The New Sudoku Players' Forum

by **ravel** » Mon Jun 04, 2007 4:34 pm

Code: Select all: *---------------------------------------* | 3 8 4 | 19 17 79 | 5 2 6 | | 6 7 1 | 2 5 3 | 4 8 9 | | 2 5 9 | 4 8 6 | 3 7 1 | |-----------+---------------+-----------| |#19 6 8 |#139 4 79 | 2 5 37 | |#19 2 7 |#1359 13 58 | 6 4 38 | | 4 3 5 | 6 27 28 | 1 9 78 | |-----------+---------------+-----------| | 5 4 3 | 7 9 1 | 8 6 2 | | 7 1 2 | 8 6 4 | 9 3 5 | | 8 9 6 | 35 23 25 | 7 1 4 | *---------------------------------------*

Alternative to the cycle: UR 19 in r45c14 with strong link for 9 in row 5 => r4c4<>1, strong link for 1 in row 4 => r5c4<>9.

by **re'born** » Mon Jun 04, 2007 6:02 pm

ravel wrote:
Code: Select all
*---------------------------------------* | 3 8 4 | 19 17 79 | 5 2 6 | | 6 7 1 | 2 5 3 | 4 8 9 | | 2 5 9 | 4 8 6 | 3 7 1 | |-----------+---------------+-----------| |#19 6 8 |#139 4 79 | 2 5 37 | |#19 2 7 |#1359 13 58 | 6 4 38 | | 4 3 5 | 6 27 28 | 1 9 78 | |-----------+---------------+-----------| | 5 4 3 | 7 9 1 | 8 6 2 | | 7 1 2 | 8 6 4 | 9 3 5 | | 8 9 6 | 35 23 25 | 7 1 4 | *---------------------------------------*
Alternative to the cycle: UR 19 in r45c14 with strong link for 9 in row 5 => r4c4<>1, strong link for 1 in row 4 => r5c4<>9.

There is an interesting alternative using this uniqueness. To avoid a BUG grid:

Code: Select all: *-----------------------------------------------------------* | 3 8 4 | 19 17 79 | 5 2 6 | | 6 7 1 | 2 5 3 | 4 8 9 | | 2 5 9 | 4 8 6 | 3 7 1 | |-------------------+-------------------+-------------------| | 19 6 8 | 13+9 4 79 | 2 5 37 | | 19 2 7 | 59+13 13 58 | 6 4 38 | | 4 3 5 | 6 27 28 | 1 9 78 | |-------------------+-------------------+-------------------| | 5 4 3 | 7 9 1 | 8 6 2 | | 7 1 2 | 8 6 4 | 9 3 5 | | 8 9 6 | 35 23 25 | 7 1 4 | *-----------------------------------------------------------*

we must have r4c4=9, r5c4=1 or r5c4=3. But, trivially, r5c4=9 would preclude all three of these things from happening, hence r5c4<>9.

by **JPF** » Tue Jun 05, 2007 1:21 pm

an other one :

Code: Select all: . . . . . . . . . . 1 2 3 4 . . . . . 5 . . 6 . 7 . . . 8 . . . 7 . . . . 3 9 . . . 5 7 . . . . 4 . . . 6 . . . 4 . 9 . . 2 . . . . . 7 8 1 3 . . . . . . . . . .

000000000012340000050060700080007000039000570000400060004090020000078130000000000
JPF

by **re'born** » Tue Jun 05, 2007 3:19 pm

JPF wrote:an other one :

Code: Select all
. . . . . . . . . . 1 2 3 4 . . . . . 5 . . 6 . 7 . . . 8 . . . 7 . . . . 3 9 . . . 5 7 . . . . 4 . . . 6 . . . 4 . 9 . . 2 . . . . . 7 8 1 3 . . . . . . . . . .
000000000012340000050060700080007000039000570000400060004090020000078130000000000
JPF

Wonderful puzzle JPF. SudoCue suggests 7 coloring deductions to solve this, but it can be done with just two bidirectional x-cycles (and they're even on the same digit). Very nicely done.

