## Fun puzzle. So many methods to solve. No CHAINS required.

Post puzzles for others to solve here.
If you like finny fish, you'll enjoy this one.

Code: Select all
`2 . . | . 4 . | . 8 .. . 4 | . . . | 9 . 1. 1 . | . . 9 | 2 3 .---------------------. 3 . | . . 6 | 5 . .. . 7 | 2 . . | . . 66 . . | . 5 . | . . .---------------------. . 1 | . 3 . | . 9 .. 7 . | . . 4 | 1 . .4 . . | 6 . . | . . 8`
wapati
2010 Supporter

Posts: 527
Joined: 13 September 2006
Location: Brampton, Ontario, Canada

Wapati wrote:If you like finny fish, you'll enjoy this one.

Code: Select all
` *--------------------------------------------------------------------* | 2       59      359   | 1357    4       1357 | 6       8       57  | | 3578    58      4     | 3578    6       2    | 9       57      1   | | 578     1       6     | 578     78      9    | 2       3       4   | |-----------------------+----------------------+---------------------| | 189     3       289   | 14789   1789    6    | 5       124     79  | | 1589    4589    7     | 2       189     138  | 38      14      6   | | 6       2489    289   | 134789  5       1378 | 378     124     379 | |-----------------------+----------------------+---------------------| | 58      6       1     | 578     3       578  | 4       9       2   | | 3589    7       23589 | 589     289     4    | 1       6       35  | | 4       259     2359  | 6       129     15   | 37      57      8   | *--------------------------------------------------------------------*`

[r8c4](-9-[r46c4])-9-[r8c1]=9=[X-Wing: r45c15]-9-[r4c9](-7-[r6c9]=7=
=[r7c6]-7-[r6c6])-7-[r6c7]=7=[r9c7]-7-[r9c8]-5-[r9c6]-1-[r56c6],

and the cells r56c67 are all and only populated by “3,8”. So, r8c4 cannot be “9” and the puzzle is solved.

Carcul
Carcul

Posts: 724
Joined: 04 November 2005

carcul wrote:[r8c4](-9-[r46c4])-9-[r8c1]=9=[X-Wing: r45c15]-9-[r4c9](-7-[r6c9]=7=
=[r7c6]-7-[r6c6])-7-[r6c7]=7=[r9c7]-7-[r9c8]-5-[r9c6]-1-[r56c6]

Once again there's too much sand for my truck... "(-7-[r6c9]=7= =[r7c6]-7-..."

You started such a nice chain there, why not keep it simple:

[r8c4](-9-[r46c4])-9-[r8c1]=9=[X-Wing: r45c15]-9-[r4c9](-7-[r1c9])-7-[r4c5]=7=[r3c5]-7-[r1c46]

=> r8c4<>9

RW
RW
2010 Supporter

Posts: 1010
Joined: 16 March 2006

This one needs at least 4.

Chain gang..I dunno.

Code: Select all
`. . . | . 7 . | . 1 .. 7 . | 1 . . | . 5 63 . . | . . . | 8 . .---------------------. . . | . 4 . | . . .. 3 . | 6 9 1 | . . 76 . 1 | . 3 . | . 4 .---------------------. 2 9 | 3 . . | . . .. . 7 | . 8 . | . 2 .1 . . | 2 . . | 4 . .`
wapati
2010 Supporter

Posts: 527
Joined: 13 September 2006
Location: Brampton, Ontario, Canada

So way nasty for me.

This is about my limit, nice one.

Code: Select all
`. 9 2 | . . . | 7 8 .1 . . | . 7 . | . . 47 . . | 9 . 3 | . . 6---------------------. . 9 | 7 . 5 | 3 . .. 1 . | . . . | . 7 .. . 5 | 8 . 4 | 6 . .---------------------9 . . | 3 . 7 | . . 12 . . | . 8 . | . . 7. 3 7 | . . . | 8 6 .`

I have a question, I am sure here is wrong. <sigh>

I was wondering what the pattern is, for "good puzzles" when you take the givens and add a correct not given and see whether it is now an "easy".

