The New Sudoku Players' Forum

[Pat]

noticed the same givens in boxes 1,5,7
(not what you'd call symmetry)

too tough for me

..6...5.4.9.....3.4.8.....6...9.43......8..7....6....29..2....5.6..9..1.8.4..52..

[ play ]

25 cells given
(layout 251 of the Patterns Game)

Code: Select all


 . . 6 | . . . | 5 . 4
 . 9 . | . . . | . 3 .
 4 . 8 | . . . | . . 6
-------+-------+------
 . . . | 9 . 4 | 3 . .
 . . . | . 8 . | . 7 .
 . . . | 6 . . | . . 2
-------+-------+------
 9 . . | 2 . . | . . 5
 . 6 . | . 9 . | . 1 .
 8 . 4 | . . 5 | 2 . .



[ArkieTech]

Code: Select all

 *-----------------------------------------------------------------------------*
 | 1237    1237    6       | 1378    1237    123789  | 5       289     4       |
 |*1257    9      *1257    | 45-178  2456-17 26-178  |b178     3      b178     |
 | 4       12357   8       | 1357    12357   12379   | 179     29      6       |
 |-------------------------+-------------------------+-------------------------|
 | 12567   12578   1257    | 9       1257    4       | 3       568     18      |
 | 12356   12345   12359   | 135     8       123     | 1469    7       19      |
 | 1357    134578  13579   | 6       1357    137     | 1489    4589    2       |
 |-------------------------+-------------------------+-------------------------|
 | 9       137     137     | 2       13467   13678   | 4678    468     5       |
 |a25      6      a25      | 3478    9       378     | 478     1       378     |
 | 8       137     4       | 137     1367    5       | 2       69      379     |
 *-----------------------------------------------------------------------------*
25ur:r28c13=>178r2c1379 => -178r2c456; lclste

[pjb]

Terrific solution, Dan. I can only solve using boring multiple chains / ALSs.

Phil

[Sudtyro2]

Dan & Phil,
Pretty subtle logic for me, but here goes a try (to understand Dan's solution)...
The AUR internals approach requires (17)r2c1 = (17)r2c3, so that when either premise is true, the combination with (178)r2c79 forms a naked(?) triple and hence => -178r2c456. But, there's a bonus: The internals strong link above must actually be conjugate, meaning that only one 1-digit or one 7-digit is allowed in r2c13. Otherwise, r2c1379 would house only three digits in four cells...a contradiction. I think I'll go for happy hour (and an aspirin) now before tackling the externals approach.

SteveC

[David P Bird]

SteveC, try looking at it this way:
to disrupt the (25)UR either (2) or (5) must be false in r2c13 and therefore true in r2c456
As r2c456 must hold (4) & (6) this means there will be no room for 178 in these cells

(25)UR:r28c13[False] = (25#1 + 46)r2c456[True] => r2c456 <> 178

DPB

[daj95376]

My solver found a UR Type 3 matching Dan's eliminations. However, it needed a second step -- BUG+1 -- to finish solving the puzzle.

Code: Select all

 +-----------------------+
 | . . 6 | . . . | 5 . 4 |
 | . 9 . | . . . | . 3 . |
 | 4 . 8 | . . . | . . 6 |
 |-------+-------+-------|
 | . . . | 9 . 4 | 3 . . |
 | . . . | . 8 . | . 7 . |
 | . . . | 6 . . | . . 2 |
 |-------+-------+-------|
 | 9 . . | 2 . . | . . 5 |
 | . 6 . | . 9 . | . 1 . |
 | 8 . 4 | . . 5 | 2 . . |
 +-----------------------+

 r8  b7  Hidden Pair                     =25   r8c13

 r28c13  <25> UR Type 3.2244             -178 r2c46 & -17 r2c5

 r1  b2  Locked Candidate 1              -8    r1c8

   c8b3  Locked Pair                     -29   r3c7,r69c8

 r2  b1  Locked Pair                     -12   r1c12,r2c56

 r1  b1  Naked  Pair                     -37   r1c56

         BUG+1                           =7    r6c3


_

[blue]

My solver found a UR Type 3 matching Dan's eliminations. However, it needed a second step -- BUG+1 -- to finish solving the puzzle.

There's an ALS loop with Dan's eliminations and more, that has the same problem.

Code: Select all

+-------------------------+-------------------------+--------------------+
| 137-2   (1237)   6      | 1378    1237     123789 | 5      289   4     |
| (1257)  9        (1257) | 45-178  2456-17  26-178 | (178)  3     (178) |
| 4       (12357)  8      | 1357    12357    12379  | 179    29    6     |
+-------------------------+-------------------------+--------------------+
| 12567   258-17   1257   | 9       1257     4      | 3      568   18    |
| 12356   245-13   12359  | 135     8        123    | 1469   7     19    |
| 1357    458-137  13579  | 6       1357     137    | 1489   4589  2     |
+-------------------------+-------------------------+--------------------+
| 9       (137)    137    | 2       13467    13678  | 4678   468   5     |
| 25      6        25     | 3478    9        378    | 478    1     378   |
| 8       (137)    4      | 137     1367     5      | 2      69    379   |
+-------------------------+-------------------------+--------------------+

(2=5,178)r2c1379 - (5=2,137)r1379c2 - loop => -2r1c1,-178r2c456,-137r456c2


XSudo calls it "ALS-XZ Rule, Double Link ".

[Pat]

My solver found a UR Type 3 matching Dan's eliminations.
However, it needed a second step -- BUG+1 -- to finish solving the puzzle.

or the 2nd step can be a "turbot"

[Leren]

blue wrote : (2=5,178)r2c1379 - (5=2,137)r1379c2 - loop => -2r1c1,-178r2c456,-137r456c2

I see the same ALS XZ Rule loop with one more elimination - 8 r1c8 (total of 17 eliminations).

That's a common problem with loops if a one move wonder is your preferred solution method - they make for plenty of eliminations but more often than not they don't solve a cell.

Just to prove me wrong yesterday's Dan Daily puzzle solved with a loop - the exception rather than the rule.

Leren

[blue]

I see the same ALS XZ Rule loop with one more elimination - 8 r1c8 (total of 17 eliminations).

Yes, I forgot about that one. XSudo shows it when I switch it to the mode where it adds the "Link sets".

That's a common problem with loops if a one move wonder is your preferred solution method - they make for plenty of eliminations but more often than not they don't solve a cell.

Just to prove me wrong yesterday's Dan Daily puzzle solved with a loop - the exception rather than the rule.

Right. See an old post of mine, here, and eleven's follow up comment -- "Dan's Diablerie January 15, 2014".