Alternatively,

Code: Select all: *-----------------------------------------------------------* | 3689 4 368 | 7 158 159 | 2 159 1359 | | 7 1 2 | 3 4 59 | 689 589 569 | | 389 5 38 | 189 6 2 | 7 4 139 | |-------------------+-------------------+-------------------| | 156 8 16 | 1259 3 7 | 4 19 129 | | 4 3 9 | 128A 128A 6 | 5 7 128 | | 15B 2 7 | 4 158B 159- | 3 6 189 | |-------------------+-------------------+-------------------| | 18 67 4 | 15 9 3 | 68 2 567 | | 2 9 5 | 6 7 8 | 1 3 4 | | 138 67 138 | 125 125 4 | 689 589 5679 | *-----------------------------------------------------------*

A = {1,2,8} on r5c45, B = {1,5,8} on r6c15, x = 8, z = 1.

The ALS xz-rule implies r6c6<>1, solving the puzzle.

by **Ocean** » Wed Jun 06, 2007 4:44 pm

Thanks Claudia and JPF for the nice puzzles!

Claudia's puzzle has two 4-node bidirectional cycles.
[r1c4]=3=[r7c4]=9=[r3c4]-9-[r2c6]-3-[r1c4]
[r3c5]=4=[r9c5]=6=[r9c6]-6-[r3c6]-4-[r3c5]

JPF's first puzzle has a 9-node xy-ring, and the second puzzle has 2 x-rings (8 and 6 nodes, respectively).

The three puzzles are included among the examples in the first post in this thread. In my opinion good and instructive examples!

Also, thanks to re'born and ravel for showing alternative solution paths.

by **re'born** » Wed Jun 06, 2007 9:23 pm

Here is a doozy.

Code: Select all: *-----------* |27.|6..|.8.| |86.|.2.|.1.| |..9|...|4..| |---+---+---| |...|7..|..3| |...|8.2|...| |7..|..6|...| |---+---+---| |..7|...|9..| |.5.|.6.|.41| |.1.|..9|.68| *-----------*

I used a finned x-wing, some (multi-)coloring, a UR single, an x-wing, an xy-wing and...a 6-ring bidirectional y-cycle. Now it is somebody else's turn to come in and say, "Well, yes, but if you look over here you'll see that the ALS xz-rule..."

by **JPF** » Wed Jun 06, 2007 10:12 pm

Here, re'born wrote:
JPF wrote:
Code: Select all
1 . . | . . . | . . 2 . 3 . | 2 . 4 | . 5 . . . . | . . . | 6 . . -------+-------+------- . . 6 | . . . | 1 . . . . . | 7 . 3 | . . . . . 8 | . . . | 9 . . -------+-------+------- . . 1 | . . . | . . . . 7 . | 5 . 2 | . 3 . 8 . . | . . . | . . 9 ER=7.6
JPF,
You should submit this puzzle to the Bicycle Collection. It is a real beauty. Just write in the pencilmarks and there is a 4-ring bidirectional y-cycle staring you right in the face. After that an xy-wing and an empty rectangle will reduce it to a BUG+1. Fantastic.

Done. Thanks re'born.

JPF

by **JPF** » Wed Jun 06, 2007 10:40 pm

Still with the same pattern :

Code: Select all: 1 . . | . . . | . . 2 . 3 . | 4 . 5 | . 1 . . . . | . . . | 6 . . -------+-------+------- . . 6 | . . . | 2 . . . . . | 3 . 7 | . . . . . 8 | . . . | 9 . . -------+-------+------- . . 2 | . . . | . . . . 7 . | 1 . 9 | . 5 . 6 . . | . . . | . . 3

JPF

by **Ocean** » Mon Jun 11, 2007 11:40 am

Thanks re'born and JPF for new good examples. Now we also have an 11-node xy-ring, plus two puzzles which were categorized as xy-ring + one 'extreme' technique (the 'extremes' being finned x-wing and empty rectangle).

by **JPF** » Fri Jun 15, 2007 9:22 pm

Could it be qualified ?

Code: Select all: . . . | . . . | . . . . 1 . | . 2 . | . 3 . . . . | 4 5 6 | . . . -------+-------+------- . . 7 | . . . | 8 . . . 3 5 | . 8 . | 9 1 . . . 6 | . . . | 4 . . -------+-------+------- . . . | 6 9 5 | . . . . 7 . | . 1 . | . 8 . . . . | . . . | . . .

