when the chain is read from right to left...

Don't expect it to read from right to left because it's not a chain, it's a network.

[daj95376]

Don't expect it to read from right to left because it's not a chain, it's a network.

It's a network as long as you insist on carrying the initial assumption forward and use it to destroy the integrity of the final SL. By doing so, you violate condition (2) for a chain/AIC.

Code: Select all

9r13c2 = 9r1c13   is     a valid SL in [b1]

9r13c2 = 9r1c3    is not a valid SL in [b1]


However, the Empty Rectangle Pattern confuses things because it wants to be read:

Code: Select all

l-to-r   ==>>   9r13c2 = 9r1c13

                9r3c2  = 9r1c123   <<==   r-to-l


As I (may have) mentioned earlier, purists use to write 9r13c2 = 9r1c123 to show that (ERI) 9r1c2 is false no matter which direction the SL is read. This accounted for it being eliminated when the SL is present in a loop.


[Edit: cleaned up wording in final paragraph. Nothing significant.]

[bat999]

...However...

Are you saying that "...9r13c2 = 9r1c13" makes it a valid chain that can't be read from r-to-l?

[daj95376]

...However...

Are you saying that "...9r13c2 = 9r1c13" makes it a valid chain that can't be read from r-to-l?

I'm saying that "... 9r13c2 = 9r1c13" is an acceptable SL that makes it a valid chain. It's just difficult to visualize when read r-to-l because of the nuances of the Empty Rectangle Pattern when the ERI cell -- 9r1c2 -- is occupied.

_

[bat999]

I've re-visited my solution.
Not happy that the other chain was difficult for me to read from r-to-l.

Mark II solution...

Code: Select all

.---------------------.-------------------.----------------.
| f179   267-9    269 | 8     1567   3    |  156   59   4  |
|  17    8        5   | 1467  1467   9    |  16    2    3  |
|  3     6-9      4   | 2     156    156  |  1568  589  7  |
:---------------------+-------------------+----------------:
| e579   4       d89  | 3     12789  18   | c78    6    25 |
|  2     67       3   | 467   45678  4568 |  9     78   1  |
| e579   1        689 | 679   26789  68   |  3     4    25 |
:---------------------+-------------------+----------------:
|  4    a59       19  | 169   1369   2    | b57    357  8  |
|  6     3        7   | 5     48     48   |  2     1    9  |
|  8     259      129 | 19    139    7    |  4     35   6  |
'---------------------'-------------------'----------------'

From l-to-r "If r7c2<>9 then r1c1=9".
From r-to-l "If r1c1<>9 then r7c2=9".

(9=5)r7c2 - (5=7)r7c7 - (7=8)r4c7 - (8=9)r4c3 - (9)r46c1 = (9)r1c1 => r13c2<>9
=> -9r13c2; stte
(Because r1c2 and r3c2 can see both ends of the chain)

EDIT
Corrected with help from daj95376