The New Sudoku Players' Forum

[RSW]

Not particularly difficult, but this puzzle contains a fairly rare pattern that I've been searching for, for a while. I wanted to see if my solver program would find it.

Code: Select all

. 1 .|. 3 .|. . .
. . .|. . .|. . .
. . 9|7 . .|. 6 .
-----+-----+-----
8 9 .|5 7 .|. 2 .
5 . 6|. 1 .|. 9 .
7 . .|. 2 .|. . 1
-----+-----+-----
. 5 8|. . .|. 1 9
. . .|. . .|. 7 8
. . .|6 . .|. 5 .


010030000000000000009700060890570020506010090700020001058000019000000078000600050

[Leren]

Code: Select all

*-------------------------------------------*
| 6   1   257  |a28   3  2589   | 89  4 257 |
|d24  78  257  |e1248 6  124589 | 189 3 257 |
| 234 38  9    | 7    58 12458  | 18  6 25  |
|--------------+----------------+-----------|
| 8   9   1    | 5    7  34     | 34  2 6   |
| 5   2   6    |f34-8 1  348    | 7   9 34  |
| 7   34  34   | 9    2  6      | 5   8 1   |
|--------------+----------------+-----------|
|c23  5   8    |b23   4  7      | 6   1 9   |
| 19  6   234  | 123  59 1235   | 234 7 8   |
| 19  347 2347 | 6    89 18     | 234 5 34  |
*-------------------------------------------*

(8=2) r1c4 - r7c4 = r7c1 - (2=4) r2c1 - r2c4 = (4) r5c4 => - 8 r5c4; stte

Leren

[RSW]

That was quick.

I should have mentioned that it can be solved without chains, though maybe not as a single stepper.

[SpAce]

So what was the rare pattern? UR Type 5?

I should have mentioned that it can be solved without chains, though maybe not as a single stepper.

What is the path without chains? (W-Wing and Y-Wing are chains, just short ones.)

[RSW]

True enough. I did actually have one Y-Wing in my solution.

[SteveG48]

Code: Select all

 *------------------------------------------------------------------------------*
 | 6       1       257     |  8-2     3       2589    | 89      4       257     |
 | 24      78      257     |  148-2   6       124589  | 189     3       257     |
 |d234    c38      9       |  7      c58      12458   | 18      6       25      |
 *-------------------------+--------------------------+-------------------------|
 | 8       9       1       |  5       7       34      | 34      2       6       |
 | 5       2       6       |  348     1       348     | 7       9       34      |
 | 7       34      34      |  9       2       6       | 5       8       1       |
 *-------------------------+--------------------------+-------------------------|
 |e23      5       8       |ae23      4       7       | 6       1       9       |
 |b19      6       234     | a123    b59      135-2   | 234     7       8       |
 | 19      347     2347    |  6       89      18      | 234     5       34      |
 *------------------------------------------------------------------------------*


(2=31)r78c4 - (1=95)r8c15 - (5=83)r3c25 - 3r3c1 = (3,2)r7c14 => -2 r12c4,r8c6 ; stte

[Cenoman]

There are a few patterns, not so rare though, all yielding the same set of eliminations, totally useless for solving the puzzle:

Code: Select all

 +---------------------+-----------------------+-------------------+
 |  6     1     257    |  28*    3    259-8*   |  89    4    257   |
 |  24    78    257    |  14-28  6    12459-8* |  189   3    257   |
 |  234   38    9      |  7      58*  1245-8*  |  18    6    25    |
 +---------------------+-----------------------+-------------------+
 |  8     9     1      |  5      7    34*      |  34    2    6     |
 |  5     2     6      |  48-3   1    348*     |  7     9    34    |
 |  7     34    34     |  9      2    6        |  5     8    1     |
 +---------------------+-----------------------+-------------------+
 |  23    5     8      |  23     4    7        |  6     1    9     |
 |  19    6     234    |  123    59   25-13    |  234   7    8     |
 |  19    347   2347   |  6      89   18*      |  234   5    34    |
 +---------------------+-----------------------+-------------------+

Look at the 8 cells b2p13689, r469c6; they contain 7 digits (1234589) => one digit must there twice; only 8 can be twice (in b2p18 and r59c6), all other digits are there.
=> - 28r2c4, -3r5c4, -13r8c6, -8r123c6
(cannibalistic 8123c6 eliminations: this group is in sight of both 8b2p18, 8r59c6, one of which is true)

Same eliminations with:
- Doubly linked ALS's: (124589)b2p13689, (1348)r459c6, RC 1,4
- Sue de Coq (extended): (124589)r123c6, (258)b2p18, (1348)r459c6, RC (258) resp. (14), or RC (25) resp. (148)
- loop (1=8)r9c6 - r5c6 = (8-4)r5c4 = (4-1)r2c4 = (1)r8c4
(RC = Restricted Commons)

Anyhow, puzzle solved in one step by one AIC:
(8=2)r1c4 - (2=3)r7c4 -r7c1 = r3c1 - (3=8)r3c2 =>-8r3c5; ste

[RSW]

My solution was a two stepper.
The "rare" pattern I'd been looking for shows up after basics and a Y-Wing.

Code: Select all

 +-------------+----------------+------------+
 | 6   1  *257 | 28   3  2589   | 89  4 *57  |
 | 4-2 78 *257 | 1248 6  124589 | 189 3 *257 |
 | 234 38  9   | 7    58 1458   | 18  6  25  |
 +-------------+----------------+------------+
 | 8   9   1   | 5    7  34     | 34  2  6   |
 | 5   2   6   | 348  1  348    | 7   9  34  |
 | 7   34  34  | 9    2  6      | 5   8  1   |
 +-------------+----------------+------------+
 | 23  5   8   | 23   4  7      | 6   1  9   |
 | 19  6   234 | 123  59 1235   | 234 7  8   |
 | 19  347 247 | 6    89 18     | 234 5  34  |
 +-------------+----------------+------------+


Unique Rectangle UR+3 (type 2 variant) (5/7)r12c39 => -2r2c1 stte

Looking at it, you wouldn't expect this variety of UR to be uncommon, but it was surprisingly difficult finding a puzzle that had it. The puzzle is based on a PM grid posted by Mike Barker:
post34342.html#p34342

[Leren]

Code: Select all

.24.6..18............93.........63...624....1..7.5.......89.7....6.4..85..1.....3
.....47.5..2.37.......2..68.5....4.381...9.......461......1.5.49.........8......6
.9....25....2......6.....8...4.2...37264....15....7..8....84.7.158.7.......15....
.1...8.6..9.6...2.4..9..1...43..7......5.9..........35........4....815....1.95..8
....8.....5...6..4......7.62....9..1.932..6..1483......8.4...27.....71........3..

Some other puzzles with the required pattern taken from a Hodoku exemplar list. Curiously, in each case the UR is preceded by an XY Wing to make the pattern appear. Leren

[RSW]

Thanks. I'll add those to my collection. I guess the difficulty in finding some of these is because uniqueness patterns can be rather fleeting and thus easy to miss, unless a UR check is done after every elimination.

Edit:
I overlooked spAce's mention of the UR Type 5. As I noted, that wasn't quite the pattern I had in mind, though the pattern of this puzzle could decay into a type 5 with a further elimination. Anyway, these are all variants of Type 2.

I hadn't considered the Type 5 to be as rare as the pattern posted here, because I'd found at least one example of a Type 5 early in my UR testing. Maybe I was just lucky.

[Leren]

Hodoku describes these UR examples as Type 5, which you can see here although Mike Barker did describe the pattern as you detailed. Oh well, a rose by any other name ..... Leren