## Gurth's Puzzles

Everything about Sudoku that doesn't fit in one of the other sections
hey can u rate this one?

pls i updated my solution for a diffrent attempt in its orginal post.

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

Difficulty rating: 7.2 x ?? bricks = ??

This Sudoku can be solved using the following logical methods:
48 x Hidden Single
4 x Direct Hidden Pair
3 x Naked Single
2 x Pointing
2 x Claiming
1 x Naked Pair
1 x Hidden Pair
1 x Unique Rectangle type 4
1 x Bidirectional Cycle
3 x Forcing Chain

but it does confirms you present idea that all puzzle should first be checked to see if simple moves alone can actually solves it befor testing more complex moves then give it a rating based on complexity of advanced moves.

(this puzzle can't be solved just using simple box/lines & pairs/quads
. )

if you spot the unique rectangles it solves in 1 move. as the rest falls to singles naked ect.
Last edited by StrmCkr on Tue Jan 02, 2007 2:10 am, edited 2 times in total.
Some do, some teach, the rest look it up.

StrmCkr

Posts: 861
Joined: 05 September 2006

gurth wrote:Mauricio,
Thanks for your 24-bricker. I'll check it soon and report back.

That 24 bricker is a poor one, ER 3.0 .

Now a nice set of sudokus for everyone's pleasure. I don't list the mutations, only give the number of mutations, so can anyone (gurth) confirm the numbers?

The sudoku with the most mutations my program found is this
Code: Select all
`. . 4 . . . . . 61 . . . 3 . 4 . .. 8 . . . 5 . 3 .4 . . . . 7 5 . .. 5 . . 1 . . 8 .. . 6 5 . . . . 4. 2 . 3 . . . . 5. . 8 . 4 . . 2 .7 . . . . 1 8 . . 29 mutations, solvable with singles`

Code: Select all
`. . 2 7 . . 5 . .. 9 . . 3 . . . 41 . . . . 4 . 9 .4 . . . . 3 9 . .. 5 . . 8 . . . .. . 6 2 . . . . 7. 1 . 5 . . . . .. . 8 . 6 . 4 . .2 . . . . 7 . 6 . 28 mutations, ER 7.2`

Code: Select all
`. . 8 1 . . . 6 .3 . . . 4 . . . 2. 6 . . . 2 3 . .4 . . . . . 8 . .. 5 . . 6 . . 7 .. . . 9 . . . . 19 . . 7 . . . 3 .. 7 . . 8 . . . 4. . 2 . . 3 1 . .  26 mutations, ER 7.3`

Code: Select all
`. . 4 6 . . 3 . .5 . . . 4 . . . 8. 2 . . . 1 . 6 .4 . . . . 5 9 . .. 5 . . 8 . . 2 .. . 6 7 . . . . 53 . . . . . . . 1. 1 . . 2 . 6 . .. . 2 . . 3 . 4 . 21 mutations, ER 8.3`

Code: Select all
`. . . 8 . . . 9 .. . 3 . 1 . 6 . .. 2 . . . 5 . . 74 . . . . 1 3 . .. 5 . . 6 . . 1 .. . . 7 . . . . 22 . . 1 . . 8 . .. 6 . . 7 . . . 9. . 4 . . 3 . 5 . 21 mutations, ER 8.3`

Code: Select all
`. 4 . 8 . . . 3 .1 . . . 5 . . . 2. . 5 . . 2 9 . .4 . . . . 5 . . .. 5 . . 1 . . 6 .. . 6 4 . . . . 8. 3 . 1 . . . . 49 . . . 8 . 3 . .. . . . . 6 . 7 . 21 mutations, ER 8.9`

Code: Select all
`. 2 . 9 . . . . 79 . . . 1 . 3 . .. . 3 . . 7 . 4 .4 . . . . 3 5 . .. . . . 6 . . 7 .. . 6 5 . . . . 9. 8 . 3 . . . . .. . 9 . 2 . . . 65 . . . . 8 1 . . 19 mutations, ER 9.0`

