The New Sudoku Players' Forum

[ghfick]

Are there any examples of classic 9x9 puzzles with 2 TH? With one TH in, say, blocks 1, 2, 4 and 5 and the second TH in blocks 5, 6, 8 and 9. Can block 5 provide the same 3 digits for the 2 TH or possibly a set of 3 different digits for each TH? If there are many such puzzles, would any of these puzzles benefit in a "meaningful" way from the exclusions from both TH?

[Leren]

From Phil's Folly site.

The following puzzle (Regis, by Shye) has 2 consecutive type 1 TH's:

.12.3456.6.52.13.443.65....7..1.........2.........3..8....16.451.45.26.3.5634.21.

That is True if you ignore basic fish. You'll find that the TH's are slightly degenerate and an X Wing will eliminate the need for both TH's.

Put that puzzle into Hodoku, which doesn't do TH's and it solves easily.

Leren

[ghfick]

Thanks Leren,
The puzzle (Regis, by Shye) has 2 TH with 2 blocks common to each TH. Are there examples of classic 9x9 puzzles with just one block common to each TH?
Gordon

[champagne]

Hi Gordon,
here an example from mith's file

Code: Select all

.5.....21...6.2....3......6.24....67..12.64.8..8.7421.....61.7....7.8..2...42..8.
456 987 321
189 632 754
237 145 896

924 813 567
571 296 438
368 574 219

842 361 975
693 758 142
715 429 683

The solution grid has 2 TH,
one of type 2 in boxes 5689
one of type 1 in boxes 5623
The puzzle is for the first one and is rated very very high.
Many changes must be done in the clues , except may be in box 5, to have a puzzle with the TH in the second one
and we don't know if another very high rating is possible

and here both have the same three digits in the TH

[champagne]

Thanks Leren,
Are there examples of classic 9x9 puzzles with just one block common to each TH?
Gordon

This likely exists, but a puzzle hitting both and keeping the TH threat active would have too many clues -->> easy to solve

[Leren]

Code: Select all

*-------------------------------------------------------------*
| 46789  5     679   | 389   3489    379 | 3789   2      1    |
| 14789  14789 79    | 6     134589  2   | 35789  3459   3459 |
| 124789 3     279   | 1589  14589   579 | 5789   459    6    |
|--------------------+-------------------+--------------------|
| 359    2     4     | 18    18     *359 |*359    6      7    |
| 3579   79    1     | 2    *359     6   | 4     *359    8    |
| 3569   69    8     |*359   7       4   | 2      1     *359  |
|--------------------+-------------------+--------------------|
| 2489   489   2359  |*359   6       1   |*359    7      3459 |
| 1469   1469  3569  | 7    *359     8   | 16     4-123  2    |
| 1679   1679  35679 | 4     2      *359 | 16     8     *359  |
*-------------------------------------------------------------*

Type 1 Trigadon - Digits 359 in Boxes 5689 => - 123 r8c8

The pm for the Trigadon in Boxes 5689. Appears to be Type 1. The puzzle solves easily after that and it's hard to see a Trigadon in Boxes 2356.

Leren

[coloin]

I tried to make one …. But the TH pattern is in 4 boxes ( say B1245 ) with the 2 or 3 clues from the pattern away
from this - ie in box 9 …. So it’s not possible to have one with the same 3 digits …

For 2 Th with different digits there would have to be 3 Th clues in box 1 , 3 Th clues in box 9 … and the remaining 3 clues all over the puzzle …. I don’t think it’s possible to have a puzzle with 666111111 clue frequency …

[champagne]

The puzzle solves easily after that and it's hard to see a Trigadon in Boxes 2356.
Leren

In fact, the second TH is already "solved" with r3c9=6.

[Leren]

Hi Champagne, I can see it now in the solution, the type of "solved" Trigadon in the puzzle clues like we had in the T&E(1) nightmare thread we had the other day.

