The New Sudoku Players' Forum

[denis_berthier]

.
Here is one more puzzle with the same 90° rotation invariant "radiation" pattern.

Code: Select all

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

2...5...3.6..9..2...3.4.7.....4.7...917...435...5.9.....4.8.6...2..7..9.5...2...7 # 95636 FNBTHYK C28/S8.f
SER = 7.2
non-minimal

Has anyone studied this pattern in the Patterns Game?

[P.O.]

Code: Select all

after singles:

2      4789   189    1678   5      168   b18+9   1468   3               
1478   6      158    1378   9      138    158    2      148             
18    c58+9   3      1268   4      1268   7      1568  c168-9           
368   d3+58  a±2×568 4      13     7     a1+289  168    1689           
9      1      7      28     6      28     4      3      5               
3468   348    268    5      13     9      128    7      168             
137    379    4      139    8      135    6      15     2               
1368   2      168    136    7      13456  1358   9      148             
5      389    1689   1369   2      1346   138    148    7   

r4n2{c3 c7} - c7n9{r4 r1} - r3n9{c9 c2} - c2n5{r3 r4} => r4c3 <> 5
singles: ( r7c6b8 n5  r9c7b9 n3  r7c8b9 n1  r3c8b3 n5  r8c7b9 n5  r2c3b1 n5  r4c2b4 n5 )

2      4789  189   1678  5     168   189  c4+68  3             
1478   6     5     1378  9     138   18    2     148           
18    b8-9   3     1268  4     1268  7     5    b168+9           
368    5     268   4     13    7     1289 d6+8   1689           
9      1     7     28    6     28    4     3     5             
3468   348   268   5     13    9     128   7     168           
37     379   4     39    8     5     6     1     2             
136×8  2     16×8  136   7     1346  5     9     48             
5     a±8+9 e16+89 169   2     146   3    e4-×8  7         

r9c2{n8 n9} - r3n9{c2 c9} - b3n6{r3c9 r1c8} - r4c8{n6 n8} - r9n8{c8 c3} => r8c1 r8c3 r9c8 <> 8
ste.


[denis_berthier]

.
The main reason why I proposed this puzzle is the contrast between its very high Q2 rating (95636) and its elementary solution by only 2 steps in BC4.

Code: Select all

Resolution state after Singles and whips[1]:
   +-------------------+-------------------+-------------------+
   ! 2     4789  189   ! 1678  5     168   ! 189   1468  3     !
   ! 1478  6     158   ! 1378  9     138   ! 158   2     148   !
   ! 18    589   3     ! 1268  4     1268  ! 7     1568  1689  !
   +-------------------+-------------------+-------------------+
   ! 368   358   2568  ! 4     13    7     ! 1289  168   1689  !
   ! 9     1     7     ! 28    6     28    ! 4     3     5     !
   ! 3468  348   268   ! 5     13    9     ! 128   7     168   !
   +-------------------+-------------------+-------------------+
   ! 137   379   4     ! 139   8     135   ! 6     15    2     !
   ! 1368  2     168   ! 136   7     13456 ! 1358  9     148   !
   ! 5     389   1689  ! 1369  2     1346  ! 138   148   7     !
   +-------------------+-------------------+-------------------+
164 candidates.

Here are two of the 4 2-step solutions in BC4:

biv-chain[4]: r3n9{c2 c9} - b6n9{r4c9 r4c7} - r4n2{c7 c3} - b4n5{r4c3 r4c2} ==> r3c2≠5
singles ==> r2c3=5, r3c8=5, r7c8=1, r8c7=5, r7c6=5, r9c7=3, r4c2=5
biv-chain[4]: b3n6{r1c8 r3c9} - r3n9{c9 c2} - r9c2{n9 n8} - r9c8{n8 n4} ==> r1c8≠4
stte

biv-chain[4]: r4n2{c3 c7} - b6n9{r4c7 r4c9} - r3n9{c9 c2} - b1n5{r3c2 r2c3} ==> r4c3≠5
singles ==> r4c2=5, r2c3=5, r3c8=5, r7c8=1, r8c7=5, r7c6=5, r9c7=3
biv-chain[4]: c8n4{r9 r1} - b3n6{r1c8 r3c9} - r3n9{c9 c2} - r9c2{n9 n8} ==> r9c8≠8
stte
P.O.: your second step could be shorter.

[P.O.]

hi Denis, effectively i didn't check; to reduce the search time i make a few reductions: when an elimination is included in an elimination set, like here, I only look for the chains that eliminate the set; when i write my solution i generally catch these inaccuracies not this time.

[denis_berthier]

hi Denis, effectively i didn't check; to reduce the search time i make a few reductions: when an elimination is included in an elimination set, like here, I only look for the chains that eliminate the set; when i write my solution i generally catch these inaccuracies not this time.

Do you mean that you start by looking for "elimination sets", i.e. anti-backdoor-pairs in this case?

[JPF]

Has anyone studied this pattern in the Patterns Game?

This pattern is probably not minimal, i.e. it doesn't exist any minimal puzzles with these clues.
Puzzles studied in the Patterns Game have to be minimal.