I didn't say that well.

I wonder whether most "good" puzzles have any, more than 1, lots of squares, that if filled in render the puzzle easy.

I'd like to know if there are more than one squares that may be critical.
wapati
2010 Supporter

Posts: 527
Joined: 13 September 2006
Location: Brampton, Ontario, Canada

WOW! This one is past my limit.

I sort-of know Sashimi X.

Hrrmmm. Here is a borrible. Happy Dancing!

Code: Select all
`. . . | . . . | . . .. 8 6 | . 1 . | 5 2 .1 . 7 | . . . | 3 . 8---------------------. . 2 | 5 . 7 | 1 . .. 3 1 | . 6 . | 2 5 .. . . | . 9 . | . . .---------------------. . 4 | . . . | 6 . .. . 3 | . 8 . | 9 . .7 . . | 6 . 1 | . . 2`
wapati
2010 Supporter

Posts: 527
Joined: 13 September 2006
Location: Brampton, Ontario, Canada

wapati wrote:I have a question, I am sure here is wrong. <sigh>

I was wondering what the pattern is, for "good puzzles" when you take the givens and add a correct not given and see whether it is now an "easy".
You are talking about "backdoor" cells. It depends on what you define as "easy", what a backdoor is. With the basics i have implemented (box/line, tuples, x-wing, UR1) your puzzle has 15.
When you allow the Simple Sudoku techniques (box/line, tuples, x-,xy-wing, swordfish, multicoloring) only one puzzle is known, that does not have a single backdoor (nr 210 in my old list):

33: Ocean #10/M21/D21 (ER 9.8, gsfr 99650, suexr 977, RMS 8)
.....1..2.3..4..5.6..2.......5.....3.7..8..4.2.....9..9....4.......5..7...41..6..
ravel

Posts: 998
Joined: 21 February 2006

wapati wrote:This one needs at least 4.

Chain gang..I dunno.
Code: Select all
`. . . | . 7 . | . 1 . . 7 . | 1 . . | . 5 6 3 . . | . . . | 8 . . --------------------- . . . | . 4 . | . . . . 3 . | 6 9 1 | . . 7 6 . 1 | . 3 . | . 4 . --------------------- . 2 9 | 3 . . | . . . . . 7 | . 8 . | . 2 . 1 . . | 2 . . | 4 . .`

4 of what?
Code: Select all
` *-----------------------------------------------------------------------------* | 24589   458     24568   | 4589    7       345689  | 239     1       249     | | 489     7       48      | 1       2       3489    | 39      5       6       | | 3       1       2456    | 459     56      4569    | 8       7       249     | |-------------------------+-------------------------+-------------------------| | 7       9       258     | 58      4       258     | 6       3       1       | | 245     3       245     | 6       9       1       | 25      8       7       | | 6       58      1       | 7       3       258     | 259     4       29      | |-------------------------+-------------------------+-------------------------| | 458     2       9       | 3       1       45      | 7       6       58      | | 45      456     7       | 459     8       4569    | 1       2       3       | | 1       568     3       | 2       56      7       | 4       9       58      | *-----------------------------------------------------------------------------*`

[r4c3](-8-[r6c2]-5-[r1c2])-8-[r2c3]-4-[r1c2]-8-[r1c4]=8=[r4c4]-8-[r4c3]

=> r4c3<>8

Sorry if I spoiled your fun carcul...

RW
RW
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Posts: 1010
Joined: 16 March 2006

RW wrote:4 of what?
[RW

I would need x, xy, xyz, swordish and ER/Turbot to complete it.

Your way looks shorter.
wapati
2010 Supporter

Posts: 527
Joined: 13 September 2006
Location: Brampton, Ontario, Canada

wapati wrote:I would need x, xy, xyz, swordish and ER/Turbot to complete it.