Code: Select all

*-----------------------------------------------*
| 4    5   6  |*39   8    379  |*39+7  2    1   |
| 1    8   79 | 6   *39   2    | 3579 *359  4   |
| 2    3   79 | 1    4   *59+7 | 8     59  *6   |
|-------------+----------------+----------------|
| 359  2   4  | 8    1   *359  |*359   6    7   |
| 3579 79  1  | 2   *359  6    | 4    *359  8   |
| 3569 69  8  |*359  7    4    | 2     1   *359 |
|-------------+----------------+----------------|
| 8    4   2  | 359  6    1    | 359   7    359 |
| 69   169 35 | 7    35   8    | 16    4    2   |
| 67   167 35 | 4    2    359  | 16    8    359 |
*-----------------------------------------------*

This PM is towards the end of the solution. Even at this late stage there are two still extra guardian digits 7 in the pattern.

Leren

[champagne]

I tried to make one …. But the TH pattern is in 4 boxes ( say B1245 ) with the 2 or 3 clues from the pattern away
from this - ie in box 9 …. So it’s not possible to have one with the same 3 digits …

For 2 Th with different digits there would have to be 3 Th clues in box 1 , 3 Th clues in box 9 … and the remaining 3 clues all over the puzzle …. I don’t think it’s possible to have a puzzle with 666111111 clue frequency …

Here it seems "relatively" easy to have both TH active.
Start from
.5.....21...6.2....3........24....67..12.64.8..8.7421.....61.7....7.8..2...42..8.
the puzzle without the given r3c9
Then find other clues to get a valid puzzle (can have a guardian '6' in r9c9).
No idea here about the chances to still have a very high rating

And you surely can then add clues in boxes 2 and 3 to get a non minimal puzzle where both TH are easier to see.

I could likely do that using a modified code of the TH finder, but it takes time.

[champagne]

Hi Champagne, I can see it now in the solution, the type of "solved" Trigadon in the puzzle clues like we had in the T&E(1) nightmare thread we had the other day.

Code: Select all

*-----------------------------------------------*
| 4    5   6  |*39   8    379  |*39+7  2    1   |
| 1    8   79 | 6   *39   2    | 3579 *359  4   |
| 2    3   79 | 1    4   *59+7 | 8     59  *6   |
|-------------+----------------+----------------|
| 359  2   4  | 8    1   *359  |*359   6    7   |
| 3579 79  1  | 2   *359  6    | 4    *359  8   |
| 3569 69  8  |*359  7    4    | 2     1   *359 |
|-------------+----------------+----------------|
| 8    4   2  | 359  6    1    | 359   7    359 |
| 69   169 35 | 7    35   8    | 16    4    2   |
| 67   167 35 | 4    2    359  | 16    8    359 |
*-----------------------------------------------*

This PM is towards the end of the solution. Even at this late stage there are two still extra guardian digits 7 in the pattern.

Leren

I think that adding r1c6=7 as clue would not change much the hardness of the puzzle, but to have something really special, we have to do what is proposed in the previous post

[Leren]

Without r3c9 = 6 there are 197 solutions with unique ones with extra clues at r1c7 = 3, r2c5 = 3, r9c7 = 6. or r9c9 = 3. The first 3 => Trigadon already found. 4th Can't anything. Will leave it to the experts.

Leren

[champagne]

a single replacement does not lead to a good example
r9c7=6 -> original r3c9=6 : one TH solved
and hitting the THs, the skfr rating falls already at 9.1 or 8.3

[marek stefanik]

I remembered this puzzle found by jovi in her search for TH puzzles with 4 empty boxes:

Code: Select all

+-------+-------+-------+
| . 1 2 | . . . | . 3 4 |
| 3 5 . | . . . | 6 . 2 |
| 4 . . | . . . | 1 5 . |
+-------+-------+-------+
| . . . | . 1 7 | . . . |
| . . . | 5 . 2 | . . . |
| . . . | 8 6 . | . . . |
+-------+-------+-------+
| . 4 3 | . . . | . 2 5 |
| 1 . 5 | . . . | 3 . 6 |
| 2 6 . | . . . | 4 1 . |
+-------+-------+-------+
.12....3435....6.24.....15.....17......5.2......86.....43....251.5...3.626....41.

