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[tarek]

Code: Select all

+-------+-------+-------+
| . . . | 1 2 . | . . 9 |
| . . . | . 9 8 | 1 4 . |
| . . . | 4 . . | . 8 5 |
+-------+-------+-------+
| 8 . 4 | . . 6 | . 5 . |
| 3 7 . | . . . | . . . |
| . 9 . | 8 . . | . 7 . |
+-------+-------+-------+
| . 1 . | . . . | . . . |
| . 3 5 | 7 . 9 | . . . |
| 2 . 7 | . . . | . . . |
+-------+-------+-------+
...12...9....9814....4...858.4..6.5.37........9.8...7..1........357.9...2.7......


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[SpAce]

Code: Select all

.----------.---------------------.--------------------.
| 4  8  3  | 1    2       5      |  7      6     9    |
| 7  5  2  | 6    9       8      |  1      4     3    |
| 1  6  9  | 4    3       7      |  2      8     5    |
:----------+---------------------+--------------------:
| 8  2  4  | 39   7       6      | b39     5     1    |
| 3  7  16 | 259  145     124    |  4689  b29    2468 |
| 5  9  16 | 8    14     a12[3]4 | b346    7     246  |
:----------+---------------------+--------------------:
| 9  1  8  | 25   456     24     |  456    3     7    |
| 6  3  5  | 7    48-1    9      |  48    c2(1)  248  |
| 2  4  7  | 35   1568  a[1]3    |  5689   9-1   68   |
'----------'---------------------'--------------------'

(1,3)r96c6 = (392)b6p715 - (2=1)r8c8 => -1 r8c5,r9c8; stte

uncompressed, slightly different: Show

(1=3)r9c6 - r6c6 = r6c7 - (3=9)r4c7 - r9c7 = (9)r9c8 => -1 r9c8; stte

Just for fun... As many probably know, the Apollo Guidance Computers were implemented with just NOR gates. If they got us to the moon, they should probably work for sudoku too. Here's my (hidden) solution with NOR ( ':' ) gates only.

NORs only:

Code: Select all

(1r9c6:3r9c6) : ((3r9c6:3r9c6):(3r6c6:3r6c6)) : (3r6c6:3r6c7) : ((3r6c7:3r6c7):(3r4c7:3r4c7)) : (3r4c7:9r4c7) : ((9r4c7:9r4c7):(9r9c7:9r9c7)) : (9r9c7:9r9c8) => -1 r9c8; stte

Interestingly, if NOT gates are also allowed, it's exactly the same as the normal AIC form (as a product of sums) with both ORs and ANDs replaced with NORs.

ORs, ANDs, NOTs:

Code: Select all

(1r9c6|3r9c6) & (-3r9c6|-3r6c6) & (3r6c6|3r6c7) & (-3r6c7|-3r4c7) & (3r4c7|9r4c7) & (-9r4c7|-9r9c7) & (9r9c7|9r9c8) => -1 r9c8; stte

NORs, NOTs:

Code: Select all

(1r9c6:3r9c6) : (-3r9c6:-3r6c6) : (3r6c6:3r6c7) : (-3r6c7:-3r4c7) : (3r4c7:9r4c7) : (-9r4c7:-9r9c7) : (9r9c7:9r9c8) => -1 r9c8; stte

That's probably the simplest boolean form for an AIC! I wouldn't have guessed.

[Cenoman]

Code: Select all

 +-----------------+----------------------+---------------------+
 |  4    8    3    |  1     2      5      |  7      6    9      |
 |  7    5    2    |  6     9      8      |  1      4    3      |
 |  1    6    9    |  4     3      7      |  2      8    5      |
 +-----------------+----------------------+---------------------+
 |  8    2    4    |  39    7      6      |  39     5    1      |
 |  3    7    16   |  259  b145   b124    |  4689*  29   2468*  |
 |  5    9    16   |  8    c14     1234   |  346    7    246    |
 +-----------------+----------------------+---------------------+
 |  9    1    8    |  25    456    24     |  456    3    7      |
 |  6    3    5    |  7    a48-1   9      |  48*    12   248*   |
 |  2    4    7    |  35    1568   13     |  5689   19   68     |
 +-----------------+----------------------+---------------------+

UR(48)r58c79 using externals
(4|8)r8c5 == (4)r5c56 - (4=1)r6c5 => -1 r8c5; ste

[SpAce]

UR(48)r58c79 using externals
(4|8)r8c5 == (4)r5c56 - (4=1)r6c5 => -1 r8c5; ste

Beautiful!

