The New Sudoku Players' Forum

[m_b_metcalf]

I know that backdoors are reviled by most folks here, but I'm interested to know how easy they are to spot if one knows that one is present. To that end, I wiill post a few such puzzles here, and I'll be watching to see what the response is.

Mike

Code: Select all

 1 . . . . . . . 2
 . 3 . . 2 . . 4 .
 . . 2 5 . 6 3 . .
 . . 7 6 . 5 8 . .
 . . . . 7 . . . .
 . . 9 2 . 8 6 . .
 . . 5 9 . 3 7 . .
 . 7 . . 5 . . 9 .
 9 . . . . . . . 8

1.......2.3..2..4...25.63....76.58......7......92.86....59.37...7..5..9.9.......8

[Hajime]

Could not find the backdoor yet (or must be more than one?) but a great puzzle for 2 Jellyfish and one WXYZ wing
Start:

Code: Select all

   +-------------------+--------------+-----------------+ 
   |   1    45689  468 |3478 3489  479|  59   5678   2  | 
   | 5678     3     68 | 178   2   179| 159    4   15679| 
   |  478    489    2  |  5  1489   6 |  3    178   179 | 
   +-------------------+--------------+-----------------+ 
   |  234    124    7  |  6  1349   5 |  8    123   1349| 
   |234568 124568 13468| 134   7   149|12459  1235 13459| 
   |  345    145    9  |  2   134   8 |  6    1357 13457| 
   +-------------------+--------------+-----------------+ 
   | 2468   12468   5  |  9  1468   3 |  7    126   146 | 
   | 23468    7   13468| 148   5   124| 124    9    1346| 
   |   9    1246   1346| 147  146 1247| 1245 12356   8  | 
   +----------------------------------------------------+ 


Then
Jellyfish (1)r3467c2589 => (-1)r2c9 (-1)r5c2 (-1)r5c8 (-1)r5c9 (-1)r8c9 (-1)r9c2 (-1)r9c5 (-1)r9c8 |
Jellyfish (4)r3467c1259 => (-4)r1c2 (-4)r1c5 (-4)r5c1 (-4)r5c2 (-4)r5c9 (-4)r8c1 (-4)r8c9 (-4)r9c2 (-4)r9c5
r9c5=6 Naked Single
multiple more Singles up to:

Code: Select all

   +---------------+-------------+-----------+ 
   |  1   58    48 |3478 3489 479| 59  6   2 | 
   |5678   3    68 | 178   2  179|159  4 1579| 
   | 47    9    2  |  5   14   6 | 3   8  17 | 
   +---------------+-------------+-----------+ 
   |  2    4    7  |  6   39   5 | 8   1  39 | 
   |3568 1568  1368| 134   7  149| 2  35  359| 
   | 35   15    9  |  2   13   8 | 6   7   4 | 
   +---------------+-------------+-----------+ 
   | 468  168   5  |  9   148  3 | 7   2  16 | 
   |3468   7  13468| 148   5   2 | 14  9  136| 
   |  9    2   134 | 147   6  147|145 35   8 | 
   +-----------------------------------------+ 


Then
Pointing, Claiming | (7)r1,b2 => (-7)r2c4 (-7)r2c6 | (5)b6,r5 => (-5)r5c1 (-5)r5c2 | (9)c7,b3 => (-9)r2c9
Turbot Crane (4)r1c3=r3c1-r7c1=r7c5 => (-4)r1c5
WXYZ-Wing Type B on {1389} in b2e4,b2e2,c5e46 (-1)b2c5 => (-1)r3c5
r3c5=4 Naked Single
stte

[rjamil]

Could not find the backdoor yet (or must be more than one?) but a great puzzle for 2 Jellyfish and one WXYZ wing

OR

After 2 Jellyfish moves, an M-Wing move will solve the puzzle (without Turbot Crane move):

Code: Select all

 +------------------+----------------+--------------+
 | 1     58  *48    | 3478  39+8 479 | 59   6   2   |
 | 5678  3    68    | 18    2    19  | 159  4   57  |
 | 7-4   9    2     | 5     14   6   | 3    8   17  |
 +------------------+----------------+--------------+
 | 2     4    7     | 6     39   5   | 8    1   39  |
 | 368   68   1368  | 134   7    149 | 2    35  359 |
 | 35    15   9     | 2     13   8   | 6    7   4   |
 +------------------+----------------+--------------+
 | 68+4  168  5     | 9    *148  3   | 7    2   16  |
 | 368   7    1368-4| 148   5    2   | 14   9   36  |
 | 9     2    13-4  | 147   6    147 | 145  35  8   |
 +------------------+----------------+--------------+

