Looking for some very very very hard sudoku

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

Postby ravel » Mon May 22, 2006 9:16 am

RW wrote:It seems to be a lot harder to make superfiendish puzzles with few clues. Can anybody explain this?

No, not really, i can only say, that the most low clue puzzles have many simple steps from the beginning (giving e.g. nearly all placements of one or two numbers), otherwise it is very hard to keep them unique. I also noticed that the 34-clues on average seem to be harder than the 17-clues.

Also, have you ran the known 17s through your program to find out if there are any really tough there?

As i said elsewhere, in the moment i only can check puzzles one by one and the program is very slow. So also when the program will be able to read the puzzles from the list, going through the whole list would take too long for me.
Nick70 had posted his ratings here, but without listing the toughies.
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Postby maria45 » Wed Aug 02, 2006 4:17 pm

About the most difficult 17-clue-sudoku I encountered in the first 86 puzzles of a collection of 450 sudokus with 17 clues is this:
Code: Select all
#77

   1 2 3   4 5 6   7 8 9
 +-------+-------+-------+
a| . . . | 4 7 . | . 3 . |
b| . 1 5 | . . . | . . . |
c| . . . | . . . | . 2 . |
 +-------+-------+-------+
d| 4 . . | 3 2 . | . . . |
e| . 6 . | . . . | 9 . . |
f| . . . | 8 . . | . . . |
 +-------+-------+-------+
g| . . . | . . 1 | 5 . 6 |
h| 3 . . | . . . | . . . |
k| . . . | . . . | 1 . . |
 +-------+-------+-------+


but which is solved by some simple forcing chains. I observed like Ravel that the 17-clue puzzles must be easier than the real toughies because they have to generate already in the beginning or just a few numbers later nearly always one number complete, i.e. for example, fill the 1 in all cells. To prove this, one could think about constructing/finding a real toughie with one number in all cells already given. An algorithm could be: take a 17-clue, add all 1, then reduce the not needed other numbers. If it is still a toughie, the hypothesis is false.

Greetings, Maria
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Postby ravel » Thu Aug 03, 2006 9:07 am

As i said in the hardest sudokus thread i have scanned those 450 puzzles, which Eppstein did not solve with rather simple methods. None was hard enough for my list. So i was more surprised, that Oceans BB with only 20 clues could be that hard.

This one (note that all 3's are resolved with singles at the beginning) can be solved with one 5 cell chain:
Code: Select all
2689  289    289  | 4    7      5    | 68   3      1         
678   1      5    | 2    68     3    | 4    6789   789       
678   3      4    | 16   1689   689  | 678  2      5         
-------------------------------------------------------
4     5      789  | 3    2      679  | 678  1      78         
128   6      3    | 15   145    47   | 9    4578   2478       
129   279    279  | 8    14569  4679 | 3    4567   247       
-------------------------------------------------------
289   24789  2789 | 79   3      1    | 5    4789   6         
3     4789   1    | 56   4568   468  | 2    4789   4789       
5     4789   6    | 79   48     2    | 1    4789   3         

r5c8=5 => r6c5=5 => r3c5=9 => r3c4=1 => r5c4=5
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Just saw this puzzle and thought of snow-crystals

Postby claudiarabia » Sun Oct 29, 2006 1:16 pm

maria45 wrote:About the most difficult 17-clue-sudoku I encountered in the first 86 puzzles of a collection of 450 sudokus with 17 clues is this:
Code: Select all
#77

   1 2 3   4 5 6   7 8 9
 +-------+-------+-------+
a| . . . | 4 7 . | . 3 . |
b| . 1 5 | . . . | . . . |
c| . . . | . . . | . 2 . |
 +-------+-------+-------+
d| 4 . . | 3 2 . | . . . |
e| . 6 . | . . . | 9 . . |
f| . . . | 8 . . | . . . |
 +-------+-------+-------+
g| . . . | . . 1 | 5 . 6 |
h| 3 . . | . . . | . . . |
k| . . . | . . . | 1 . . |
 +-------+-------+-------+


but which is solved by some simple forcing chains. I observed like Ravel that the 17-clue puzzles must be easier than the real toughies because they have to generate already in the beginning or just a few numbers later nearly always one number complete, i.e. for example, fill the 1 in all cells. To prove this, one could think about constructing/finding a real toughie with one number in all cells already given. An algorithm could be: take a 17-clue, add all 1, then reduce the not needed other numbers. If it is still a toughie, the hypothesis is false.

Greetings, Maria


Constructing Sudokus I found regarding the sudokus with 17-20 clues you will find at the bottom of difficulty-level ranging from ER 1,2-2,6 many sudokus, then only a few sudokus in the middle level from 3-6 and then suddenly beginning from ER-Level 7,1 they are mashrooming again.

