The New Sudoku Players' Forum

[Yogi]

7...8.2196..3.9...94...23.64.982....27.9..16.5........1..2638..8.4.9....3....8.5.

This is Leren's Puzzle 74 after some basics. Can it be advanced or solved with the Hidden Rectangle technique, say 57r24c79 or 35r48c89?

[Yogi]

Code: Select all

+----------------------+----------------------+----------------------+
| 7      35     35     | 456    8      456    | 2      1      9      |
| 6      1258   1258   | 3      1457   9      | 457    478    4578   |
| 9      4      158    | 157    157    2      | 3      78     6      |
+----------------------+----------------------+----------------------+
| 4      136    9      | 8      2      1567   | 57     37     357    |
| 2      7      38     | 9      345    45     | 1      6      3458   |
| 5      1368   1368   | 1467   1347   1467   | 479    234789 23478  |
+----------------------+----------------------+----------------------+
| 1      59     57     | 2      6      3      | 8      479    47     |
| 8      256    4      | 157    9      157    | 67     237    1237   |
| 3      269    267    | 147    147    8      | 4679   5      1247   |
+----------------------+----------------------+----------------------+


[Leren]

After all basics you get to here:

Code: Select all

*------------------------------------------------------*
| 7 35   35   |#46    8    #46     | 2    1     9      |
| 6 128  128  | 3     17    9      |*57+4 478  *5+48-7 |
| 9 4    18   | 157   157   2      | 3    78    6      |
|-------------+--------------------+-------------------|
| 4 16   9    | 8     2     16     |*57   37   *57+3   |
| 2 7    38   | 9     345   45     | 1    6     48     |
| 5 1368 1368 |#46+17 1347 #6+17-4 | 49   2489  248    |
|-------------+--------------------+-------------------|
| 1 59   57   | 2     6     3      | 8    479   47     |
| 8 26   4    | 157   9     157    | 67   23    123    |
| 3 269  267  | 147   147   8      | 679  5     12     |
*------------------------------------------------------*

Hidden UR (57) r24c79 => - 7 r2c9 and Hidden UR (46) r16c46 => - 4 r6c6

Leren

[RSW]

I'm curious as to the difference between a UR and a hidden UR. To me, these patterns are just UR's, or perhaps more correctly: AUR's (almost UR's). What is the definition of a hidden UR?

In my notation, I would have:
(4/6)r16c46 UR+2/1SL (type 4 variant 1): bilocal digit 6 (column 4) => -4r6c6
(5/7)r24c79 UR+3/4SL (SL Pattern: aaaa) => -7r2c9
where UR+m/nSL refers to the number of extra candidates as 'm', and the number of internal strong links as 'n'.

[Leren]

AFAIK the difference is just words - see here, here and here, for example. Leren

[RSW]

Thanks. That's what I thought, but I wanted to make sure I wasn't missing out on some new solving technique.

[Vorlauf]

Leren wrote:Hidden UR (57) r24c79 => - 7 r2c9 and Hidden UR (46) r16c46 => - 4 r6c6

I see and understand the logic behind the hidden UR (57) r24c79 =>-7.

The logic behind the UR (46) r16c46 =>-4 r6c6 evades me.
Would you please explain how we come to eliminate candidate 4 from r6c6.

Vorlauf

[yzfwsf]

Would you please explain how we come to eliminate candidate 4 from r6c6.
Vorlauf

2*bicell(r1c46)+1*sl(6 in column 4)，If r6c6=4 then r1c6=6 and r1c4=4,therefor r6c4=6.

[Vorlauf]

Would you please explain how we come to eliminate candidate 4 from r6c6.
Vorlauf

2*bicell(r1c46)+1*sl(6 in column 4)，If r6c6=4 then r1c6=6 and r1c4=4,therefor r6c4=6.

Thanks yzfws! Logic makes perfect sense.
Is there a UR classification for this? I have been using the Hodoku classification of URs from type 1 to type 7 and none seem to apply in this case.

Vorlauf

[yzfwsf]

Is there a UR classification for this?
Vorlauf

In my solver, the UR formed by these bi-value cells and single digit strong chains are all classified as Type 7.

