## The hardest sudokus

Everything about Sudoku that doesn't fit in one of the other sections
Mauricio's puzzle
Code: Select all
`6 . .|. . 2|. 5 95 2 .|. 4 .|. 1 .. . 3|5 . .|2 . .-----+-----+-----3 . .|1 9 4|5 . .. 1 .|6 5 8|. 3 .. . 5|2 7 3|. . 1-----+-----+-----. . 4|. . 5|1 . .. 3 .|. 2 .|. 4 57 5 .|4 . .|. . 8 `
has 242 minimal sudokus, 62 of them are non isomorphic. Out of those 9 have a rating of 14 points, the rest 13. All have ER 11.0.
The solutions are nearly identical, in the puzzles with 14 points an addiditional step is needed (always r1c2<>5). This is one of them:
Code: Select all
`6.......9.2..4..1...35..2......9.5...1...8.3...5273.....4..51...3..2..4.7..4....8`
ravel

Posts: 998
Joined: 21 February 2006

ravel wrote:Wow,
congratulations for the new Explainer record, Mike.

My rating is not so exciting, 16 points, but for the first hard step it needs 6 subnets (!), which i think is a record, too.

Here is a cousin of the first, almost an isomorph, but the central value is a repeat of r3c3 and r7c7, rather than of r1c1 and r9c9:
Code: Select all
` 3 . . . . . . . 4 . 8 . 2 . . . 7 . . . 6 . . . 5 . . . 1 . 9 . 8 . . .      SE >=11.4  . . . . 6 . . . .  . . . . . 7 . 2 . . . 5 . . . 6 . . . 9 . . . 1 . 8 . 4 . . . . . . . 3`

It also reaches SE 11.4 then gives "java.lang.OutOfMemoryError: Java heap space".

Both of these puzzles have not only a symmetric clue pattern, but the values themselves also have an extraordinary degree of symmetry: box 1 reflects box 9, two values in box 3 reflect those in box 7, and the the two 'cross-bars' are identical.

Regards,

Mike Metcalf

m_b_metcalf
2017 Supporter

Posts: 9661
Joined: 15 May 2006
Location: Berlin

Just curious ... For either of the 11.4+ puzzles, would anyone care to post the complete candidate grid just at the point where SE goes into never-never-land?
r.e.s.

Posts: 337
Joined: 31 August 2005

As Mike said, this puzzle is very similar to its brother, 16 points and 6 subnets in the first step.

I dont know, which eliminations Sudoku Explainer can make from the starting grid (after 2 hidden pairs):
Code: Select all
` *-----------------------------------------------------------------------* | 3      257    1279    | 15678  15789   569    | 28      169    4      | | 159    8      149     | 2      13459   34569  | 139     7      169    | | 1279   247    6       | 13478  134789  349    | 5       139    28     | |-----------------------+-----------------------+-----------------------| | 2567   1      2347    | 9      2345    8      | 347     3456   567    | | 25789  23457  234789  | 1345   6       2345   | 134789  13459  15789  | | 5689   3456   3489    | 1345   1345    7      | 13489   2      15689  | |-----------------------+-----------------------+-----------------------| | 18     237    5       | 3478   234789  2349   | 6       149    1279   | | 267    9      237     | 34567  23457   1      | 247     8      257    | | 4      267    18      | 5678   25789   2569   | 1279    159    3      | *-----------------------------------------------------------------------*`
But even with using subnets in contradiction chains my program can only make 11 eliminations of numbers, which would lead to at least one other elimination then.
Code: Select all
`3 subnets, progress 2: r1c4<>6, r9c6<>6, r4c1<>6, r6c9<>66 subnets, progress 8: r1c2<>5, r2c3<>47 subnets, progress 11: r2c9<>6, r4c8<>67 subnets, progress 8: r3c9<>38 subnets, progress 8: r8c7<>4, r9c8<>5`

Only 8 candidates could be eliminated with a single subnet:
Code: Select all
`r3c5<>34, r5c7<>34, r1c5<>5, r5c9<>5, r2c6<>9, r8c4<>7`
[Added:] As i saw now, SE found 6 of them (not the two 3's), then got out of memory.
ravel