JPF

by **re'born** » Sat Jun 16, 2007 11:05 am

JPF wrote:Could it be qualified ?

Code: Select all: *--------------------------------------------------------------------* | 2589 56 28 | 13 7 13 | 25 24569 24589 | | 567 1 4 | 89 2 89 | 567 3 57 | | 23789 289 238 | 4 5 6 | 127 279 12789 | |----------------------+----------------------+----------------------| | 1249 249 7 | 1259 6 1249 | 8 25 3 | | 24 3 5 | 27 8 247 | 9 1 6 | | 1289 289 6 | 1259 3 129 | 4 257 257 | |----------------------+----------------------+----------------------| | 2348 248 1238 | 6 9 5 | 1237 247 1247 | | 456 7 9 | 23 1 23 | 56 8 45 | | 235 56 123 | 78 4 78 | 1235 2569 1259 | *--------------------------------------------------------------------*

where a Y-wing style (though I would like it we changed the name of this technique to something that does not refer to xy-wings and which correlates to what it really looks like, namely remote naked pairs...perhaps semi-remote naked pairs) between r1c2,r8c7<56> implies r1c7<>5 (there is also an xyz-wing that will make this same exclusion). After cleaning up the grid a bit, we get

Code: Select all: *-----------------------------------------------------------* | 59 56A 8 | 13 7 13 | 2 456a9 459 | | 56a7B 1 4 | 89 2 89 | 567 3 57 | | 237b9 29 23 | 4 5 6 | 1 7B9b 8 | |-------------------+-------------------+-------------------| | 1249 249 7 | 1259 6 1249 | 8 25 3 | | 24 3 5 | 27 8 247 | 9 1 6 | | 1289 289 6 | 1259 3 129 | 4 257 257 | |-------------------+-------------------+-------------------| | 2348 248 123 | 6 9 5 | 37 247 1247 | | 456 7 9 | 23 1 23 | 56 8 45 | | 235 56 123 | 78 4 78 | 35 256A9- 1259 | *-----------------------------------------------------------*

Now a little 3D-coloring implies r9c8<>9, which solves the puzzle.
[r9c8]-9-[r3c8]-7-[r3c1]=7=[r2c1]=6=[r1c2]-6-[r1c8]=6=[r9c8]

I can find a few bidirectional cycles, but none yet that really crack the puzzle open.

by **claudiarabia** » Sat Jun 16, 2007 12:15 pm

Code: Select all: . 6 . . 4 . 2 . . . . . . . 7 . . . 9 . 8 5 . . . 1 . . . 7 1 . . . . . . . 5 . . . 8 . . . . . . . 6 3 . . . 8 . . . 5 9 . 3 . . . 9 . . . . . . . 1 . 3 . . 7 . SE 6-6

A multisolutional sudoku came before my eyes yesterday (not here:-)). I changed some clues and out came this: Beside the bi-directional X-cycle, there are many other techniques like X-wing, 2 xy-wing and three turbot-fishes. The sudoku-Assistenten solves it with one X-wing and a sky-scraper only. I often discovered more turbots in one sudoku than it was announced by the program previously. When you find the right Turbot-fish, you may circumwent other steps.

Happy solving

by **re'born** » Sun Jun 17, 2007 12:08 pm

claudiarabia wrote:
Code: Select all
. 6 . . 4 . 2 . . . . . . . 7 . . . 9 . 8 5 . . . 1 . . . 7 1 . . . . . . . 5 . . . 8 . . . . . . . 6 3 . . . 8 . . . 5 9 . 3 . . . 9 . . . . . . . 1 . 3 . . 7 . SE 6-6
A multisolutional sudoku came before my eyes yesterday (not here:-)). I changed some clues and out came this: Beside the bi-directional X-cycle, there are many other techniques like X-wing, 2 xy-wing and three turbot-fishes. The sudoku-Assistenten solves it with one X-wing and a sky-scraper only. I often discovered more turbots in one sudoku than it was announced by the program previously. When you find the right Turbot-fish, you may circumwent other steps.

Happy solving

Claudia, well done turning someone else's mistake into something that kept me entertained for far too long.