M-Wing: 48 @ r1c3 148 @ r7c5 SL 8 @ r17c5 SL 4 @ r7c15 => -4 @ r3c1 r89c3; stte

R. Jamil

[Hajime]

Could not find the backdoor yet (or must be more than one?) but a great puzzle for 2 Jellyfish and one WXYZ wing

OR

After 2 Jellyfish moves, an M-Wing move will solve the puzzle (without Turbot Crane move):

Code: Select all

 +------------------+----------------+--------------+
 | 1     58  *48    | 3478  39+8 479 | 59   6   2   |
 | 5678  3    68    | 18    2    19  | 159  4   57  |
 | 7-4   9    2     | 5     14   6   | 3    8   17  |
 +------------------+----------------+--------------+
 | 2     4    7     | 6     39   5   | 8    1   39  |
 | 368   68   1368  | 134   7    149 | 2    35  359 |
 | 35    15   9     | 2     13   8   | 6    7   4   |
 +------------------+----------------+--------------+
 | 68+4  168  5     | 9    *148  3   | 7    2   16  |
 | 368   7    1368-4| 148   5    2   | 14   9   36  |
 | 9     2    13-4  | 147   6    147 | 145  35  8   |
 +------------------+----------------+--------------+

M-Wing: 48 @ r1c3 148 @ r7c5 SL 8 @ r17c5 SL 4 @ r7c15 => -4 @ r3c1 r89c3; stte

R. Jamil

You forgot candidate 4 in r1c5 ? So r1c5=3489. Does that make a difference?
The Turbot Crane in my solution is completely superfluous.

[rjamil]

Hi Hajime,

You forgot candidate 4 in r1c5 ? So r1c5=3489. Does that make a difference?
The Turbot Crane in my solution is completely superfluous.

Actually, first 2 Jellyfish moves also removes 4 from r1c5, as mentioned in your Jellyfish (4) move but forgot to remove from pm grid.

R. Jamil

[shye]

are they really reviled?

i had the same path as others. you can combine the jellyfish into one with an MSLS, but thats a bit overcomplicated

Code: Select all

  4 14      14      1 14
+-------+-------+-------+
| 1 . . | . . . | . . 2 |
| . 3 . | . 2 . | . 4 . |
| # # 2 | 5 # 6 | 3 # # | 789
+-------+-------+-------+
| # # 7 | 6 # 5 | 3 # # | 239
| . . . | . 7 . | . . . |
| # # 9 | 2 # 8 | 6 # # | 357
+-------+-------+-------+
| # # 5 | 9 # 3 | 7 # # | 268
| . 7 . | . 5 . | . 9 . |
| 9 . . | . . . | . . 8 |
+-------+-------+-------+

20 cells (r3467c12589)
20 links (1c8, 4c1, 14c259, 789r3, 239r4, 357r6, 268r7)
all candidates covered, links become truths

after singles and claiming 7s in r1b2

Code: Select all

,------------------,----------------,--------------,
| 1     58   48    | 3478 #389  479 | 59   6   2   |
| 5678  3    68    |#18    2   #19  | 159  4   579 |
| 47    9    2     | 5     4-1  6   | 3    8   17  |
:------------------+----------------+--------------:
| 2     4    7     | 6     39   5   | 8    1   39  |
| 3568  568  1368  | 134   7    149 | 2    35  359 |
| 35    15   9     | 2    #13   8   | 6    7   4   |
:------------------+----------------+--------------:
| 468   168  5     | 9     148  3   | 7    2   16  |
| 368   7    13468 | 148   5    2   | 14   9   36  |
| 9     2    134   | 147   6    147 | 145  35  8   |
'------------------'----------------'--------------'

||3r1c5 - (3=1)r6c5
||8r1c5 - (8=1)r2c4
||9r1c5 - (9=1)r2c6
=> -1r3c5 stte

really pretty grid

[RSW]

I guess my question is: Which advanced techniques must be tried before looking for a backdoor?

Like the others, I found the two jellyfish, and then found backdoor -5r1c2 which gives a singles solution from that point.