Code: Select all
`. . 8 3 . . . . 75 . . . 8 . . 2 .. 6 . . . 7 9 . .4 . . . . 6 7 . .. 5 . . . . . 9 .. . 6 2 . . . . 11 . . . . . . . 3. . . . 4 . 8 . .. . 2 . . 8 . 6 . 16 mutations, ER 9.1`

Code: Select all
`. . . 2 . . . . 8. . 2 . 8 . . . .. 7 . . . 4 . 9 .4 . . . . 9 5 . .. 5 . . 6 . . 8 .. . 6 4 . . . . 31 . . . . . 7 . .. . 3 . . . . . 6. 9 . . . 1 . 5 . 11 mutations, ER 9.9`

Now some brickers
Code: Select all
`. . . 1 . . . 3 .4 . . 2 6 . . . .. . . 3 4 5 . . .. . 7 . . . 8 . .. 5 2 . . . 7 1 .3 8 1 . . . 9 . .. . . 7 3 2 . . .. . . . 8 1 . . 5. 9 . . . 4 . . . 28 bricks, ER 7.2`

Code: Select all
`. . . . . . . 6 .. . . 2 . 1 . . .. . . 3 4 5 . . .. 5 3 . . . 1 . .. 4 2 . . . 5 7 .. 7 1 . . . 8 4 .. . . 9 1 7 . . .. . . 5 3 . . . 4. 2 . . . . . . . 27 bricks, ER 8.4`

Code: Select all
`. . . . . . . 7 .9 . . 2 6 . . . .. . . 3 4 5 . . .. . 3 . . . 6 5 2. . 1 . . . 7 9 .7 6 5 . . . 1 . .. . . 4 2 6 . . .. . . . 1 . . . 8. 4 . . . 8 . . . 25 bricks, ER 9.0`

StrmCkr wrote:pls i updated my solution for a diffrent attempt in its orginal post.
Code: Select all
`8 . 6|5 . .|. . . . . .|. 4 .|3 9 7 . 4 .|. . 1|. . . -----+-----+----- . . .|3 . 5|. 2 . . 2 .|. 8 .|. . 5 . . 1|. . 7|. . . -----+-----+----- 4 . .|. . 3|. . 6 6 . .|. . .|9 5 . . 9 .|7 . .|4 . . `

Difficulty rating: 7.2 x ?? bricks = ??
According to my understanding, it has 9 bricks.
Mauricio

Posts: 1174
Joined: 22 March 2006

udosuk

Posts: 2698
Joined: 17 July 2005

By hand I stopped at:

Code: Select all
`8 . . | 5 . 9 | . . .. . . | . 4 . | 3 9 7. 4 . | 2 . 1 | 5 6 8----------------------. . . | 3 . 5 | . 2 .. 2 . | 1 8 . | . . 55 . 1 | . 2 7 | . . . ----------------------4 . . | . . 3 | . . 66 . . | . 1 . | 9 5 .. 9 . | 7 . . | 4 . .----------------------`

At r1c7 the alternatives are 1,2. Letting a 2 I could proceed to the end
Archangel

Posts: 5
Joined: 30 December 2006

GC33 SE 7.2 ?????

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

A case requiring the categorically essential.
_______________________________________________________

Mauricio,
SE rates your 24-bricker at 3.0, due to one naked pair.
__________________________________________________________

StrmCkr, count bricks as follows:

Code: Select all
` *-----------* |8.6|5..|...| |...|.4.|397| |.4.|..1|...| |---+---+---| |...|3.5|.2.| |.2.|.8.|..5| |..1|..7|...| |---+---+---| |4..|..3|..6| |6..|...|95.| |.9.|7..|4..| *-----------*   SE 7.2`

In box 1: 86.
In box 2: nil.
In box 3: 39, 37, 97.
In box 4: nil.
In box 5: 35, 57.
In box 6: nil.
In box 7: 46.
In box 8: nil.
In box 9: 95, 94.

