The New Sudoku Players' Forum

[Lummox JR]

Hmmm, don't follow yet.

Say I got as far as shown below.

In box 7, 9 is locked in column 3. One of those three must be a nine.

r7c3=9 leads to an impossible case
r8c3=9 leads to an impossible case
r9c3=9 leads to a solution

Therefore r9c3=9

This is clearly T&E.

Please explain to me, starting from where I am below, what technique is different from this, not related to T&E and thus deserving of another jargon term "uniqueness" and somehow superior to T&E.

When you put it that way, all techniques are T&E. As indeed they are on some level; they all boil down to that. But what all non-T&E tests have in common is that they exhibit some sort of pattern.

The uniqueness test is not T&E because it has a pattern, it has refinements to raw logic.

In the case of your puzzle, however, the uniqueness test does not apply at the place where you left off. There is an X-wing, but the real killer clue is an XYZ-wing that will unlock a clue for remote pairs to find. After that, though, the uniqueness test will reveal something.

[QBasicMac]

In the case of your puzzle, however, the uniqueness test does not apply.

Not "my" puzzle. This thread was started by stuartn who gave the puzzle I show.

However, assuming "uniqueness test" is some bona fide technique, if it doesn't apply to the puzzle I showed, then of course, I withdraw my question.

I thought someone was saying it did apply, and I simply couldn't see what anyone was talking about.

Sorry,

Mac

[Nick67]

I'm confused now

Hi CathyW,

I hope it might make you feel better that your application of the Uniqueness Rule
in this recent post was just right!

Just for everyone else, let me re-post that puzzle:

Code: Select all

-         -         126       -         679       79        569       2569      1269     
-         16        -         -         -         -         36        -         136     
25        256       -         -         69        -         -         -         269     
-         26        -         -         -         -         -         269       269     
-         123       12        -         -         -         35        235       -       
36        -         -         -         -         -         -         36        -       
36        -         -         -         -         -         -         -         36       
-         -         68        -         -         -         689       69        -       
25        235       28        -         79        79        38        -         -       


The unique rectangle is defined by cells r1c5,c6 and r9c5,6.
Note that the top corners are both in box 2,
and the bottom corners are both in box 8. Recognizing this
pattern immediately lets us see that 6 is the final value for r1c5.
(If it wasn't 6, then the puzzle would have multiple solutions.)
Which of course is exactly what CathyW wrote in her post!

Think I'll have to study the thread on defining the uniqueness descriptions a bit more.

A lot of good material there ... I found MadOverlord's Ultimate Guide version 0.2 to be very helpful.

[Nick67]

After looking at this same puzzle again:

Code: Select all


 *-----------*
 |146|5.8|.3.|
 |572|936|184|
 |398|14.|..5|
 |---+---+---|
 |621|3.9|45.|
 |935|.64|2..|
 |784|251|396|
 |---+---+---|
 |21.|..5|...|
 |45.|61.|8..|
 |86.|..3|5..|
 *-----------*

 
 *-----------------------------------------------------------*
 | 1     4     6     | 5     27    8     | 79    3     279   |
 | 5     7     2     | 9     3     6     | 1     8     4     |
 | 3     9     8     | 1     4     27    | 67    267   5     |
 |-------------------+-------------------+-------------------|
 | 6     2     1     | 3     78    9     | 4     5     78    |
 | 9     3     5     | 78    6     4     | 2     17    178   |
 | 7     8     4     | 2     5     1     | 3     9     6     |
 |-------------------+-------------------+-------------------|
 | 2     1     379   | 478   789   5     | 679   467   379   |
 | 4     5     39    | 6     1     27    | 8     27    39    |
 | 8     6     79    | 47    279   3     | 5     1247  1279  |
 *-----------------------------------------------------------*



.... I see that there is a valid "unique rectangle" in this puzzle after all.
Cells r7c3,9 and cells r8c3,9 form the rectangle. Here we see that 3 must
be the final value of either r7c3 or r7c9 (there are no other 3's in the row).
Now if 9 was the other final value for that pair of cells, then there
would be multiple solutions to the puzzle. (Given 1 solution, we could
swap the 3's and 9's in the 4 rectangle cells to come up with
another solution.) So, we can eliminate 9 as a candidate from r7c3 and r7c9.

So the 2 cells become a naked pair with candidates 3 and 7,
and we can eliminate the other 7's in that row, leaving
the puzzle in this state:

Code: Select all


 *-----------*
 |146|5.8|.3.|
 |572|936|184|
 |398|14.|..5|
 |---+---+---|
 |621|3.9|45.|
 |935|.64|2..|
 |784|251|396|
 |---+---+---|
 |21.|..5|...|
 |45.|61.|8..|
 |86.|..3|5..|
 *-----------*

 
 *-----------------------------------------------------------*
 | 1     4     6     | 5     27    8     | 79    3     279   |
 | 5     7     2     | 9     3     6     | 1     8     4     |
 | 3     9     8     | 1     4     27    | 67    267   5     |
 |-------------------+-------------------+-------------------|
 | 6     2     1     | 3     78    9     | 4     5     78    |
 | 9     3     5     | 78    6     4     | 2     17    178   |
 | 7     8     4     | 2     5     1     | 3     9     6     |
 |-------------------+-------------------+-------------------|
 | 2     1     37    | 48    89    5     | 69    46    37    |
 | 4     5     39    | 6     1     27    | 8     27    39    |
 | 8     6     79    | 47    279   3     | 5     1247  1279  |
 *-----------------------------------------------------------*



There is still a fair amount of work to do.
Simple Suduko reports these steps:

- locked candidates (the 7's in column 7 are locked in box 3) - lets us remove other 7's from box 3
- X-wing (2's in rows 3 and 8) - lets us remove 2 from r9c8
- Exclusion based on Colors ( candidate 7) - lets us remove 7 from r9c9
- Exclusion based on Multiple Colors (candidate 7) - lets us
remove 7 from both r9c3 and r7c9
- and at last a bunch of naked singles.

So, the uniqueness approach didn't immediately solve the puzzle ...
but was helpful.

[Myth Jellies]

I have to disagree with the quote that all techniques are T&E.

In actuality, all logical techniques can be replaced be an equivalent T&E technique. Thus all techniques could be potentially described in T&E terms. If you understand the logical, non-T&E technique, though, no trial and error is required to perform it at all.

Some of the uniqueness techniques I understand completely, and have no problem applying without any trial and error at all.

Other uniqueness scenarios I do not understand or remember so well and would sort of have to perform confirming trials in my head if I wanted to use them. I don't use those particular versions for that reason, but that is my shortcoming, and not the fault of the method.