Gurth's Puzzles

Everything about Sudoku that doesn't fit in one of the other sections

Re: Interesting jades

Postby udosuk » Thu Dec 07, 2006 2:47 pm

Mauricio wrote:A few nice jades:
Code: Select all
....8..94.......2.8.4...3...4..9.7...7.........3....5.7...69...6.1..8.....5.2..6
SE 7.3, 40 singles

.3.6...8.56...2......243....4.85..99....1.......471........7.3..8.....5...8....6
SE 8.3, 31 singles

..5976........9...8...4.2.9.2.....856..21.......4..........89.....327.664.......
SE 8.4, 27 singles

2.8.4....5......2...5.3.6.....39.5....6.....3.7..21.........75...1.8.....437....
SE 9.0, 18 singles

These 4 puzzles are invalid according to my solver...:(
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Re: Interesting jades

Postby Mauricio » Thu Dec 07, 2006 6:41 pm

These 4 puzzles are invalid according to my solver...:(

I corrected the typos, now they have to be valid.
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Re: Interesting jades

Postby udosuk » Fri Dec 08, 2006 4:18 am

Mauricio wrote:Edit: Corrected a few typos when I changed 0's by .'s. I like 0's more.

Thanks!:)

If you manipulate the text using a program such as Notepad, you can easily convert all the .'s to 0's (and vice versa) using the "Replace All" function...:idea:
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Jade Collection

Postby gurth » Fri Dec 08, 2006 9:32 am

Mauricio,

Thanks for adding this very nice collection of jades for all fans of such.

And thanks, udosuk, for clearing up the typos so quickly.

_______________________________________________________________________________________
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Postby Mauricio » Tue Dec 12, 2006 4:44 am

More sudokus with the 456789 lines, one very difficult and a pearl.

Code: Select all
..24....6
.8..5..4.
9....63..
4.....7..
.5.....8.
..6.....9
..17....4
....8..3.
2....91..   SE 10.0


The pearl
Code: Select all
..14....3
.9..5..6.
2....61..
4.....7..
.5.....8.
..6.....9
..37....1
.4..8....
1....92..


Off the 456789 lines, here is this very large pearl.
Code: Select all
1..9...7.
.5...7..9
....4.6..
.....38..
2..6....5
..4.5..6.
..1..8..6
.9.1..7..
8...2..1.


Enjoy!
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GC12 : A Pearl Solitaire

Postby gurth » Tue Dec 12, 2006 12:30 pm

GC12 : Pearl Solitaire

Code: Select all
  . . 7 4 . . . . 3
  . 5 . . 9 . . 2 .
  8 . . . . . 1 . .
  6 . . . . 3 . . .
  . 4 . . . . . 5 .
  . . . 1 . . . . 7
  . . 3 . . . . . 9
  . 2 . . 8 . . 4 .
  1 . . . . 5 6 . .   SE 7.3, Pearl 7.3


To solve the first cell, SE uses many 7+ chains, up to 7.3: quite a sizeable Pearl. The remaining 58 cells are all singles!

That is not quite how pearl-oysters are defined: they require one hard STEP, not one hard CELL.
Unless we choose to regard solving a CELL as one STEP. That's not very satisfactory. Better to invent a new term for this beauty: a Pearl Solitaire - meaning a pearl followed by singles only.

Any challengers to GC12?

________________________________________________________

Mauricio,

Just seen your latest offerings. Wow, 10.0 on the 456789 lines is terrific. I'll try my hand on it once I have given dml's masterpieces a bit more of the attention they compel. Congratulations on your beautiful pearls.
____________________________________________________________________________________________
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Postby Mauricio » Wed Dec 13, 2006 5:45 pm

One more with 456789 lines, posted too in the hardest sudoku's thread.

Code: Select all
..14....6
.4..5..2.
9....63..
4.....7..
.5.....8.
..6.....9
..87....3
....8..1.
3....94.. SE 9.9
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Invalid Sudoku : "To Danny"

Postby gurth » Fri Dec 15, 2006 9:15 am

Invalid Sudoku : "To Danny".

Code: Select all
#To Danny

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

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



This invalid masterpiece of the culinary art is dedicated to Danny (I forget your number, daj* !) who I know will appreciate it. It may be up your street too, RW.

____________________________________________________________________
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Large jades

Postby Mauricio » Fri Dec 15, 2006 8:24 pm

Just three jades:
The first one is already posted in the hardest sudoku's thread
Code: Select all
3..6....8
.4..5..2.
..8..4...
4....86..
.5..9....
..67....3
..1...9..
8......4.
.3...1..7   ER 9.9, 8 singles


Code: Select all
8..5...6.
..7.8...1
.4...1...
4....86..
.5..4..9.
...1....8
7......4.
.6..3...9
..1..65..   ER 9.3, 19 singles


Code: Select all
3..7..9..
.9..3..1.
..7..5..2
4....61..
.5..7..3.
..69....7
..53.....
.3..5.6..
6......2.   ER 9.2, 20 singles
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GC16 and GC17

Postby gurth » Mon Dec 18, 2006 9:25 am

GC16 Octopus: A Feast of Swordfish.