[P.O.]

i guess there's something more to come as finding size 1 backdoors in singles is very easy, the loops for finding size 2 to 4 backdoors being a bit more involved;
of course you know this thread:
http://forum.enjoysudoku.com/one-flew-over-the-backdoors-t31086.html

[denis_berthier]

.
In SudoRules, Singles backdoors are easily found:
- load SudoRules with only backdoors selected, i.e. in section 3e of the config file, set:
(bind ?*Backdoors* TRUE)
- init SudoRules with the puzzle:
(init "1.......2.3..2..4...25.63....76.58......7......92.86....59.37...7..5..9.9.......8")
- ask for the backdoors:
(find-backdoors)

SudoRules finds two BRT backdoors:
n9r1c5 n8r1c2


Now, you can also look for backdoors wrt to any set of rules (with the confluence property)
SudoRules finds:
- 3 W1-backdoors:
n8r8c3 n9r1c5 n8r1c2

- 37 S4-backdoors:
n5r9c8 n1r9c7 n4r9c6 n3r9c3 n3r8c9 n1r8c4 n8r8c3 n6r8c1 n6r7c9 n8r7c5 n1r7c2 n4r7c1 n1r6c5 n5r6c2 n3r6c1 n5r5c9 n3r5c8 n9r5c6 n4r5c4 n1r5c3 n6r5c2 n8r5c1 n9r4c9 n3r4c5 n1r3c9 n4r3c5 n7r3c1 n7r2c9 n9r2c7 n1r2c6 n8r2c4 n5r2c1 n5r1c7 n9r1c5 n3r1c4 n4r1c3 n8r1c2



As for the question, how easy is it to find them, it's as easy or as difficult as finding an anti-backdoor: you have to try all the candidates one by one. Whether a candidate leads to some result or not is totally dependent on the puzzle and there's no way to know before trying it.

I don't know if backdoors are reviled, but using them corresponds to guessing (which has indeed always been reviled) - while using an anti-backdoor corresponds to using T&E.


For the present puzzle, as already shown by previous solutions, backdoors are quite useless.

Code: Select all

Resolution state after Singles and whips[1]:
   +----------------------+----------------------+----------------------+
   ! 1      45689  468    ! 3478   3489   479    ! 59     5678   2      !
   ! 5678   3      68     ! 178    2      179    ! 159    4      15679  !
   ! 478    489    2      ! 5      1489   6      ! 3      178    179    !
   +----------------------+----------------------+----------------------+
   ! 234    124    7      ! 6      1349   5      ! 8      123    1349   !
   ! 234568 124568 13468  ! 134    7      149    ! 12459  1235   13459  !
   ! 345    145    9      ! 2      134    8      ! 6      1357   13457  !
   +----------------------+----------------------+----------------------+
   ! 2468   12468  5      ! 9      1468   3      ! 7      126    146    !
   ! 23468  7      13468  ! 148    5      124    ! 124    9      1346   !
   ! 9      1246   1346   ! 147    146    1247   ! 1245   12356  8      !
   +----------------------+----------------------+----------------------+
202 candidates.

biv-chain[3]: r2c3{n8 n6} - b3n6{r2c9 r1c8} - b3n8{r1c8 r3c8} ==> r3c1≠8, r3c2≠8
jellyfish-in-columns: n4{c3 c7 c4 c6}{r9 r8 r5 r1} ==> r9c5≠4, r9c2≠4, r8c9≠4, r8c1≠4, r5c9≠4, r5c2≠4, r5c1≠4, r1c5≠4, r1c2≠4
jellyfish-in-columns: n1{c3 c7 c4 c6}{r9 r8 r5 r2} ==> r9c8≠1, r9c5≠1, r9c2≠1, r8c9≠1, r5c9≠1, r5c8≠1, r5c2≠1, r2c9≠1
singles ==> r9c5=6, r9c2=2, r7c8=2, r5c7=2, r4c1=2, r1c8=6, r3c8=8, r6c8=7, r4c8=1, r4c2=4, r3c2=9, r6c9=4, r8c6=2
whip[1]: r6n5{c2 .} ==> r5c1≠5, r5c2≠5
whip[1]: r1n7{c6 .} ==> r2c4≠7, r2c6≠7
whip[1]: b6n9{r5c9 .} ==> r2c9≠9
biv-chain[3]: b2n7{r1c6 r1c4} - c4n3{r1 r5} - r5n4{c4 c6} ==> r1c6≠4
biv-chain[3]: r1n4{c3 c4} - c5n4{r3 r7} - c5n8{r7 r1} ==> r1c3≠8
stte

[m_b_metcalf]

I guess my question is: Which advanced techniques must be tried before looking for a backdoor?

To be clear, all the puzzles that I will present can be solved with nothing more than one backdoor and singles, as found by Denis. (As he also found, there may be several, independent backdoors.)

Mike

[RSW]

Thanks for the explanation. So, in this case, the backdoor 8r1c2 will give a solution using nothing more than singles.

[m_b_metcalf]

Thanks for the explanation. So, in this case, the backdoor 8r1c2 will give a solution using nothing more than singles.

Exactly.