The New Sudoku Players' Forum

[shye]

Code: Select all

+-------+-------+-------+
| . 7 6 | . . . | . . . |
| 3 5 8 | . . . | . . . |
| 4 2 . | . . 6 | . . 5 |
+-------+-------+-------+
| . . . | . 9 3 | . 1 . |
| . . . | 1 5 . | . 2 . |
| . . 4 | 7 . . | . . . |
+-------+-------+-------+
| . . . | . . . | . 8 9 |
| . . . | 9 8 . | 2 . 7 |
| 8 9 5 | . . . | 1 3 . |
+-------+-------+-------+
.76......358......42...6..5....93.1....15..2...47............89...98.2.7895...13.

estimated rating: 8.4

[totuan]

Code: Select all

 *-----------------------------------------------------------------------------*
 | 19      7       6       | 23458   1234    124589  | 38      49      12      |
 | 3       5       8       | 24      1247    12479   | 469    %4679    12      |
 | 4       2       19      | 38      17      6       | 38      79      5       |
 |-------------------------+-------------------------+-------------------------|
 | 2567   *68      27      | 2468    9       3       | 4567    1      *68+4    |
 | 679    *368     39      | 1       5       48      | 4679    2      *368+4   |
 | 12569  *368+1   4       | 7       26      8-2     | 569    #569    *368     |
 |-------------------------+-------------------------+-------------------------|
 | 27      146     27      | 3456    1346    145     | 456     8       9       |
 | 16      1346    13      | 9       8       145     | 2      %456     7       |
 | 8       9       5       | 246     2467    247     | 1       3       46      |
 *-----------------------------------------------------------------------------*

My path for this one – not sure it’s the same like shye’s:
- MUG(368)r456c29 => (1)r6c2=(4)r45c9
- If r6c8<>6 => [(1)r6c2==(4)r45c9-(4=6)r9c9-r8c8=(6-7)r2c8=r3c8-(7=1)r3c5-r3c3=r1c1] => r6c1<>1
(2=6)r6c5-(6)r6c8=[(1)r6c2==(4)r45c9-(4=6)r9c9-r8c8=(6-7)r2c8=r3c8-(7=1)r3c5-r3c3=r1c1]-(1)r6c1=(1-38)r6c29=(8)r6c6 => r6c6<>2, lclste

A simpler with 2 steps:
- UR(38)r56c29 => (8)r4c29=(3)r8c2
- MUG(368)r456c29 => (1)r6c2=(4)r45c9
01: (8)r4c29==(34-1)r78c2=(1-38)r6c29=(8)r6c6 => r4c4<>8
02: (8)r6c6=(38-1)r6c29==(4)r45c9-(4=6)r9c9-(6=24)r29c4-(4)r4c4=r5c6 => r5c6<>8, lclste

Thanks for the puzzle!
totuan

[P.O.]

basics:

Hidden Text: Show

Code: Select all

intersections:
((((7 0) (9 5 8) (2 4 6 7)) ((7 0) (9 6 8) (2 4 7)))
 (((7 0) (2 8 3) (4 6 7 9)) ((7 0) (3 8 3) (7 9)))
 (((3 0) (7 4 8) (2 3 4 5 6)) ((3 0) (7 5 8) (1 2 3 4 6)))
 (((2 0) (9 4 8) (2 4 6)) ((2 0) (9 5 8) (2 4 6 7)) ((2 0) (9 6 8) (2 4 7))))

QUAD COL: ((4 9 6) (4 6 8)) ((5 9 6) (3 4 6 8)) ((6 9 6) (3 6 8)) ((9 9 9) (4 6))
(((1 9 3) (1 2 3 4 8)) ((2 9 3) (1 2 4 6)))

intersections:
((((8 0) (4 9 6) (4 6 8)) ((8 0) (5 9 6) (3 4 6 8)) ((8 0) (6 9 6) (3 6 8)))
 (((3 0) (5 9 6) (3 4 6 8)) ((3 0) (6 9 6) (3 6 8))))

QUAD BOX: ((1 8 3) (4 9)) ((2 7 3) (4 6 9)) ((2 8 3) (4 6 7 9)) ((3 8 3) (7 9))
(((1 7 3) (3 4 8 9)) ((3 7 3) (3 8 9)))

PAIR ROW: ((3 4 2) (3 8)) ((3 7 3) (3 8)) 
(((3 5 2) (1 3 7)))

QUAD BOX: ((7 2 7) (1 4 6)) ((8 1 7) (1 6)) ((8 2 7) (1 3 4 6)) ((8 3 7) (1 3))
(((7 1 7) (1 2 6 7)) ((7 3 7) (1 2 7)))

PAIR COL: ((4 3 4) (2 7)) ((7 3 7) (2 7)) 
(((5 3 4) (3 7 9)))


Code: Select all

19      7       6       23458   1234    124589  38      49      12               
3       5       8       24      1247    12479   469     4679    12               
4       2       19      38      17      6       38      79      5               
2567    68      27      2468    9       3       4567    1       468             
679     368     39      1       5       48      4679    2       3468             
12569   1368    4       7       26      28      569     569     368             
27      146     27      3456    1346    145     456     8       9               
16      1346    13      9       8       145     2       456     7               
8       9       5       246     2467    247     1       3       46     

1r6c1 => r8c8 <> 4,5,6
 r6c1=1 - r1c1{n1 n9} - r1c8{n9 n4}
 r6c1=1 - r1c1{n1 n9} - r3n9{c3 c8} - r6n9{c8 c7} - r6n5{c7 c8}
 r6c1=1 - r8c1{n1 n6}
 
=> r6c1 <> 1
bte:


Hidden Text: Show

Code: Select all

( n1r6c2   n3r6c9   n8r6c6   n4r5c6 )

intersection:
((((1 0) (8 1 7) (1 6)) ((1 0) (8 3 7) (1 3)))

ste.


[marek stefanik]

Code: Select all

+-------+-------+-------+
| . 7 6 | . . . | . . 12|
| 3 5 8 | . . . | . . 12|
| 4 2 . | . . 6 | . . 5 |
+-------+-------+-------+
| . . . | . 9 3 | . 1 . |
| . . . | 1 5 . | . 2 . |
| . . 4 | 7 . . | . . . |
+-------+-------+-------+
| . . . | . . . | . 8 9 |
| . . . | 9 8 . | 2 . 7 |
| 8 9 5 | . . . | 1 3 . |
+-------+-------+-------+

If 21r12c9 in that order, then we get a symmetry along the main diagonal (123456789 → 987654321), hence by gsp the solution is also symmetrical, which is impossible (mainly because the diagonal could only contain 5s). So 12r12c9 in order.

Marek

[eleven]

Ooh, i am ashamed, that i did not see this almost (digital) diagonal symmetry.
Very nice!

[shye]

thanks for solving! the near-symmetry was my own solution too, while i was working on the puzzles in my Anti-GSP post last year i wanted to include an example of this, using the symmetry for a weak link (2r1c9 - 1r2c9 in this puzzle) but found it hard to make a working example. it wasnt until now that i had the idea for this simpler setup