The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |...|...|.4.|
 |5.2|...|8..|
 |..8|5.6|.7.|
 |---+---+---|
 |.8.|.27|.1.|
 |..4|.1.|3..|
 |.1.|68.|.2.|
 |---+---+---|
 |.9.|8.4|7..|
 |..6|...|9.1|
 |.5.|...|...|
 *-----------*


Play/Print this puzzle online

[SteveG48]

Code: Select all

 *------------------------------------------------------------*
 |f1379  367   1379  | 2     379   8     |  6-1   4     5     |
 | 5     3467  2     | 37    347   1     |  8     9     36    |
 |b1349  34    8     | 5     349   6     |ab12    7     23    |
 *-------------------+-------------------+--------------------|
 |e36    8     35    | 4     2     7     |  56    1     9     |
 |e67    2     4     | 9     1     5     |  3     68    78    |
 |e79    1     579   | 6     8     3     |  45    2     47    |
 *-------------------+-------------------+--------------------|
 |e123   9     13    | 8     356   4     |  7     356   26    |
 | 3478  347   6     | 37    357   2     |  9     358   1     |
 |d2378  5     37    | 1     367   9     | c246   368   48    |
 *------------------------------------------------------------*

(1)r3c7 = (2)r3c7 - r9c7 = r9c1 - (12=3679)r4567c1 - (379=1)r1c1 => -1 r1c7 ; stte
        = (1)r3c1 ---------------/



[SteveG48]

Or better:

Code: Select all

 *-----------------------------------------------------------*
 |b1379  367   1379  | 2     379   8     | 16    4     5     |
 | 5     3467  2     | 37    347   1     | 8     9     36    |
 |a1349 a34    8     | 5    a349   6     | 12    7    a23    |
 *-------------------+-------------------+-------------------|
 |b36    8     35    | 4     2     7     | 56    1     9     |
 |b67    2     4     | 9     1     5     | 3     68    78    |
 |b79    1     579   | 6     8     3     | 45    2     47    |
 *-------------------+-------------------+-------------------|
 |b123   9     13    | 8     356   4     | 7     356   6-2   |
 | 3478  347   6     | 37    357   2     | 9     358   1     |
 | 2378  5     37    | 1     367   9     | 246   368   48    |
 *-----------------------------------------------------------*


(2=1)r3c1259 - (1=2)r14567c1 => -2 r7c9 ; stte

[gurth]

[Leren]

Code: Select all

*--------------------------------------------------------------*
| 1379  367   1379   | 2     379   8      | 16    4     5      |
| 5     3467  2      | 37    347   1      | 8     9     36     |
| 1349 a34    8      | 5     349   6      | 12    7    a23     |
|--------------------+--------------------+--------------------|
| 36    8     35     | 4     2     7      | 56    1     9      |
| 67    2     4      | 9     1     5      | 3     68    78     |
| 79    1     579    | 6     8     3      | 45    2     47     |
|--------------------+--------------------+--------------------|
|b123   9    b13     | 8     356   4      | 7     356   6-2    |
| 3478 b347   6      | 37    357   2      | 9     358   1      |
| 2378  5    b37     | 1     367   9      | 246   368   48     |
*--------------------------------------------------------------*

ALS XZ Rule: X = 4, Z = 2: (2=4) r3c29 - (4=2) r7c13, r8c2, r9c3 => - 2 r7c9; stte

Leren

[JC Van Hay]

Code: Select all

+--------------------+------------+------------------+
| 1379    367   1379 | 2   379  8 | 16     4    5    |
| 5       3467  2    | 37  347  1 | 8      9    36   |
| 39(14)  34    8    | 5   349  6 | -2(1)  7    3(2) |
+--------------------+------------+------------------+
| 36      8     35   | 4   2    7 | 56     1    9    |
| 67      2     4    | 9   1    5 | 3      68   78   |
| 79      1     579  | 6   8    3 | 45     2    47   |
+--------------------+------------+------------------+
| 13(2)   9     13   | 8   356  4 | 7      356  6(2) |
| 37(48)  347   6    | 37  357  2 | 9      358  1    |
| 37(28)  5     37   | 1   367  9 | 246    368  48   |
+--------------------+------------+------------------+


[1r3c7=(1-4)r3c1=HT(482)r897c1-2r7c9=2r3c9]-2r3c7; stte

[SteveG48]

[1r3c7=(1-4)r3c1=HT(482)r897c1-2r7c9=2r3c9]-2r3c7; stte

JC, I see what happens here, but what does HT stand for?

[Leren]

SteveG48 wrote : JC, I see what happens here, but what does HT stand for?

Hi Steve, I think you'll find that HT stands for Hidden Triple.

Leren

[SteveG48]

Thanks, Leren. These things are always obvious after the fact.

[daj95376]

_

Yes, but if you think about it, a Hidden Pair/Triple should only affect candidates in the units containing it. In this case, that would be [c1] and [b7]. However, JC is using the forced "2" in r7c1 to affect -2r7c9.

Code: Select all

1r3c7 = (1-4)r3c1 = [(4-8)r8c1 = (8-2)r9c1 = 2r7c1] - 2r7c9 = 2r3c9  =>  -2 r3c7


Alternate:

Code: Select all

1r3c7 = (1-4)r3c1 = (4-8)r8c1 = (8-2)r9c1 = 2r9c7  =>  -2 r3c7


[Edit: removed reference to Locked Set].

_

[SteveG48]

_

Yes, but if you think about it, a Hidden Pair/Triple should only affect candidates in the units containing it.

Why? We use locked sets in which the position(s) of a critical candidate is known to make links into other units all the time. Both Leren and I have done so in today's solutions. Why shouldn't a hidden triple be used in the same way? My own approach here would be (1)r3c7 = r3c1 - (1=2)r14567c1 ....etc., but why is that OK and the HT not?