[Leren]

There was some attempt to "classify" hidden UR's on this forum here and possibly elsewhere but I don't think this has proven popular, because of the number of different cases.

For a manual solver the common principle is to start from the elimination digit and "get around" the 4 UR cells to prove the a-b-a-b deadly pattern using 3 strong links, which are either one of two instances in a row, column or cell in the UR cells.

For this puzzle the path was all anti-clockwise using 1. Bi-value cell r1c6. 2. Bi-value cell r1c4. 3. 2 sixes in Column 4 r4c16.

This might have worked slightly differently had there been just 2 sixes in Row 4 in r6c46 and you could have gone; 1. Bi-value cell r1c6. 2. Bi-value cell r1c4. 3. 2 sixes in Row 4 r6c46; a mixture of clockwise and anticlockwise travel.

Hope this helps. Leren

[RSW]

Here are a couple more interesting puzzles with multiple UR's. In addition to eliminating some of the deadly candidates, both puzzles have UR's leading to less common direct eliminations of internal guardian candidates.

Steve Stumble 9/12/2020
steve-stumble-9-12-2020-t38258.html
098100400300400001050900700010002000605000802000300060000009020400003009009008370

Tarek's June 21, 2020 puzzle
june-21-2020-t38063.html
070400502000000600000800041095010000820006000000000708310004000008057009209030000

Another interesting one is Mith's "The Descent"
the-descent-t38214.html
It has an interesting UR+4, essentially two superimposed UR's:
000800000009076000001000540020000003030450020400032010056000100000780000000009008

[Leren]

The last puzzle ...8.......9.76.....1...54..2......3.3.45..2.4...32.1..56...1.....78.........9..8 was the most interesting, UR-wise.

Code: Select all

*--------------------------------------*
|*235  67 *23 | 8   4  15 | 679 679 12 |
| 25   4   9  | 15  7  6  | 38  38  12 |
| 67   8   1  | 2   9  3  | 5   4   67 |
|-------------+-----------+------------|
| 69   2   5  | 169 16 78 | 4   78  3  |
| 1    3   78 | 4   5  78 | 69  2   69 |
| 4    69  78 | 69  3  2  | 78  1   5  |
|-------------+-----------+------------|
| 8    5   6  | 3   2  4  | 1   79  79 |
| 239  19 *23 | 7   8  15 |*236 356 4  |
|*37-2 17  4  | 156 16 9  |*23  35  8  |
*--------------------------------------*

6 Cell DP in cells Marked * => - 2 r9c1

Code: Select all

*----------------------------------------*
|#235  67 #23 | 8     4  15 | 679 679 12 |
| 25   4   9  | 15    7  6  | 38  38  12 |
| 67   8   1  | 2     9  3  | 5   4   67 |
|-------------+-------------+------------|
| 69   2   5  |*169  *16 78 | 4   78  3  |
| 1    3   78 | 4     5  78 | 69  2   69 |
| 4    69  78 | 69    3  2  | 78  1   5  |
|-------------+-------------+------------|
| 8    5   6  | 3     2  4  | 1   79  79 |
|#39-2 19 #23 | 7     8  15 | 36  356 4  |
| 37   17  4  |*15-6 *16 9  | 2   35  8  |
*----------------------------------------*

Hidden UR (16) in cells marked * => - 6 r9c4 Hidden UR (23) in cells marked # => - 2 r8c1

Leren

[RSW]

This is what I get from the third puzzle. However, it's necessary to check for it at the beginning, or else it quickly disappears.