[denis_berthier]

Solved using only the most elementary reversible patterns (and no assumption of uniqueness):

Hidden Text: Show

singles
whip[1]: c8n3{r9 .} ==> r9c7 ≠ 3, r7c7 ≠ 3
whip[1]: r8n2{c9 .} ==> r7c8 ≠ 2
naked-single ==> r7c8 = 3
z-chain-rc[3]: r7c6{n4 n2} - r5c6{n2 n1} - r6c5{n1 .} ==> r6c6 ≠ 4
biv-chain[4]: r4c7{n9 n3} - b5n3{r4c4 r6c6} - r6n2{c6 c9} - r5c8{n2 n9} ==> r5c7 ≠ 9
biv-chain[3]: c7n9{r9 r4} - r4c4{n9 n3} - r9c4{n3 n5} ==> r9c7 ≠ 5
singles ==> r7c7 = 5, r7c4 = 2, r7c6 = 4, r7c5 = 6
biv-chain-rc[3]: r5c6{n1 n2} - r5c8{n2 n9} - r9c8{n9 n1} ==> r9c6 ≠ 1
stte

Or with a slightly longer 2D-chain in rc-space:

Hidden Text: Show

singles
whip[1]: c8n3{r9 .} ==> r9c7 ≠ 3, r7c7 ≠ 3
whip[1]: r8n2{c9 .} ==> r7c8 ≠ 2
naked-single ==> r7c8 = 3
z-chain-rc[3]: r7c6{n4 n2} - r5c6{n2 n1} - r6c5{n1 .} ==> r6c6 ≠ 4
biv-chain-rc[5]: r5c8{n2 n9} - r9c8{n9 n1} - r9c6{n1 n3} - r9c4{n3 n5} - r7c4{n5 n2} ==> r5c4 ≠ 2
singles ==> r7c4 = 2, r7c6 = 4
biv-chain-rc[3]: r5c6{n1 n2} - r5c8{n2 n9} - r9c8{n9 n1} ==> r9c6 ≠ 1
stte

[Sudtyro2]

Code: Select all

+--------------+-------------------+------------------+
| 4   8   3    |  1    2      5    |  7      6   9    |
| 7   5   2    |  6    9      8    |  1      4   3    |
| 1   6   9    |  4    3      7    |  2      8   5    |
+--------------+-------------------+------------------+
| 8   2   4    | f39   7      6    |  9-3    5   1    |
| 3   7   16   |  259  145    124  |  4689  c29  2468 |
| 5   9   16   |  8    14    e1234 |  346    7  d246  |
+--------------+-------------------+------------------+
| 9   1   8    |  25   456    24   |  456    3   7    |
| 6   3   5    |  7    148    9    |  48     12  248  |
| 2   4   7    | a3#5  1568  b13   |  5689  b19  68   |
+--------------+-------------------+------------------+

Nothing fishy about the previous amazing solutions, so here's the exception...
Kraken 1-Fish(3)c4\r4 + rfr9c4(#)
(3)r9c4 - (3=19)r9c68 - (9=2)r5c8 - r6c9 = (2-3)r6c6 = (3)r4c4 => -3 r4c7; stte
[Edited to correct chain]

SteveC

[Ngisa]

Code: Select all

+--------------+---------------------+--------------------+
| 4    8    3  | 1      2       5    | 7       6     9    |
| 7    5    2  | 6      9       8    | 1       4     3    |
| 1    6    9  | 4      3       7    | 2       8     5    |
+--------------+---------------------+--------------------+
| 8    2    4  |d39     7       6    | 39      5     1    |
| 3    7    16 |e259    145     124  | 4689    2-9   2468 |
| 5    9    16 | 8      14     c1234 | 346     7     246  |
+--------------+---------------------+--------------------+
| 9    1    8  | 25     456     24   | 456     3     7    |
| 6    3    5  | 7      148     9    | 48      12    248  |
| 2    4    7  | 35     1568   b13   | 5689   a19    68   |
+--------------+---------------------+--------------------+


(9=1)r9c8 - (1=3)r9c6 - (3)r6c6 = (3-9)r4c4 = (9)r5c4 => - 9r5c8; stte

Clement