It is like with the snow-cristals. When the degree is about 0-3 celsius you have a plenty of crystals. From -3 - -20 degree celsius there are almost no crystals. From minus 20 degree celsius again appear plenty of cristal shapes. The Japanese found it out. So I think there is a connection between Sudoku and kryology and that's why the Japanese are involved in both.

Claudia
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test this "invictus" grid : good luck :-)

Postby dml » Fri Nov 17, 2006 2:27 pm

+------+-----+------+
| 6 . . | 1 . . | . . 3 |
| . . 4 | . 2 . | . . . |
| . . . | . . 7 | 8 . . |
+-----+-----+------+
| . . 7 | . . 6 | 1 . . |
| . . 5 | . . . | . . 2 |
| 8 . . | 9 . . | . . 4 |
+-----+------+-----+
| 1 . . | . 4 . | . 6 . |
| . . . | . . 5 | 7 . . |
| . 3 . | 8 . . | . . . |
+-----+------+-----+
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Postby Carcul » Wed Nov 22, 2006 11:50 am

Dml wrote:test this "invictus" grid : good luck:)


Grid tested. Here is the result:

Code: Select all
 *-------------------------------------------------------------*
 | 6      7      289  | 1      589    489  | 2459   2459   3   |
 | 359    189    4    | 6      2      389  | 59     159    7   |
 | 2359   129    13   | 345    359    7    | 8      12459  6   |
 |--------------------+--------------------+-------------------|
 | 2349   249    7    | 2345   358    6    | 1      3589   589 |
 | 349    1469   5    | 34     1378   1348 | 369    3789   2   |
 | 8      126    13   | 9      1357   123  | 356    357    4   |
 |--------------------+--------------------+-------------------|
 | 1      5      289  | 7      4      239  | 239    6      89  |
 | 249    2489   2689 | 23     1369   5    | 7      2389   189 |
 | 7      3      269  | 8      169    129  | 2459   2459   159 |
 *-------------------------------------------------------------*

1. [r8c4]=2=[r4c4](-2-[r6c6]=2=[r6c2]=6=[r6c7]-6-[r5c7])=5=[r3c4]-5-
-[r3c1]=5=[r2c1]-5-[r257c7]-2-[r7c6|r8c8], => r7c6/r8c8<>2.

2. [r8c4]=2=[r4c4]=5=[r3c4]-5-[r3c1]=5=[r2c1]=3=[r2c6]-3-[r7c6]=3=
=[r7c7]=2=[r7c3]-2-[r8c123]=2=[r8c4], => r8c4=2.

3. [r1c5]=5=[r1c78]-5-[r2c78]=5=[r2c1]=3=[r2c6]-3-[r7c6](-9-[r9c56]-6-
-[r9c3])=3=[r7c7]=2=[r7c3]-2-[(r9c3)]-9-[r8c12]-8-[r2c2]=8=[r1c3]-8-[r1c5], => r1c5<>8.

4. [r1c5]=5=[r1c78]-5-[r2c78]-1,9-[r2c2]-8-[r1c3]-9-[r1c5], => r1c5<>9.

5. [r1c6]-8-[r2c6]-3-[r7c6]=3=[r7c7]=2=[r7c3]-2-[r9c356]-9-[r9c78]=9=
=[r1c78]-9-[r1c3]-8-[r1c6], => r1c6<>8 and the puzzle is solved.

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INVICTUS by dml

Postby gurth » Thu Nov 30, 2006 9:13 am

INVICTUS by dml

It's 7.10am. My before-breakfast fun was to solve this nice SE=8.2 puzzle from dml using the method of StrmCkr. As I owe it to you two, I dedicate my solution to you both and post it in reply to your two threads.

I started by using SS (my usual cop-out from work) to get to the grid below.
Code: Select all
 *-----------*
 |6..|1..|..3|
 |..4|.2.|...|
 |...|..7|8..|
 |---+---+---|
 |..7|..6|1..|
 |..5|...|..2|
 |8..|9..|..4|
 |---+---+---|
 |1..|.4.|.6.|
 |...|..5|7..|
 |.3.|8..|...|
 *-----------*
 *--------------------------------------------------------------------*
 | 6      7      289    | 1      589    489    | 2459   2459   3      |
 | 359    189    4      | 6      2      389    | 59     159    7      |
 | 2359   129    13     | 345    359    7      | 8      12459  6      |
 |----------------------+----------------------+----------------------|
 | 2349   249    7      | 2345   358    6      | 1      3589   589    |
 | 349    1469   5      | 34     1378   1348   | 369    3789   2      |
 | 8      126    13     | 9      1357   12     | 356    357    4      |
 |----------------------+----------------------+----------------------|
 | 1      5      289    | 7      4      239    | 239    6      89     |
 | 249    489    2689   | 23     1369   5      | 7      2389   189    |
 | 7      3      269    | 8      169    129    | 2459   2459   159    |
 *--------------------------------------------------------------------*

Column 4 is the most obvious group for immediate analysis, and we find several controlling candidates in this column: 3c4, 4c4, 2d4, 3d4, 4d4, and 3h4. Each of these controls all the cells in the column. So let's look to see which of them also control more other cells. Right off the top, 3c4 looks promising: it'll hit c3 and f3 immediately, and put a 4 in a6. All that stands out a mile, so we test 3c4 and it turns out to be a magic candidate which solves the puzzle by singles only!