Code: Select all
  1 . . 2 . . 3 . .
  . . 4 . . 5 . . 6
  . 8 . . . . . . .
  2 . . 3 . . 1 . .
  . . 5 . . . . . 4
  . 9 . . . 8 . . .
  3 . . 1 . . 2 . .
  . . 6 . . 4 . . 5
  . . . . 8 . . . .   SE 6.7


Who was it that said they loved Swordfish? This puzzle has 6.

It also qualifies as an Effortless Extreme, as there is only one chain to support that 6.7 rating. (Please correct me if I am wrong, RW).

SE Analysis results:
Difficulty rating: 6.7 / 10
This Sudoku can be solved using the following logical methods:
58 x Hidden Single
1 x Direct Hidden Pair
1 x Naked Single
1 x Pointing
9 x Naked Pair
2 x X-Wing
4 x Hidden Pair
5 x Naked Triplet
6 x Swordfish
1 x XY-Wing
1 x Forcing X-Chain

But SS solves with no XY-Wing.

Can anyone tell me: is the octopus eating the Swordfish, or are the Swordfish eating the octopus?
___________________________________________________________________________

GC17 : A 9.1 Pearl

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


This niner became a pearl in an interesting way: originally it had the same rating but 3c4 and 0k6. That was no pearl at all! But only one single was easily placed: the 3k6.

When that happens, you may be able to transform the puzzle into a pearl by adding in that first solved cell as a clue, and then finding another clue has become redundant, which on removal will restore minimality. That is what happened here.
________________________________________________________________________________________

Mauricio, just saw your latest 3 jades. They are fantastic! Thanks a ton.
Last edited by gurth on Tue Dec 19, 2006 8:26 am, edited 1 time in total.
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Re: GC16 and GC17

Postby udosuk » Mon Dec 18, 2006 4:42 pm

gurth wrote:GC17 : A 9.1 Pearl
Code: Select all
  1 . . . 2 . . 9 .
  . 7 . . . 1 8 . .
  . . 5 . . . . . 6
  2 . . 1 . . . 4 .
  . . . . 3 . . . .
  . 9 . . . 8 . . .
  . . . 9 . . 7 . .
  . . . . 4 . . 3 .
  . 8 6 . . 3 . . 5
This niner became a pearl in an interesting way: originally it had the same rating but 3d4 and 0k6. That was no pearl at all! But only one single was easily placed: the 3k6.
So what is the original puzzle looking like?
d4 (r4c4) cannot be 3 because e5 (r5c5) is 3...
I'm assuming by "0k6" you mean k6 (r9c6) becomes empty...:?:
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reTypo

Postby gurth » Tue Dec 19, 2006 12:23 pm

Sorry, udosuk, my mistake! My "3d4" should have read "3c4". I'll edit it now.
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Various plus CHALLENGE

Postby gurth » Thu Dec 28, 2006 11:01 am

Effortless Extreme (?):

Code: Select all
GC25
  . . . . . . . 7 .
  . 3 5 6 . . . . .
  4 . 6 3 . . . . .
  1 2 3 . . . . . .
  . . . . 1 9 . . .
  . . . . . . 5 . 4
  . . . 8 . . 6 . 1
  . 8 2 . . 3 . . .
  . 7 . . . 4 . . 8


Note: May be imported without export duty (or permission) to any thread.
____________________________________________________________________________

GC26

Code: Select all
  . 2 . . . 9 . . 6
  . . 3 . 8 . . 5 .
  . . . 7 . . 3 . .
  . . 6 . . 7 . . 9
  . 5 . . 2 . . 8 .
  4 . . . . . . . .
  . . 9 . . 6 . . .
  . 8 . . 5 . . . .
  7 . . 4 . . . . 1   SE 9.0

______________________________________________________________________
GC27

Code: Select all
  2 . . . . 9 . 5 .
  . 1 . . 8 . . . 4
  . . 3 7 . . . . .
  . . 6 . . . . . 9
  . 5 . . 1 . . 8 .
  4 . . . . . 7 . .
  . . . . . 6 1 . .
  7 . . . 5 . . 2 .
  . 8 . 4 . . . . 3   SE 8.5


Can mutate with 3a6, 4a6, 1a8, 7b9, 7d3, 2d9, 3f1, 8f1, 4g7, 4h8, 9h8, or 5k9.
Mutability Rating = SE x mutations = 8.5 x 12 = 102.0
Comparisons?
_________________________________________________________________________________


Gurth's Bombshell (GC28) : A New Challenge

Code: Select all
 *-----------*
 |...|..3|..2|
 |..4|...|.5.|
 |26.|9..|7..|
 |---+---+---|
 |...|.1.|.8.|
 |95.|...|3..|
 |.1.|49.|2..|
 |---+---+---|
 |8..|...|1..|
 |...|..2|..6|
 |1.9|.7.|...|
 *-----------*   SE 8.4

In nature, vertical and horizontal lines dominate. (Force of Gravity). Our eyes sit horizontally on our faces, not diagonally.