Total: 9 bricks.
Brick rating = 7.2 x 9 = 64.8
Very close to GC28!
SE reveals a very pretty Unique Rectangle in this Sudoku.
*-----------*
|8.6|5.9|...|
|...|.4.|397|
|.4.|2.1|568|
|---+---+---|
|7..|3.5|.2.|
|.2.|18.|..5|
|5.1|.27|...|
|---+---+---|
|4..|..3|..6|
|6..|.1.|95.|
|.9.|7..|4..|
*-----------*

*-----------------------------------------------------------*
| 8 37 6 | 5 37 9 | 12 14 124 |
| 12 15 25 | 68 4 68 | 3 9 7 |
| 39 4 379 | 2 37 1 | 5 6 8 |
|-------------------+-------------------+-------------------|
| 7 68 48 | 3 69 5 | 168 2 149 |
| 39 2 349 | 1 8 46 | 67 347 5 |
| 5 368 1 | 469 2 7 | 68 348 349 |
|-------------------+-------------------+-------------------|
| 4 15 258 | 89 59 3 | 1278 178 6 |
| 6 378 2378 | 48 1 248 | 9 5 23 |
| 12 9 2358 | 7 56 268 | 4 138 123 |
*-----------------------------------------------------------*

At this point SS gets stuck, unable to see the UR.
___________________________________________________________
gurth

Posts: 358
Joined: 11 February 2006
Location: Cape Town, South Africa

gurth wrote:SE reveals a very pretty Unique Rectangle in this Sudoku.
Code: Select all
` *-----------------------------------------------------------* | 8     37    6     | 5     37    9     | 12    14    124   | | 12    15    25    | 68    4     68    | 3     9     7     | | 39    4     379   | 2     37    1     | 5     6     8     | |-------------------+-------------------+-------------------| | 7    *68    48    | 3     69    5     |-168   2     149   | | 39    2     349   | 1     8     46    | 67    347   5     | | 5    -368   1     | 469   2     7     |*68    348   349   | |-------------------+-------------------+-------------------| | 4     15    258   | 89    59    3     | 1278  178   6     | | 6     378   2378  | 48    1     248   | 9     5     23    | | 12    9     2358  | 7     56    268   | 4     138   123   | *-----------------------------------------------------------*`

Very pretty indeed! I'm not an UR expert so don't know what type of UR it is...

r6c2=8 or r4c7=6 or r4c7=8 will create the DR (deadly rectangle) {68} in r46c27, therefore r6c2<>8 and r4c7=1... The puzzle is then solved with singles...

There is another UR in r35c13, though not very useful...

Gurth, about your mysterious new technique, is it uniqueness based? Or pattern based (on 1 digit)?
udosuk

Posts: 2698
Joined: 17 July 2005

gurth wrote:GC33 SE 7.2 ?????
Code: Select all
`  2 . . 5 . . . . .  . 3 . . 1 . . . .  . . . . . 8 9 . 7  . 5 . . 3 . . 6 .  . . 9 . . . 3 2 .  1 . . . . . . . .  . . . . 7 2 . . 1  . . 8 . . 3 . . .  . . 6 . . . . 5 4`

A case requiring the categorically essential.

After singles & BLIs (box-line interactions):
Code: Select all
` *--------------------------------------------------------------------* | 2      489    147    | 5      469    4679   | 46     148    3      | | 489    3      47     | 79     1      4679   | 2456   48     2568   | | 456    46     145    | 3      2      8      | 9      14     7      | |----------------------+----------------------+----------------------| | 478    5      2      | 789    3      479    | 1      6      89     | | 4678   4678   9      | 178    468    14567  | 3      2      58     | | 1      68     3      | 2      689    569    | 457    4789   589    | |----------------------+----------------------+----------------------| | 459    49     45     | 4689   7      2      | 68     3      1      | | 47     1247   8      | 146    5      3      | 267    79     269    | | 3      1279   6      | 189    89     19     | 278    5      4      | *--------------------------------------------------------------------*`

There is a naked triple in box 3, but are we supposed to start applying your mysterious new technique right here?