Posts: 998
Joined: 21 February 2006

I started from this pattern,
Code: Select all
`*.......*.*.*.*.*...*...*....*.*.*.*.....*.....*.*.*.*...*...*...*.*.*.*.*.......*`

and the result of finding some hours.
6.......3.4.7.6.1...7.......8.1...2.....4.....2.5.7.9...5...7...1.2...4.3.......6 ER=6.9
6.......3.4.7...1...7.......8.1.9.2.....4.....2.5...9...5...7...1.2.3.4.3.......6 ER=7.2
6.......3.4.2.8.5...1...9...2.8.5.1.....9.....7...4.....2...5...8.4...7.3.......6 ER=7.2
6.......3.4.2.8.5...1...9...2.8.5.1.....9.....7.3.......2...5...8.4...7.3.......6 ER=7.2
3.......8.5...2.7...9...4.....3.4.1.....9.....7.8.6.2...2...1...9.6.8.5.4.......7 ER=7.3
7.......4.9.5.1.8...8...3...5.8.3.6.....4.....4.7.2.9...1...7.....6.8...3.......2 ER=7.4
7.......9.8.3.2.5...6...2...3.9.1.8.....6.....5.2.4.6...2...3...9.5...4.5.......1 ER=8.2
4.......5.8.3.9.....1...2...7.6...8.....9.....3.8.5.9...5...6...4.1.8.5.2.......3 ER=8.3
9.......3...7.3.6...4...5...1...6.8.....5.....9.2.7.....2...1...7.9.8.3.5.......4 ER=8.9
3.......7.4...5.9...2...6.....8.9.1.....2.....8.3.4.5...5...1...9.6.8.4.7.......9 ER=9.0
1.......5.6.8.3.2...2...4...2.5.6.7.....3.....8.1.2.....8...1...7.6...5.4.......9 ER=9.1

continue hoping a result will become this pattern.
Code: Select all
`*.......*.*...*.*...*...*......*.*.*.....*.....*.*.*.....*...*...*.*...*.*.......*`
Eioru

Posts: 182
Joined: 16 August 2006

Hi Eioru,

i am not sure about the purpose of your post. The puzzles are easy (max. 4 points) compared to the hardest and the second pattern is very well searched by JPF and Mike M. So it is unprobable to find any more big nuggets there.
ravel

Posts: 998
Joined: 21 February 2006

Have we got hard sudokus for all the possible potential patterns with 21 clues and under ?.....
Code: Select all
`21a133    b322   c333   d333   e233   f132 313     232    303    331    303    323 331     223    033    302    331    232    and others20a133   b033 303    322 331    32219a222   b123 232    321 222    232`

No we hadnt ! - "and others" refered to JPFs and MMs efforts:
Code: Select all
`21 3131513132031314131319*313131313`

Will the 19* of this pattern be difficult ?
Code: Select all
`*.......*.*...*.*...*...*........*.*.....*.....*.*.......*...*...*.*...*.*.......*`
coloin

Posts: 1746
Joined: 05 May 2005

coloin wrote:Will the 19* of this pattern be difficult ?
Hard to say, but i dont expect it. Do you remember Nick70's exhaustive search for all sudokus with this pattern, which also looks promisimg ?
Code: Select all
`*...*.......*...*...*...*...*...*...*...*...*...*...*...*...*...*...*.......*...*`
There are (only) 851 puzzles, and only one is a toughie with 10 steps and ER 9.1:
Code: Select all
`100050000000200030004000600090003000600070005000100070001000200030009000000060001`
ravel

Posts: 998
Joined: 21 February 2006

Will the 19* of this pattern be difficult ?
Code: Select all
`*.......* .*...*.*. ..*...*... .....*.*. ....*.... .*.*..... ..*...*.. .*.*...*. *.......* `

yes they are just as difficult you can mirror the puzzle along the middle column swamping all rows horizontally like this .

and the rating stays the same
Code: Select all
` *-----------* |9..|...|..5| |.7.|..1|.2.| |..3|...|8..| |---+---+---| |...|2.7|.4.| |...|.5.|...| |.1.|6..|...| |---+---+---| |..8|...|3..| |.2.|4..|.6.| |5..|...|..9| *-----------*`

you can do the same thing on ocean's new's present and christmas as well and the rateing stays the same...

my 2 cents ....(isn't this called automorphes??)

strmckrs
Some do, some teach, the rest look it up.

