The New Sudoku Players' Forum

[shye]

Code: Select all

+-------+-------+-------+
| 1 . . | 2 . . | 3 . . |
| . 4 . | . 5 . | . 6 . |
| . . 7 | . . 8 | . . 9 |
+-------+-------+-------+
| 3 . . | . . . | . 1 2 |
| . 6 . | . . . | 4 . 5 |
| . . 9 | . . 7 | 6 8 3 |
+-------+-------+-------+
| 2 . . | . 6 5 | . . 4 |
| . 5 . | 3 . 9 | . 2 1 |
| . . 8 | 1 4 2 | 5 3 6 |
+-------+-------+-------+
1..2..3...4..5..6...7..8..93......12.6....4.5..9..76832...65..4.5.3.9.21..8142536

a silly one
estimated rating 4.2

[blue]

Code: Select all

+---------------+-------------------+-----------------+
|  1   c89  b56 |  2     c79    b46 |  3     b45  c78 |
| c89   4   a23 | c79     5     a13 | a12     6   c78 |
| b56  a23   7  | b46    a13     8  | a12    b45   9  |
+---------------+-------------------+-----------------+
|  3   c78  b45 | b56+4  c89    b46 | c79     1    2  |
| c78   6   a12 | c89    a23+1  a13 |  4     c79   5  |
| b45  a12   9  | b45    a12     7  |  6      8    3  |
+---------------+-------------------+-----------------+
|  2   a13  a13 | c78     6      5  | c89+7  c79   4  |
| b46   5   b46 |  3     c78     9  | c78     2    1  |
| c79  c79   8  |  1      4      2  |  5      3    6  |
+---------------+-------------------+-----------------+

Cute puzzle

3 BUG-Lite+1's in 3 digit sets, covering all of the unsolved cells.
R5c5=1, r4c4=4, r7r7=7, stte.

[Cenoman]

At first, same solution as blue's. After basics, the puzzle is made of three independent sub-puzzles, for digits (7,8,9) (4,5,6) (1,2,3) resp.
Each of the sub-puzzles is a BUG+1 pattern => +7 r7c7, +4 r4c4, +1 r5c5; ste

Just to display a solution different of blue's:

Code: Select all

 +-----------------+-------------------+------------------+
 |  1    89  ^56   |  2     79    4-6  |  3     45   78   |
 |  89   4   *23   |  79    5     1-3  |  12    6    78   |
 |  56   23   7    |  46    13    8    |  12    45   9    |
 +-----------------+-------------------+------------------+
 |  3    78  ^45   |  456   89   ^46   |  79    1    2    |
 |  78   6   *12   | #89    123  *13   |  4     7-9  5    |
 |  45   12   9    |  45    12    7    |  6     8    3    |
 +-----------------+-------------------+------------------+
 |  2    13   13   | #78    6     5    |  789  #79   4    |
 |  46   5    46   |  3     78    9    |  78    2    1    |
 |  79   79   8    |  1     4     2    |  5     3    6    |
 +-----------------+-------------------+------------------+

each sub-puzzle can be solved by a Y-Wing:
(3=2)r2c3 - (2=1)r5c3 - (1=3)r5c6 => -3 r2c6
(6=5)r1c3 - (5=4)r4c3 - (4=6)r4c6 => -6 r1c6
(9=8)r5c4 - (8=7)r7c4 - (7=9)r7c8 => -9 r5c7; ste

Funny puzzle Thank you shye, for finding and posting it.

[eleven]

It's a little brother of Easter Monster, one of the rare puzzles with backdoor size 3.

[marek stefanik]

Combining all 3 DPs:
candidate symmetry along the r1c1–r9c9 diagonal (1)(23)(4)(56)(7)(89) => remaining digits on the diagonal are from 147, stte

[eleven]

Yes, that's nice. If you reflect the puzzle at the diagonal and renumber it, you get a different one with the same candidates to resolve.

Code: Select all

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

The reflected/renumbered solution (in the open cells) to one must be a solution to the other. However i can't conclude from that, that in general the open cells solve symmetric, if the candidates are symmetric.
Maybe it can be proved otherwise.

[shye]

another way is to swap the given DPs (12r48c89 & 46r79c59) which changes nothing about the logic of the puzzle. then the givens will be symmetric and diagonal symmetry applies. at the end of the solve, just swap the givens back into place

thanks for solving everyone!

[eleven]

I should have remembered that.
about-red-ed-s-sudoku-symmetry-group-t6526-195.html#p200098