Code: Select all

 +--------------------+-----------------+-------------------+
 | 23567   467  23457 | 8     1249 1345 | 23679 3679  12679 |
 | 2358    48   9     | 1235  7    6    | 238   38    12    |
 | 23678   678  1     | 239   29   3    | 5     4     2679  |
 +--------------------+-----------------+-------------------+
 |#1569-78 2    578   | 169   169 #178  | 46789 56789 3     |
 |#16789   3    78    | 4     5   #178  | 6789  2     679   |
 | 4       6789 578   | 69    3    2    | 6789  1     5679  |
 +--------------------+-----------------+-------------------+
 | 23789   5    6     | 23    24   34   | 1     379   2479  |
 | 1239    149  234   | 7     8    1345 | 23469 3569  24569 |
 | 1237    147  2347  | 12356 1246 9    | 23467 3567  8     |
 +--------------------+-----------------+-------------------+


Superimposed Unique Rectangles (1/7|1/8)r45c16:
(1/7)r45c16 UR+4/3SL (Pattern aab-) => -7r5c1
(1/8)r45c16 UR+4/3SL (Patterb aab-) => -8r5c1

I don't think it really helps to get to the solution, but I thought it was just about as hidden as you're likely to find.

Then after basics:

Code: Select all

 +-----------+-----------+------------+
 | 235 67 23 | 8   4  15 | 679 679 12 |
 | 25  4  9  | 15  7  6  | 38  38  12 |
 | 67  8  1  | 2   9  3  | 5   4   67 |
 +-----------+-----------+------------+
 | 69  2  5  | 169 16 78 | 4   78  3  |
 | 1   3  78 | 4   5  78 | 69  2   69 |
 | 4   69 78 | 69  3  2  | 78  1   5  |
 +-----------+-----------+------------+
 | 8   5  6  | 3   2  4  | 1   79  79 |
 | 239 19 23 | 7   8  15 | 236 356 4  |
 | 237 17 4  | 156 16 9  | 23  35  8  |
 +-----------+-----------+------------+


Unique Rectangle (2/3)r18c13 UR+2/1SL (type 4 variant 1): bilocal digit 3 (row 1) => -2r8c1
Unique Rectangle (1/6)r49c45 UR+2/1SL (type 4 variant 1): bilocal digit 1 (row 4) => -6r9c4
Unique Rectangle (1/6)r49c45 UR+2/1SL (type 4 variant 1): bilocal digit 6 (row 9) => -1r4c4

Then a short AIC to solution.

-------------

As for the first (Steve Stumble) puzzle

Code: Select all

 +----------------+-----------+-----------+
 | 2   9     8    |  1   3 7  | 4   5  6  |
 | 3  a67   a67   |  4   8 5  | 2   9  1  |
 | 1   5     4    |  9   2 6  | 7   38 38 |
 +----------------+-----------+-----------+
 | 79  1     37   |  8   6 2  | 59  4  35 |
 | 6   34    5    |  7   9 14 | 8   13 2  |
 | 89  48    2    |  3   5 14 | 19  6  7  |
 +----------------+-----------+-----------+
 | 78 a3678 a1367 | b56  4 9  |b156 2  58 |
 | 4  c268   16   |bc256 7 3  |b156 18 9  |
 | 5  c26    9    | c26  1 8  | 3   7  4  |
 +----------------+-----------+-----------+


a Unique Rectangle (6/7)r27c23 UR+2/1SL (type 4 variant 1): bilocal digit 7 (column 2) => -6r7c3
b Unique Rectangle (5/6)r78c47 UR+3/3SL (Pattern aab-) => -1r8c7 -5r7c7 -6r7c3 -6r8c4
c Unique Rectangle (2/6)r89c24 UR+2/2SL (2x type 4): bilocal digit 2 (row 8), bilocal digit 2 (column 2) => -6r8c24, -6r8c4

Maybe I'm just easily amused, but I thought that UR 'b' was interesting in that non-deadly digit 1 is eliminated as well as 5 and 6.

[Yogi]

Wow. I might have got further if I had done some more of the basics on my device, but I had the blinkers on for URs. The SudokuSwami simply calls the Hidden Rectangle a UR Type 7. Easily spotted as having one Bivalue Cell connected to three others with random extra candidates, as long as the whole figure conforms to the rule of being 4 cells in 2 Rows, 2 Columns and 2 Boxes (or Blocks.) Rarely, it may involve two identical bivalue cells on a diagonal, which can lead directly to placements. I’ll have a go at the puzzles you suggested. Thanx!