After SSTS:
Code: Select all
` *--------------------------------------------------* | 2    89   17   | 5    49   479  | 6    18   3    | | 89   3    47   | 79   1    6    | 5    48   2    | | 56   46   145  | 3    2    8    | 9    14   7    | |----------------+----------------+----------------| | 48   5    2    | 789  3    479  | 1    6    89   | | 468  7    9    | 18   468  145  | 3    2    58   | | 1    68   3    | 2    689  59   | 4    7    589  | |----------------+----------------+----------------| | 59   49   45   | 6    7    2    | 8    3    1    | | 7    1    8    | 4    5    3    | 2    9    6    | | 3    2    6    | 189  89   19   | 7    5    4    | *--------------------------------------------------*`

Is your mysterious new technique still applicable?
udosuk

Posts: 2698
Joined: 17 July 2005

udosuk wrote:
gurth wrote:SE reveals a very pretty Unique Rectangle in this Sudoku.
Code: Select all
` *-----------------------------------------------------------* | 8     37    6     | 5     37    9     | 12    14    124   | | 12    15    25    | 68    4     68    | 3     9     7     | | 39    4     379   | 2     37    1     | 5     6     8     | |-------------------+-------------------+-------------------| | 7    *68    48    | 3     69    5     |-168   2     149   | | 39    2     349   | 1     8     46    | 67    347   5     | | 5    -368   1     | 469   2     7     |*68    348   349   | |-------------------+-------------------+-------------------| | 4     15    258   | 89    59    3     | 1278  178   6     | | 6     378   2378  | 48    1     248   | 9     5     23    | | 12    9     2358  | 7     56    268   | 4     138   123   | *-----------------------------------------------------------*`

Very pretty indeed! I'm not an UR expert so don't know what type of UR it is...

r6c2=8 or r4c7=6 or r4c7=8 will create the DR (deadly rectangle) {68} in r46c27, therefore r6c2<>8 and r4c7=1... The puzzle is then solved with singles...

I'm no expert on URs either, but this one had me stumped more than usual. From what I know of URs, either [r6c2]=3 or [r4c7]=1. If [r4c7]=1, then I can't deduce anything further about the UR using information within this chute/band. However, if I set [r6c2]=3, then it forces [r4c7]=1 as well. No matter what, [r4c7]=1.

Is this considered a true UR reduction? How is it classified; i.e., what is its Type?
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

This is classified as a UR+2rd and results in the indicated eliminations. The elimination r6c2<>8 occurs because there are no "8"s in the cells indicated with "@", thus if r6c2=8 then r4c7=8 resulting in the deadly pattern. The logic is the same for r4c7<>68.

Code: Select all
`UR+2rd (6,8): r46c27 => r4c7<>6,r4c7<>8,r6c2<>8+-----------------+---------------+-----------------+|  8    37     6  |   5  37    9  |   12   14  124  || 12    15    25  |  68   4   68  |    3    9    7  || 39     4   379  |   2  37    1  |    5    6    8  |+-----------------+---------------+-----------------+|  7    68*   48  |   3  69    5  | 1-68*   2@ 149@ || 39     2   349  |   1   8   46  |   67@ 347@   5@ ||  5  36-8*    1  | 469   2    7  |   68* 348  349  |+-----------------+---------------+-----------------+|  4    15   258  |  89  59    3  | 1278  178    6  ||  6   378  2378  |  48   1  248  |    9    5   23  || 12     9  2358  |   7  56  268  |    4  138  123  |+-----------------+---------------+-----------------+`
Mike Barker

Posts: 458
Joined: 22 January 2006

nice responce Mike, for my puzzle that i created by hand.

i solved it in a similar maner.

edit:

removed till i figure it out better.
Last edited by StrmCkr on Thu Jan 04, 2007 4:44 am, edited 11 times in total.
Some do, some teach, the rest look it up.