No, you wouldn't. ER + XY-wing is enough. You shouldn't trust a computer program to tell you what is required, it tells you what is required if you do the techniques in a specific order.

RW
RW
2010 Supporter

Posts: 1010
Joined: 16 March 2006

Wapati wrote:This is about my limit, nice one.

Code: Select all
` *-----------------------------------------------------* | 456   9     2   | 1456  456   16  | 7     8     3   | | 1     56    3   | 256   7     8   | 259   259   4   | | 7     458   48  | 9     245   3   | 1     25    6   | |-----------------+-----------------+-----------------| | 46    2     9   | 7     16    5   | 3     14    8   | | 8     1     46  | 26    3     269 | 2459  7     259 | | 3     7     5   | 8     129   4   | 6     129   29  | |-----------------+-----------------+-----------------| | 9     4568  468 | 3     2456  7   | 245   245   1   | | 2     456   1   | 456   8     69  | 459   3     7   | | 45    3     7   | 1245  2459  129 | 8     6     259 | *-----------------------------------------------------*`

We have r5c7=9 or r9c9=5. But:

[r5c7]=9|5=[r9c9]-5-[r5c9]=5=[r5c7],

which implies r5c7<>2,4 and the puzzle is solved (using later a trivial ATILA step).

Carcul
Carcul

Posts: 724
Joined: 04 November 2005

Wapati wrote:WOW! This one is past my limit.(...) Hrrmmm. Here is a borrible. Happy Dancing!

Code: Select all
` *---------------------------------------------------------------------* | 2345    2459    59  | 3489    245     345689 | 7       1469    1469 | | 34      8       6   | 7       1       349    | 5       2       49   | | 1       2459    7   | 49      245     4569   | 3       469     8    | |---------------------+------------------------+----------------------| | 468     46      2   | 5       3       7      | 1       4689    469  | | 9       3       1   | 48      6       48     | 2       5       7    | | 456     7       58  | 1       9       2      | 48      46      3    | |---------------------+------------------------+----------------------| | 258     125     4   | 39      7       39     | 6       18      15   | | 56      156     3   | 2       8       45     | 9       7       145  | | 7       59      589 | 6       45      1      | 48      3       2    | *---------------------------------------------------------------------*`

[r6c3]-8-[r9c3]=8=[r7c1]=2=[r7c2]-2-[r1c2]-4-[r4c2]-6-[r24c9]
-4-[r8c9]=4=[r9c7]=8=[r6c7]-8-[r6c3],

and so r6c3<>8 solving the puzzle.

Carcul
Carcul

Posts: 724
Joined: 04 November 2005

RW wrote:
wapati wrote:I would need x, xy, xyz, swordish and ER/Turbot to complete it.

No, you wouldn't. ER + XY-wing is enough. You shouldn't trust a computer program to tell you what is required, it tells you what is required if you do the techniques in a specific order.

RW

Sheesh, next you will tell me that "windows" isn't safe on the Internet.
wapati
2010 Supporter

Posts: 527
Joined: 13 September 2006
Location: Brampton, Ontario, Canada

This is hard for me, many methods required.

Code: Select all
`. . 6 | . 2 . | . . 45 9 . | . . . | . . .. . 4 | . . 9 | 8 . .---------------------. . . | . 7 4 | 1 . .. . 8 | 6 . 1 | . . 34 . . | . 3 . | . . .---------------------. . . | . 8 . | 3 . 28 5 . | . . . | . 6 .. 7 . | 2 . . | . 9 .`
wapati
2010 Supporter

Posts: 527
Joined: 13 September 2006
Location: Brampton, Ontario, Canada

wapati wrote:Sheesh, next you will tell me that "windows" isn't safe on the Internet.

Well, if you write two post that claims that it is, then maybe I would...

RW
RW
2010 Supporter

Posts: 1010
Joined: 16 March 2006

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