I love the puzzles where you end up with a nearly cleaned up board and then you can apply tons of different techniques to solve it. My best solution thus far uses the empty rectangle in box 9 to eliminate 4 from r9c4, solving the puzzle. Although the fish experts might find the finned jellyfish that eliminates 4 from r8c3 a rather satisfying solution.

by **claudiarabia** » Tue Jun 26, 2007 11:57 am

re'born wrote:Claudia, well done turning someone else's mistake into something that kept me entertained for far too long. I love the puzzles where you end up with a nearly cleaned up board and then you can apply tons of different techniques to solve it. ...

The sudoku on the wikipedia-page on the top right is very easy and has sooo many initial clues. After removing some clues I got a fantastic sudoku with 22 clues only. It is to solve with three xy-wings and a bi-directional Y-cycle.

Code: Select all: 5 3 . . 7 . . . . . . . 1 . 5 . . . . 9 8 . . . . 6 . 8 . . . 6 . . . . 4 . . 8 . 3 . . 1 . . . . 2 . . . . . 6 . . . . 2 8 . . . . 4 . 9 . . 5 . . . . . . . 7 .

Happy solving

Claudia

by **claudiarabia** » Sun Jul 01, 2007 3:52 pm

Ocean"][quote="claudiarabia wrote:
Code: Select all
4 . . . . . . . 2 . 8 . . 9 . . 7 . . . . 3 . 6 . . . . . 1 . . . 6 . . . 6 . . 4 . . 9 . . . 5 . . . 3 . . . . . 5 . 2 . . . . 7 . . 6 . . 8 . 9 . . . . . . . 4

This sudoku has a bi-directional X-Cycle next to two bi-directional Y-cycles next to 2 X-Wings and many other fancy techniques.

The Sudoku-Explainer found out this Bi-directional Y-cycle with 8 cells to eliminate the 7 in r1c3 and r7c9.

Code: Select all: *--------------------------------------------------------------------* | 4 135 69-7 | 178 157 1578 |#89 36 2 | | 156 8 23 | 124 9 145 | 15 7 36 | | 17 125 #79 | 3 12578 6 | 4 15 #89 | |----------------------+----------------------+----------------------| | 2378 49 1 | 2789 2357 35789 | 6 24 578 | | 237 6 #78 | 127 4 1357 | 1278 9 157 | | 278 49 5 | 6 127 1789 | 3 124 178 | |----------------------+----------------------+----------------------| |#68 13 4 | 5 #78 2 |#79 13 1369-7 | | 1235 7 23 | 49 6 49 | 25 8 135 | | 9 1235 #68 | 178 1378 1378 | 1257 12356 4 | *--------------------------------------------------------------------*

I found a "simple" bi-directional cycle (below) which leads to the same result and eliminates also all clues in r7c9 except of the cycle-members 6 and 9.

Code: Select all: *--------------------------------------------------------------------* | 4 135 69-7 | 178 157 1578 | 89 36 2 | | 156 8 23 | 124 9 145 | 15 7 36 | | 17 125 #79 | 3 12578 6 | 4 15 8#9 | |----------------------+----------------------+----------------------| | 2378 49 1 | 2789 2357 35789 | 6 24 578 | | 237 6 #78 | 127 4 1357 | 1278 9 157 | | 278 49 5 | 6 127 1789 | 3 124 178 | |----------------------+----------------------+----------------------| | 68 13 4 | 5 78 2 |79 13 #69-137 | | 1235 7 23 | 49 6 49 | 25 8 135 | | 9 1235 #68 | 178 1378 1378 | 1257 1235#6 4 | *--------------------------------------------------------------------*

The cycle comprises 6 cells with 4 cycle-relevant numbers

Code: Select all: -7 | | | | 79 | | 9 --------------------------------- | | 78 | | | | --------------------------------- | | 96-137 | | 68 | | 6 r3c3 r3c9 r7c9 r9c8 r9c3 r5c3 97 9 96 6 68 78

For the explainer will always take the most easy technique, he doesn't see this cycle. Also note that two of the xy-wings in the puzzle are not necessary because the 8 in r1c5 and r5c9 is eliminated by the big bi-directional X-cycle as well.

Claudia

The New Sudoku Players' Forum

The Bicycle Collection.

A sudoku with a bi-directional X-cycle

Re: A sudoku with a bi-directional X-cycle

I did it again ... with the wikipedia-sudoku above right

Another solution wields the same result.