[daj95376]

_

Yes, but if you think about it, a Hidden Pair/Triple should only affect candidates in the units containing it.

Why? We use locked sets in which the position(s) of a critical candidate is known to make links into other units all the time. Both Leren and I have done so in today's solutions. Why shouldn't a hidden triple be used in the same way? My own approach here would be (1)r3c7 = r3c1 - (1=2)r14567c1 ....etc., but why is that OK and the HT not?

I will try to justify my position.

Sudopedia says that a Hidden Triple only performs eliminations in the cells containing it. If you're happy with a Hidden Triple in r789c1 performing an elimination in r7c9, then go for it.

Note, I removed the Locked Set (LS) designation above. I think that it's just a simple chain segment that JC shortened and called a HT.


Unfortunately, Sudopedia also says that a Locked Set is the same thing as a Subset. This becomes glaringly wrong when you examine the use of any Almost Locked Set -- which is what your (1=2)r14567c1 represents.

_

[JasonLion]

I would call that a hidden almost locked set. Technically it isn't a hidden triple because of 4r3c1. Other names including the word almost would also be reasonable, though hidden ALS seems to have historical precedent.

[David P Bird]

An Almost Naked Set in N cells containing N+1 candidates
An Almost Hidden Set is N cells containing N-1 locked candidates

Both originally qualified as being Almost Locked Sets but because ANS's are predominant in most solutions, later on an ALS was only considered to be an ANS which was plain stupid. (I've said this several times before.)

The internal inference in an ANS is strong - two of the digits can't both be false in the set.
The internal inference in an AHS is weak - only one of the unlocked digits can be true.

The cells r1c789 are an ANS holding (28) as locked candidates and (1347) as the unlocked or 'floating' candidates.
It happens that if (4) and (8) are both true in these cells then (2) is forced to occupy r7c1

In more complicated patterns I have seen this sort of inference notated as "&So"
... (4)r2c1 = (248)HS:r789c1 &So (2)r7c1 - (2)r7c9 ...

But that's hardly needed in this case and it's simpler to use the smaller AHS with just (8) locked
... (4)r2c1 = (48-2)AHS:r89c1 = (2)r7c1 - (2)r7c9 ...

Or even a plain chain!
... (4)r2c1 = (4-8)r8c1 = (8-2)r9c1 = (2)r7c1 - (2)r7c9 ...

It's becoming the trend to omit the abbreviations in the notation but if they are used, the Boolean node (248)r789 would be a HS and the combined Booleans (48-2)r89c1 would be an AHS, but that's a rather fine distinction.

I maintain the purpose of a notation is to convey the logic used to reach a deduction not to set a mini-puzzle.
With that thought I'll now dismount my soap box.

[blue]

Code: Select all

+--------------------+------------+------------------+
| 1379    367   1379 | 2   379  8 | 16     4    5    |
| 5       3467  2    | 37  347  1 | 8      9    36   |
| 39(14)  34    8    | 5   349  6 | -2(1)  7    3(2) |
+--------------------+------------+------------------+
| 36      8     35   | 4   2    7 | 56     1    9    |
| 67      2     4    | 9   1    5 | 3      68   78   |
| 79      1     579  | 6   8    3 | 45     2    47   |
+--------------------+------------+------------------+
| 13(2)   9     13   | 8   356  4 | 7      356  6(2) |
| 37(48)  347   6    | 37  357  2 | 9      358  1    |
| 37(28)  5     37   | 1   367  9 | 246    368  48   |
+--------------------+------------+------------------+

1r3c7 = (1-4)r3c1 = HT(482)r897c1 - 2r7c9 = 2r3c9       => -2r3c7 (JC, re-written)

I agree with Danny: a hidden triple in c1, doesn't eliminate candidates in c9.

IMO this should be written as:

1r3c7 = (1-4)r3c1 = HP(48)r89c1 - 2r9c1 = r7c1 - r7c9 = 2r3c9 => -2r3c7

Oddly enough, a hidden triple does come up in a right to left reading:

2r3c9 = r7c9 - r7c1 = HT(248)r389c1 - 1r3c1 = 1r3c7 => -2r3c7

In line with David's comment:

The internal inference in an AHS is weak - [...]

... those could be better written as:

1r3c7 = (1-4)r3c1 = HP(48-2)r89c1 = r7c1 - r7c9 = 2r3c9 => -2r3c7
2r3c9 = r7c9 - r7c1 = HT(248-1)r389c1 = 1r3c7 => -2r3c7

---

On the lighter side (but somewhat seriously) ...

Using the forms above, why even bother with the "HP" and "HT" text ? ... why not these instead ?

1r3c7 = (1-4)r3c1 = (48-2)r89c1 = r7c1 - r7c9 = 2r3c9 => -2r3c7
2r3c9 = r7c9 - r7c1 = (248-1)r389c1 = 1r3c7 => -2r3c7

From the dark side ...

Maybe because it would invite this kind of shortening:

1r3c7 = (1-4)r3c1 = (4-2)r89c1 = r7c1 - r7c9 = 2r3c9 => -2r3c7
2r3c9 = r7c9 - r7c1 = (2-1)r389c1 = 1r3c7 => -2r3c7

On the other hand, I can accept those as easily as I can the (commonly used) ANS notation:

1r3c7 = r3c1 - (1=2)r14567c1 - r7c9 = 2r3c9 => -2r3c7
2r3c9 = r7c9 - (2=1)r14567c1 - r3c1 = 1r3c7 => -2r3c7

Opinions ?

Cheers,
Blue.

Edit: typo corrected: r379 --> r389
Edit: (oops, missed one)