StrmCkr

Posts: 861
Joined: 05 September 2006

Mike Barker's POV expressed as two discontinous nice loops, each with cycle length 3:

Using strong inferences of diagonal UR and conjugate link for UR digit 6 in b4 (or c2) ...

r4c7=1|3=r6c2=6=r4c2-6-r4c7, implies r4c7<>6

Using strong inferences of diagonal UR and grouped conjugate link for UR digit 8 in b6 ...

r6c2=3|1=r4c7=8=r6c78-8-r6c2, implies r6c2<>8

Gotta love those short loops!
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

### CHALLENGE and various

___________________________________________________________________

The Art of Guessing

Usually I don't use guessing, because it's taboo. But taboos can also be broken. As John Steinbeck said: "Thou mayest!"

Guessing can be great fun. Take GC34 below.

Code: Select all
`# GC34# SE 7.2  . . . . 1 . . . 6  3 . 5 . . 7 . . .  . . . . . 9 . 4 .  . . . . 4 . . . .  9 2 . . 5 . . 8 .  . . 1 . 6 . 2 . .  . 6 . 2 . . . . .  . . . 3 . . 5 . 7  4 . . . 9 . . . .`

SE 7.2 can mean 2 Forcing Chains, or it can mean 12. Chalk and cheese. A quick romp in the park, or a major slog. Or else just try guessing.

Note that this Sudoku displays a certain degree of rotational symmetry. 6 always symmetrical to 4, 3 to 7, 5 to 5. The other values are not so strict.

Nevertheless, when you see this sort of thing, you can be sure that there is a very high degree of probability that this pattern continues to permeate the grid nearly everywhere. That's all a guesser wants: to find a high degree of probability. It pays enormous dividends in all fields to practise the art of spotting high degrees of probability. Every time you cross the road, in fact, it is very important to be able to assess the probability of a successful guess. Will you or will you not be alive by the time you reach the other side?
____________________________________________________________________________________________

GC35 Two Doors

Code: Select all
`#GC35 Two Doors  2 . 6 . . . . . 3  . . . . 6 . . 7 .  5 . . 4 . 1 . . .  . . 4 . . 5 1 . 6  . 5 . . . . . 4 .  . . 3 6 . . 2 . .  . . . 3 . 2 . . 8  . 8 . . 7 . . . .  1 . . . . . 7 . 4  `

This is a house with two doors.

Open the East door by removing 4e8 to get a really tough SE 7.3 with 19 Forcing Chains, not to mention 3 Bidirectional Y-Cycles.

If that is not tough enough for you, close the East door and open the West door by removing 5e2.
Now it's SE 8.9 with 29 tough chains.

Either way, you might see a couple of Swordfish.
__________________________________________________________________________________________

re my CHALLENGE, nobody has offered any progress so I conclude I didn't give enough data. To remedy that, see my new post (coming very shortly) ISOMORPHS AND NORMALIZATION on the Advanced Solving Techniques forum.
gurth

Posts: 358
Joined: 11 February 2006
Location: Cape Town, South Africa

Thanks to Gurth's hint about the "ISOMORPHS AND NORMALIZATION", here is my attempt to solve his challenge GC28:

Original puzzle:
Code: Select all
`. . . . . 3 . . 2. . 4 . . . . 5 .2 6 . 9 . . 7 . .. . . . 1 . . 8 .9 5 . . . . 3 . .. 1 . 4 9 . 2 . .8 . . . . . 1 . .. . . . . 2 . . 61 . 9 . 7 . . . .`

First, count the #clues in the 3 bands, they are 8, 9, 7 respectively... So we couldn't morph it into a rotational symmetrical puzzle grid (which would need the same #clues in the top & bottom bands)... So we need to look for diagonal symmetry...

b3 is a nicely diagonal box, I'd keep it unchanged... So I decide to try using the "/" diagonal as the line of symmetry...