Code: Select all

,--------------------,--------------------,-------------------,
|#6–789 1     2      | 679    5789   5689 |T#789 3      4     |
| 3     5    #789    | 1479   4–789  1489 | 6   #789    2     |
| 4    #789   6789   | 23679  23789  3689 | 1    5     #789   |
:--------------------+--------------------+-------------------:
| 5689  2389  4689   | 349    1      7    | 25   4689   389   |
| 6789  3–789 146789 | 5      349    2    | 789  46789  13789 |
| 579   2379  1479   | 8      6      349  | 25   479    1379  |
:--------------------+--------------------+-------------------:
|T#789  4     3      | 16     789    16   |T#789 2      5     |
| 1    #789   5      | 2479   24789  489  | 3   #789    6     |
| 2     6    #789    | 379    35789  3589 | 4    1     #789   |
'--------------------'--------------------'-------------------'

TH 789# => –789r1c1, T is a remote triple (the other two triples don't seem useful)
789r17\Tc5b2 => –789r2c5
Or the digit in r7c5 appears in T in r1c7 and is then in b2 forced into r2c46 (note triple r3c239), where it makes a pair with 1, forcing 4r2c5.
789c17\Tr5b4 => –789r5c2
Or the digit in r5c7 appears in T in r7c1 and is then in b4 forced into r46c2 (note triple r239c3), where it makes a pair with 2, forcing 3r5c2.

Code: Select all

,---------------,------------------,----------------,
| 6    1    2   | 79    578   589  |T78–9 3     4   |
| 3    5    789 | 179   4     189  | 6    789   2   |
| 4    789  789 | 236   23    36   | 1    5     789 |
:---------------+------------------+----------------:
| 589  289  46  | 4–3   1    #7    | 25   4689 #89+3|
| 78   3    46  | 5    #9     2    |#78   46    1   |
| 579  279  1   |#8     6     3–4  | 25  #79+4  379 |
:---------------+------------------+----------------:
|T789  4    3   | 16   #78    16   |T#789 2     5   |
| 1    789  5   | 2479  278  #89+4 | 3   #789   6   |
| 2    6    789 |#79+3  3578  3589 | 4    1    #789 |
'---------------'------------------'----------------'

9r7\T => –9r1c7
Each guardian of TH 789# resolves 34b5p19 as 4r4c4, 3r6c6.
stte

Marek

[champagne]

I remembered this puzzle found by jovi in her search for TH puzzles with 4 empty boxes:

Code: Select all

+-------+-------+-------+
| . 1 2 | . . . | . 3 4 |
| 3 5 . | . . . | 6 . 2 |
| 4 . . | . . . | 1 5 . |
+-------+-------+-------+
| . . . | . 1 7 | . . . |
| . . . | 5 . 2 | . . . |
| . . . | 8 6 . | . . . |
+-------+-------+-------+
| . 4 3 | . . . | . 2 5 |
| 1 . 5 | . . . | 3 . 6 |
| 2 6 . | . . . | 4 1 . |
+-------+-------+-------+
.12....3435....6.24.....15.....17......5.2......86.....43....251.5...3.626....41.

Code: Select all

,--------------------,--------------------,-------------------,
|#6–789 1     2      | 679    5789   5689 |T#789 3      4     |
| 3     5    #789    | 1479   4–789  1489 | 6   #789    2     |
| 4    #789   6789   | 23679  23789  3689 | 1    5     #789   |
:--------------------+--------------------+-------------------:
| 5689  2389  4689   | 349    1      7    | 25   4689   389   |
| 6789  3–789 146789 | 5      349    2    | 789  46789  13789 |
| 579   2379  1479   | 8      6      349  | 25   479    1379  |
:--------------------+--------------------+-------------------:
|T#789  4     3      | 16     789    16   |T#789 2      5     |
| 1    #789   5      | 2479   24789  489  | 3   #789    6     |
| 2     6    #789    | 379    35789  3589 | 4    1     #789   |
'--------------------'--------------------'-------------------'

Hi Marek,

My code in test sees here four ways to have a tridagon square (box9 with extra cell not checked), all of them with the same digits, but for most of them, many cells are given in your puzzle.
Difficult here to build a puzzle of interest with two TH active.
I have another example with 6 seen potential tridagon, again box 9 not checked
..58......2.1.....3.....7.8...31..76.674.83.1......48.....81.47...6.4..34..73..6.