But the Force of Logic compels diagonal motifs in the hardest Sudokus. You will hardly find 2 clues on the same row or column in any box.

For lovers of shape, that makes for a very limited world. It is necessary to curb this tyranny of the diagonals with BRICKS. A brick is any two clues, within a box, in the same row or column. A triad abc of three clues in a row or column (inside a box) consists of three bricks: ab, ac and bc.

Count the bricks in GC28. There are 8. The BRICK RATING is SE x bricks = 8.4 x 8 = 67.2.

To curb the tyranny of the diagonals, let's see what are the highest BRICK RATINGS we can find (in minimal puzzles, of course).
_________________________

That is not the bombshell part, which is this: whereas SE rates this puzzle 8.4 (how I don't know, because it has already resorted to an 8.6 chain), you are CHALLENGED to solve this puzzle using NO chains, no nets, no fish, no wings, no colouring, no sets (locked or unlocked), no guesswork, no trial and error, no brute force and no computer. What you are required to use is intelligence and imagination.

That's how udosuk won the Emerald Challenge. And I shouldn't be surprised if he is the first to crack this CHALLENGE too.
_________________________________________________________________________________
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here yeah go... a solution to your challenge.

Postby StrmCkr » Thu Dec 28, 2006 1:08 pm

1/4 in row 5: E8 - 1/4/6/7 -> 1/4
1/4 in row 5: E9 - 1/4/7 -> 1/4
8/9 in col 2: A2 - 7/8/9 -> 8/9
8/9 in col 2: B2 - 3/7/8/9 -> 8/9

NAKED PAIR (Box): A2/B2 removes 8 from A3
NAKED PAIR (Box): A2/B2 removes 8 from C3
NAKED PAIR (Box): E8/E9 removes 4 from D7
NAKED PAIR (Box): E8/E9 removes 4 from D9

POINTING PAIR: 2s at E4/E5 points to E3, removing 2
POINTING PAIR: 5s at D6/F6 points to C6, removing 5
POINTING PAIR: 2s at G2/J2 points to D2, removing 2
POINTING PAIR: 5s at H1/H3 points to H7, removing 5

SINGLE: D3 set to 2, unique in Row
SINGLE: D3 set to 2, unique in Column

LBR: 3 exists only in box 7 and col 2, can remove from H1
LBR: 3 exists only in box 7 and col 2, can remove from H3
LBR: 6 exists only in box 5 and row E, can remove from D6
LBR: 6 exists only in box 5 and row E, can remove from F6

everything up to here is vaild..

everything up to here is vaild..

rest was a "guess" as suggest (proved my own anit proff of technique)
so it failed to apply. so i deleated the oignal test pattern, as it was disproved as a guess.


so then i came up with this.

*-----------------------------------------------------------*
| 57 89 157 | 678 4568 3 | 4689 1469 2 |
| 37 89 4 | 2678 268 1678 | 689 5 1389 |
| 2 6 135 | 9 458 148 | 7 134 1348 |
|-------------------+-------------------+-------------------|
| 467 47 2 | 3 1 57 | 569 8 579 |
| 9 5 78 | 2678 268 678 | 3 14 14 |
| 367 1 378 | 4 9 578 | 2 67 57 |
|-------------------+-------------------+-------------------|
| 8 2347 6 | 5 34 9 | 1 2347 347 |
| 457 347 57 | 1 348 2 | 489 3479 6 |
| 1 234 9 | 68 7 468 | 458 234 3458 |
*-----------------------------------------------------------*
[/code]

puzzle looks like the above

alright here we go again


takes a bit reading to understand the identification of a

yielding chain
and how it opperates

basically
this method uses identification of a given pattern of conjugated pairings combined with presence of bivaved cells to adocate which of n numbers held in most/all of the three conjugated pairs is the unknown n number linking both conjugated pairs together.


its a property ive note that directly shows a metod of sovlign a very important information theory question based on certificates of limiations. (cant really say more then that untill i finish my work on it).

basic idea is to form an elimation of repetative isometric solutions bye identifying them as one and the same.

ie a set chain will morph based on restricts (when n number were n has commonality to all cells (more specifically direct influence over aspects of a given conjugated als as these are the cells with directl placement limits)

i would write it out as

conjugated als chain is influenced directly by postion of N
where permates of solutiions of N directly related to specfic pattern of conjugated pairings yields a issometric solutions thus 1 valid solution .

ie.

when reduce and examing the cells with limatons(2 placements) as being n

2 solutions(issometric/palindron positions where the paired cells swap postions. = same solution (with a pair showing)

3 solutions where 2 are bounded by postion of pairings and the third is not. issometric soltions are the same soltuion just inverted or swaped, these are not the solution as a puzzle can only have 1 soltion.