That's what I call satisfying guesswork.

_______________________________________________________________________
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Postby StrmCkr » Fri Dec 01, 2006 12:52 pm

removed
Last edited by StrmCkr on Sat Dec 13, 2014 6:41 am, edited 5 times in total.
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Postby ravel » Fri Dec 01, 2006 2:59 pm

StrmCkr,

can you apply your method to gfroyle's beauty (some pages above), please ? I dont see where to start, though it fell out of the hardest list.
Code: Select all
6.. ... ..3
.7. .8. .9.
..2 ... 5..

... 3.. ...
.8. .1. .7.
... ..2 ...

..5 ... 1..
.9. .4. .8.
3.. ... ..2
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Postby StrmCkr » Sat Dec 02, 2006 7:26 am

removed
Last edited by StrmCkr on Sat Dec 13, 2014 6:41 am, edited 1 time in total.
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Postby ravel » Mon Dec 04, 2006 8:29 pm

Hi StrmCkr,

thanks for the elaborate response, glad to have found a challenge for you, but i must admit, i cant follow the solution at all.

Code: Select all
 *-----------------------------------------------------------------------------*
 | 6       145     89      | 124579  2579    14579   | 78      124     3       |
 | 145     7       134     | 12456   8       13456   | 246     9       146     |
 | 89      134     2       | 14679   3679    134679  | 5       146     78      |
 |-------------------------+-------------------------+-------------------------|
 | 124579  12456   14679   | 3       5679    456789  | 24689   12456   145689  |
 | 2459    8       3469    | 4569    1       4569    | 23469   7       4569    |
 | 14579   13456   134679  | 456789  5679    2       | 34689   13456   145689  |
 |-------------------------+-------------------------+-------------------------|
 | 2478    246     5       | 26789   23679   36789   | 1       346     4679    |
 | 127     9       167     | 12567   4       13567   | 367     8       567     |
 | 3       146     14678   | 156789  5679    156789  | 4679    456     2       |
 *-----------------------------------------------------------------------------*
StrmCkr wrote:as 2 cells are placed in quad four, the 4 is restricted to only fallling in E1/E3 as well as being restriced in the row.

All i can see is, that if you place 2 in e1 or 3 in e3 then e7 is fixed to 3 or 2. But no restriction for 4, neither in the row nor in the box. So i suppose you are just guessing, that 4 is in e1 or e3?
remove the 9 common restricted

What does that mean ? You assume, that there is no 9 in that box ? From a wrong premise you can follow everything, i.e. when you reinsert the 9, this can be right or wrong. It sets F9=9 ? Suppose you meant E9 ? Then yes, but all under the 2 assumptions, that i would not call educated guessing.

Sorry. i stopped reading here.
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Postby StrmCkr » Tue Dec 05, 2006 7:07 am

removed
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Postby ravel » Tue Dec 05, 2006 12:20 pm

When you look at row E, you have:
Code: Select all
 | 2459    8       3469    | 4569    1       4569    | 23469   7       4569    |
There are the following ways to place 2 and 3:
Code: Select all
 | 2       8       3       | 4569    1       4569    |   469   7       4569    |
 | 2       8       469     | 4569    1       4569    |   3     7       4569    |
 | 459     8       3       | 4569    1       4569    |   2     7       4569    |
So there are still 6 possible positions for the 4. Why should the 4 be restricted to only falling in E1/E3 ? Even if you exclude the first one for some reason, i cannot see, why it should be more probable, that the 4 is in E1 or E3 than in E469. And why dont you restrict the common 9 to those cells?
Thats why i call it a guess.

Now to the 9. Your conclusions are made based only on the candidates in box 5, right?
(i eliminated the 4's in the middle line, as you did):
Code: Select all
+-------------------------+
| 3       5679    456789  |
| 569     1       569     |
| 456789  5679    2       |
+-------------------------+
What i can see here is a hidden pair 48 (or naked quad 5679), which would lead to
Code: Select all
+-------------------------+
| 3       5679    48      |
| 569     1       569     |
| 48      5679    2       |
+-------------------------+
No question, that the 9 can be in E4 or E6.

But after eliminating and reinserting the 9 you have
Code: Select all
+-------------------------+
| 3       79      48      |
| 56      1       56      |
| 48      79      2       |
+-------------------------+
This is just a guess again. (Why dont you remove and reinsert 5 or 6 to show that they cannot be in E46 ??)
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Postby StrmCkr » Wed Dec 06, 2006 2:30 am

removed
Last edited by StrmCkr on Sat Dec 13, 2014 6:41 am, edited 1 time in total.
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