About (geometric) symmetry : the pattern is not only "90° rotation invariant" which would make it symmetric of order 4. It has also other symmetries such a symmetry regarding the vertical axis ; then this is a fully symmetrical pattern, of order 8.

After a quick run, here is what I came up with:
SER=9.3

Code: Select all

+-------+-------+-------+
| 1 . . | . 2 . | . . 3 |
| . 4 . | . 5 . | . 1 . |
| . . 6 | . 1 . | 7 . . |
+-------+-------+-------+
| . . . | 1 . 5 | . . . |
| 8 5 3 | . . . | 9 6 1 |
| . . . | 3 . 6 | . . . |
+-------+-------+-------+
| . . 8 | . 7 . | 1 . . |
| . 9 . | . 6 . | . 5 . |
| 4 . . | . 3 . | . . 2 |
+-------+-------+-------+
1...2...3.4..5..1...6.1.7.....1.5...853...961...3.6.....8.7.1...9..6..5.4...3...2


JPF

[P.O.]

Do you mean that you start by looking for "elimination sets", i.e. anti-backdoor-pairs in this case?

to search for the shortest path to a solution i used to compute anti-backdoors (1,2 and 3) then to look for chains that eliminate them, i no longer do it that way;
now, using your vocabulary, in a resolution state with a resolution theory i compute all the eliminations i can find, that means building the chains and keeping only theirs eliminations as i can recover the chains from their eliminations;
it is at this point that i do some reduction: for example as in this case: a chain does three eliminations, another chain only one that is included in the previous three, i don't keep this one elimination so i won't be able to recover this chain, the idea is that i dont miss a opportunity to solve the grid and three eliminations are more powerful than one, but this is not always true;
then i carry out all those eliminations, if the grid is solved i look for the shortest combination of eliminations, 1 to 4 in fact, and recover the chains that do them, if not i repeat the process;
at the moment i go no further than the first two states of the grid, to go further is on the todo list.

[denis_berthier]

P.O.

OK. thanks for the details

[denis_berthier]

Puzzles studied in the Patterns Game have to be minimal.

Of course, a game has to have rules. But do you know why this rule in particular? From a player's POV, minimality is irrelevant.
Besides the fun of the game, is there some general goal of this game?

After a quick run, here is what I came up with:
SER=9.3

Code: Select all

+-------+-------+-------+
| 1 . . | . 2 . | . . 3 |
| . 4 . | . 5 . | . 1 . |
| . . 6 | . 1 . | 7 . . |
+-------+-------+-------+
| . . . | 1 . 5 | . . . |
| 8 5 3 | . . . | 9 6 1 |
| . . . | 3 . 6 | . . . |
+-------+-------+-------+
| . . 8 | . 7 . | 1 . . |
| . 9 . | . 6 . | . 5 . |
| 4 . . | . 3 . | . . 2 |
+-------+-------+-------+
1...2...3.4..5..1...6.1.7.....1.5...853...961...3.6.....8.7.1...9..6..5.4...3...2


JPF

Great. The hardest I found with gsf's program (among 1000) was only 9.0.
Your puzzle is in what I called the grey zone long ago: upper side of T&E(1) or lower side or gT&E(1), SER 9.2 to 9.6
Yours is in W15 or gW13 (which is very hard for a puzzle in T&E(1)).

[RSW]

Two steps.

Code: Select all

 +------------------+----------------+-------------------+
 | 2     47    189  | 1678 5   168   | 189    1468  3    |
 | 47    6    a158  | 1378 9   138   | 18-5   2     148  |
 |d18    89-5  3    |d1268 4  d1268  | 7     d1568 d1689 |
 +------------------+----------------+-------------------+
 |c368  c358 bc2568 | 4   c13  7     | 1289  c168  c1689 |
 | 9     1     7    | 28   6   28    | 4      3     5    |
 | 3468  348   268  | 5    13  9     | 128    7     168  |
 +------------------+----------------+-------------------+
 | 137   379   4    | 139  8   135   | 6      15    2    |
 | 1368  2     168  | 136  7   13456 | 1358   9     148  |
 | 5     389   1689 | 1369 2   1346  | 138    148   7    |
 +------------------+----------------+-------------------+


(5)r2c3 = (5)r4c3 - (2=135689)r4c123589 - (9=12685)r3c14689 => -5r3c2 -5r2c7

Code: Select all

 +--------------+--------------+----------------+
 | 2    47 189  | 1678 5  168  | 189 e68-4 3    |
 | 47   6  5    | 1378 9  138  | 18   2    148  |
 | 18  c89 3    | 1268 4  1268 | 7    5   d1689 |
 +--------------+--------------+----------------+
 | 368  5  268  | 4    13 7    | 1289 68   1689 |
 | 9    1  7    | 28   6  28   | 4    3    5    |
 | 3468 34 268  | 5    13 9    | 128  7    168  |
 +--------------+--------------+----------------+
 | 37   37 4    | 9    8  5    | 6    1    2    |
 | 168  2  168  | 136  7  1346 | 5    9    48   |
 | 5   b89 1689 | 16   2  146  | 3   a48   7    |
 +--------------+--------------+----------------+


(4=8)r9c8 - (8)r9c2 = (8-9)r3c2 = (9-6)r3c9 = (6)r1c8 => -4r1c8; stte