4+ solutions is very complex to list all

basically it works like this

in target space of row/line/box apply identification of first identifable restrictions .
which are

2 conjugated pairs that merge on a single cell.
look for a bi valved sell, (type 1)
look for a second bivavled sell (type 2/3)
See if als falls in both bivavled cells + a thrid cell (type 2)
check to see if cells are linked directly (type 3)

identify n

here is a demestration of it for a type 3 chain.

"yielding chaing" type 3: (2 bivavle cells in same defined space where 1 is connected to conjugated pair)

since one bivavled cell is connected to a secondary bivavled cell common number in both bivave cells become the linking number of the conjugated als chain.

bivavled cells.
37 r2c1, 57 - r1c1
n = 7

quad 1:

r1c7 cannot = 7 as conjugated als = [137]
r1c3 [ 17]
r2c1 [ 73]
r3c3 [ 13]

sets r1c1 = 5

identicial move done in quad 6:
yield chain type 3:

bivavled cells:
r6c9 [79], r6c7 [ 67]
n = 7

r6c7 cannot = 7 as conjugated als = [567]
r4c7 [ 56]
R4c9 [57]
r6c7 [ 67]

the next move is identical to the above but applies to three overlapping "yeild chains" in same quadrant in this case quad 5.

two show elimnations and the thrid chains confirms both are true.

bivalved cells r4c2 [47], r5c3 [78]
n = 7

chain 1. = R5c3 cannot = 7 as conjugated als [467]

R3c1 [467]
R3c2 [47]
R6c1 [67]

Chain 2. = r5c3 cannot = 7 as conjugated als [387]

r6c1 = [37]
r6c3 = [378]
r5c3 = [78]

Chain 3 = r4c2, r5c3 cannot = 7 as conjugated als of [367]

R3c1 [67]
R6c1 [367]
r6c3 = [37]

therefore
r4c2=4,
r5c3=8

puzzle solves as singles.
Last edited by StrmCkr on Mon Jan 01, 2007 8:12 am, edited 6 times in total.
Some do, some teach, the rest look it up.
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Postby ronk » Thu Dec 28, 2006 1:41 pm

StrmCkr wrote:R3c8 cannot = 1as
R1c8 (yes)
R1c3 (no)
R3c3 (yes)
Code: Select all
At this point your pencilmark grid presumably is:

 57   89   157  | 678  4568 3    | 4689 1469 2
 37   89   4    | 2678 268  1678 | 689  5    1389
 2    6    135  | 9    458  148  | 7    134  1348
----------------+----------------+---------------
 467  47   2    | 3    1    57   | 569  8    579
 9    5    78   | 2678 268  678  | 3    14   14
 367  1    378  | 4    9    578  | 2    67   57
----------------+----------------+---------------
 8    2347 6    | 5    34   9    | 1    2347 347
 457  347  57   | 1    348  2    | 489  3479 6
 1    234  9    | 68   7    468  | 458  234  3458

And the 1s candidate grid is:

 .  .  1 |  .  .  . |  .  1  .
 .  .  . |  .  .  1 |  .  .  1
 .  .  1 |  .  .  1 |  .  1  1
---------+----------+----------
 .  .  . |  .  1  . |  .  .  .
 .  .  . |  .  .  . |  .  1  1
 .  1  . |  .  .  . |  .  .  .
---------+----------+----------
 .  .  . |  .  .  . |  1  .  .
 .  .  . |  1  .  . |  .  .  .
 1  .  . |  .  .  . |  .  .  .

There is nothing in just the 1s grid to prevent the following outcome:

 .  .  1 |  .  .  . |  .  .  .
 .  .  . |  .  .  1 |  .  .  .
 .  .  . |  .  .  . |  .  1  .
---------+----------+----------
 .  .  . |  .  1  . |  .  .  .
 .  .  . |  .  .  . |  .  .  1
 .  1  . |  .  .  . |  .  .  .
---------+----------+----------
 .  .  . |  .  .  . |  1  .  .
 .  .  . |  1  .  . |  .  .  .
 1  .  . |  .  .  . |  .  .  .

Note that r3c8=1. So you are either 1) relying on other undisclosed information or 2) guessing. Sorry, but I'm inclined to believe it's the latter.
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