The New Sudoku Players' Forum

[eleven]

Code: Select all

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

Harder rated, but easier.

[marek stefanik]

Yes, this one is way easier. Here is a two-step solution:

Code: Select all

.------------------.-------------------.----------------.
| 8    1      6    | 3      24     7   | 9    5     24  |
| 79   579    59   | 1      6      24  |a248  3     248 |
| 3    2      4    | 89     89     5   | 1    7     6   |
:------------------+-------------------+----------------:
| 249  3      1    | 2489   5      248 | 7    6    a248 |
| 6    45789  2589 | 24789  12489  3   | 248  248   15  |
| 247  4578   258  | 24678  1248   16  | 3    9     15  |
:------------------+-------------------+----------------:
| 5    6      3    | 248    1248   9   | 248 a1248  7   |
| 24   48     7    | 2468   3      16  | 5    1248  9   |
| 1    489    289  | 5      7     a248 | 6    248   3   |
'------------------'-------------------'----------------'

Whichever digit is true in r2c7 is forced into r4 in c9, r9 in c6 and c8 in r7. => –1r7c8

Xsudo input: Show

.------------------.-------------------.----------------.
| 8 1 6 | 3 24 7 | 9 5 24 |
| 79 579 59 | 1 6 24 | 248 3 248 |
| 3 2 4 | 89 89 5 | 1 7 6 |
:------------------+-------------------+----------------:
| 249 3 1 | 2489 5 248 | 7 6 248 |
| 6 45789 2589 | 24789 12489 3 | 248 248 15 |
| 247 4578 258 | 24678 1248 16 | 3 9 15 |
:------------------+-------------------+----------------:
| 5 6 3 | 248 1248 9 | 248 1248 7 |
| 24 48 7 | 2468 3 16 | 5 1248 9 |
| 1 489 289 | 5 7 248 | 6 248 3 |
'------------------'-------------------'----------------'
10 Truths = {248R7 248C6 248C9 2N7}
16 Links = {248r2 248r4 248c7 248b3 248b8 7n8}

Multi-link: Show

If we assume 1r7c8, we'll empty r2c7 with the fish r7c69\r24c7b38 (rank2).
To get the corresponding multi-link, we simply take the link corresponding to each truth of the subpattern rank times and add all its links.

Code: Select all

.---------.---------.---------.
| .  .  . | .  .  . | .  .  3 |
| .  .  . | .  .  3 | 3  .  4 |
| .  .  . | .  .  . | .  .  . |
:---------+---------+---------:
| .  .  . | .  .  3 | .  .  3 |
| .  .  . | .  .  . | .  .  . |
| .  .  . | .  .  . | .  .  . |
:---------+---------+---------:
| .  .  . | 3  3  . | 3  .  . |
| .  .  . | .  .  3 | .  .  . |
| .  .  . | .  .  3 | .  .  . |
'---------'---------'---------'

(11L)r2477c66799b38 / 3 => 3L
The fact that r2c9 is part of four links doesn't matter, it would have to be part of 6 links to be twice in the multi-link. This happens with endofinned fishes.

Now we can use it for what we've previously used 5 links. When we do so for each digit, we save 6 links, proving a rank0 area (the remaining link r7c8).

Code: Select all

.-----------------.-----------------.---------------.
| 8    1     6    | 3    *24    7   | 9    5   *24  |
| 79   579   59   | 1     6     24  | 248  3    248 |
| 3    2     4    | 89    89    5   | 1    7    6   |
:-----------------+-----------------+---------------:
| 249  3     1    |*2489  5     248 | 7    6    8–24|
| 6    4589  2589 | 7    *2489  3   | 248  248  1   |
| 247  478   28   | 6    *248   1   | 3    9    5   |
:-----------------+-----------------+---------------:
| 5    6     3    | 248   1     9   | 248  248  7   |
| 24   48    7    | 248   3     6   | 5    1    9   |
| 1    489   289  | 5     7     248 | 6    248  3   |
'-----------------'-----------------'---------------'

ERs 24r1b5\r4c59 => –24r4c9, stte

We can combine the steps by substituting 284 for b3p346.

Marek

Edit: Marked r4c9 with 'a' instead of 'b'. I originally meant to order the deductions, and this stayed here by accident.

[shye]

Whichever digit is true in r2c7 is forced into r4 in c9, r9 in c6 and c8 in r7. => –1r7c8

i got the same, but also by considering where the value in r2c7 could go in b5 you can then determine its not 2 or 4 thanks to b2
this one was fun too!

[marek stefanik]

Yes, you're right. I didn't continue the logic after singles, seeing it solved with fishes. You can also just use c4 instead of the two boxes. Nice find!

Marek

[eleven]

Similar:

Code: Select all

+----------------------+------------------------+-----------------------+
| 8      1      6      |   3      24     7      |  9      5     a24     |
| 79     579    59     |   1      6      24     | x248    3     a248    |
| 3      2      4      |   89     89     5      |  1      7      6      |
+----------------------+------------------------+-----------------------+
| 249    3      1      |  #248+9  5     b248    |  7      6     x248    |
| 6      45789  2589   |   24789  12489  3      |  248    248    15     |
| 247    4578   258    |   24678  1248   16     |  3      9      15     |
+----------------------+------------------------+-----------------------+
| 5      6      3      | yz248   #248+1  9      |yz248    1248   7      |
| 24     48     7      | yz2468   3      1+6    |  5      1248   9      |
| 1      489    289    |   5      7     x#248   |  6      248    3      |
+----------------------+------------------------+----------------------+

x in r2c7 must be in r4c9 and r9c6 too (*xr2c7 - r12c9 = r4c9 - *r24c6 = r9c6), leaving yz in r7c47.
So r8c5 canot be 248, is 1, and r8c6 is 6. This leaves yz in r78c4, and with xr4c9 r4c4 must be 9. stte