StrmCkr

Posts: 942
Joined: 05 September 2006

How these two pattern? I feel it's too hard to find one puzzle.
Code: Select all
`.....*.....*.*.*...*.*...*.*.....*...*..*..*...*.....*.*...*.*...*.*.*.....*.....`

Code: Select all
`.....*.....*.*.......*...*.*...*.*...*.*.*.*...*.*...*.*...*.......*.*.....*.....`
Eioru

Posts: 182
Joined: 16 August 2006

Eioru wrote:How these two pattern? I feel it's too hard to find one puzzle.
Code: Select all
`.....*.....*.*.*...*.*...*.*.....*...*..*..*...*.....*.*...*.*...*.*.*.....*.....`

Well, here's the first:

Code: Select all
` . . . . . 9 . . . . . 7 . 1 . 3 . . . 2 . 4 . . . 6 . 8 . . . . . 9 . . . 6 . . 7 . . 5 . . . 3 . . . . . 2 . 8 . . . 6 . 4 . . . 9 . 3 . 1 . . . . . 2 . . . . . SE 9.1`

Regards,

Mike Metcalf

m_b_metcalf
2017 Supporter

Posts: 9661
Joined: 15 May 2006
Location: Berlin

Two more:
Code: Select all
`.....7.....2.5.9...1.8...3.1.....8...7..9..1...4.....2.6...1.7...9.2.4.....3.....  ER 7.2.....6.....1.9.7...2.8...5.3.....1...8..7..9...6.....2.5...2.8...7.1.3.....9.....  ER 9.1`
So it seems that this pattern is comparable to many others that follow tso's rule of thumb (high ratings on average).
ravel

Posts: 998
Joined: 21 February 2006

m_b_metcalf wrote:Here is a cousin of the first, almost an isomorph, but the central value is a repeat of r3c3 and r7c7, rather than of r1c1 and r9c9:
Code: Select all
` 3 . . . . . . . 4 . 8 . 2 . . . 7 . . . 6 . . . 5 . . . 1 . 9 . 8 . . .      SE >=11.4  . . . . 6 . . . .  . . . . . 7 . 2 . . . 5 . . . 6 . . . 9 . . . 1 . 8 . 4 . . . . . . . 3`

It also reaches SE 11.4 then gives "java.lang.OutOfMemoryError: Java heap space".

I have discussed this puzzle privately with the author of Sudoku Explainer, Nicolas Juillerat, who kindly provided the information below.

Regards,

Mike Metcalf

==========================================

A very difficult and interesting puzzle. It seems to require nested chains with multiple inferences. I have not seen this before.

It is still possible to rate this puzzle with the current version of the Sudoku Explainer. But you need to start the .jar file from a command line, and to use the "-Xmx" option to tell the Java VM to use more memory (by default it only uses a fraction of the available memory). For instance:

java -Xmx500m -jar SudokuExplainer.jar

starts the application and tells the Java VM to use at most 500MB. This should be enough to solve the puzzle.

By the way, if you have installed the full Java JDK (not only the JRE), you may want to use the java command from the jdk, and to also add the "-server" option: the GUI gets less responsive but the long analyses run faster (about 2h20 instead of 3h15 on my computer).

Difficulty rating: 11.4

57 x Hidden Single
2 x Direct Hidden Pair
1 x Naked Single
5 x Pointing
2 x Naked Pair
1 x X-Wing
3 x Hidden Pair
2 x Naked Triplet
1 x Swordfish
1 x XY-Wing
1 x BUG type 1
1 x Forcing X-Chain
1 x Bidirectional Cycle
8 x Forcing Chain
2 x Nishio Forcing Chains
14 x Region Forcing Chains
5 x Cell Forcing Chains
1 x Dynamic Cell Forcing Chains
7 x Dynamic Contradiction Forcing Chains
3 x Dynamic Region Forcing Chains
3 x Dynamic Contradiction Forcing Chains (+)
11 x Dynamic Contradiction Forcing Chains (+ Forcing Chains)
2 x Dynamic Region Forcing Chains (+ Forcing Chains)
5 x Dynamic Contradiction Forcing Chains (+ Multiple Forcing Chains)
2 x Dynamic Region Forcing Chains (+ Dynamic Forcing Chains)
4 x Dynamic Contradiction Forcing Chains (+ Dynamic Forcing Chains)

m_b_metcalf
2017 Supporter

Posts: 9661
Joined: 15 May 2006
Location: Berlin

{removed}
Last edited by AW on Sat Feb 17, 2007 10:40 am, edited 1 time in total.
AW

Posts: 27
Joined: 31 January 2007

AW wrote:Is my back-door finder broken or does Mike's

Code: Select all
`500000009020100070008000300040702000000050000000006010003000800060004020900000005`

really not have any strict back-door pairs (that crack the puzzle with only naked or hidden singles remaining) ????

If I understand your meaning of "backdoor pairs" ...

(r1c5=7 and r9c6=8) or (r2c6=9 and r9c8=4) or (r5c8=3 and r7c9=6)

... require only following singles.
ronk
2012 Supporter

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

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