Now look at b1 & b9, we want them to have the same #clues... A quick way would be exchanging c123 & c456:
Code: Select all
`c123 <-> c456:. . 3 . . . . . 2. . . . . 4 . 5 .9 . . 2 6 . 7 . .. 1 . . . . . 8 .. . . 9 5 . 3 . .4 9 . . 1 . 2 . .. . . 8 . . 1 . .. . 2 . . . . . 6. 7 . 1 . 9 . . .`

But then, b1 & b9 are still not completely symmetrical to each other... And a simple way to make it happen is to cycle r7 to the bottom of r89:
Code: Select all
`r7 -> r9 | r9 -> r8 | r8 -> r7:. . 3 . . . . . 2. . . . . 4 . 5 .9 . . 2 6 . 7 . .. 1 . . . . . 8 .. . . 9 5 . 3 . .4 9 . . 1 . 2 . .. . 2 . . . . . 6. 7 . 1 . 9 . . .. . . 8 . . 1 . .`

Tada! We have ourselves a perfectly diagonally symmetrical puzzle...

The pairings are 1<->9, 3<->6, 4<->8 while 2, 5, 7 just map to themselves...

I suspect other puzzles probably wouldn't be morphed as easily...

Now try to solve this puzzle using the symmetrical property... Only singles/box-line interactions are enough... Puzzle solved in 2 minutes...
Code: Select all
`6 8 3 5 9 7 4 1 27 2 1 3 8 4 6 5 99 5 4 2 6 1 7 3 83 1 5 6 4 2 9 8 72 6 7 9 5 8 3 4 14 9 8 7 1 3 2 6 51 3 2 4 7 5 8 9 68 7 6 1 3 9 5 2 45 4 9 8 2 6 1 7 3`

Next, we morph it back... Just do the reverse of the operations above:
Code: Select all
`r7 -> r8 | r8 -> r9 | r9 -> r7:6 8 3 5 9 7 4 1 27 2 1 3 8 4 6 5 99 5 4 2 6 1 7 3 83 1 5 6 4 2 9 8 72 6 7 9 5 8 3 4 14 9 8 7 1 3 2 6 55 4 9 8 2 6 1 7 31 3 2 4 7 5 8 9 68 7 6 1 3 9 5 2 4c123 <-> c456:5 9 7 6 8 3 4 1 23 8 4 7 2 1 6 5 92 6 1 9 5 4 7 3 86 4 2 3 1 5 9 8 79 5 8 2 6 7 3 4 17 1 3 4 9 8 2 6 58 2 6 5 4 9 1 7 34 7 5 1 3 2 8 9 61 3 9 8 7 6 5 2 4`

Tada! Puzzle solved... No forcing chains, no wings, no fishes...

Now we await Gurth to demonstrate a more systematic way to morph grids to diagonal/rotational symmetry...

The way I used was just trying my luck... Perhaps I was guessing in some sense...
udosuk

Posts: 2698
Joined: 17 July 2005

udosuk wrote:Now try to solve this puzzle using the symmetrical property... Only singles/box-line interactions are enough... Puzzle solved in 2 minutes...

please show a move or two that would not be possible without "using the symmetrical property"
thanks
gsf
2014 Supporter

Posts: 7306
Joined: 21 September 2005
Location: NJ USA

if its a guess then there should be some clear way of identifying where and how to rotate the puzzle making it not a guess

im still stuck trying to figure that part out.

gurth said you can still solve this puzzle normally it just takes alot more work (forceing chains ect)

he/she mentioned that you can rotate the puzzle into a symetrical form that is issomorphic (the same puzzle) and not require any move beyond simple sudoku moves, thus avoiding all those hard + steps.
Some do, some teach, the rest look it up.

StrmCkr

Posts: 861
Joined: 05 September 2006

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