Some nice, very hard, Sudoku's

Henk · Last edited by Henk on Tue Jan 31, 2006 9:54 am; edited 1 time in total

I have created some very difficult sudoku's with my generator. I want to share them with you for two reasons:
- Are they really that difficult, or is my rating allgoritm rubbish
- I like solving difficult puzzles and I think you do too!.. Razz

The puzzles can be copy/pasted in any program you like or can be printed directly. They can be found here:

http://www.intosudoku.com/searchpuzzles.php
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Carcul · Posted: Wed Jan 25, 2006 3:46 pm Post subject:

Hi Henk.

I have checked your website and tried manually puzzle #74, which I guess is the hardest acording to your rating (High rating 19307) (correct me if I am wrong). I have solved that puzzle with two chains after the basic steps, and so, just as a personal opinion, I rate it as "Medium" (or "Hard" at most, but never "Very Hard"). So, as a final coment, I think your rating algoritm could be improved.

Regards, Carcul

Henk · Posted: Wed Jan 25, 2006 4:05 pm Post subject:

With two chains you main two forcing chains? That is incredably difficult to solve on paper isn't it? My solver has Remote Pairs, (Multi-)Color, XY-Wing and XYZ-Wing as the most difficult solving techniques. I guess I could improve this with forcing chains and the uniqueness test. But are these puzzles still solvable for humans? And how about solving those on paper?
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Carcul · Posted: Wed Jan 25, 2006 6:43 pm Post subject:

Hi Henk.

Henk · Posted: Thu Jan 26, 2006 7:39 am Post subject:

md68 · Posted: Thu Jan 26, 2006 8:27 am Post subject:

He means puzzle nr. 74.

btw..i checked most of them with other solvers and even Sadmans Sudoku needs for most of them a guess and can't solve it by logic which certainly Henks Program can without having to guess.

Henk · Posted: Thu Jan 26, 2006 9:46 am Post subject:

My solver uses the folowing to solve puzzle #74:

Single in box: 42x
Singles in row: 10x
Singles: 3x
Pointing pair: 1x
Box line reduction: 3x
Swordfish: 1x
Colors: 4x
MultiColors: 1x
XY-Wing: 3x
XYZWing 1x
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Carcul · Posted: Thu Jan 26, 2006 10:38 am Post subject:

Hi Henk.

Regarding #74, my solution is considerably shorter: after the basic steps (20 hidden singles and 4 eliminations due to locked candidates) I have used 2 chains to solve the puzzle. BTW, I have already checked puzzle #111: although not hard, it is an interesting and well constructed puzzle, showing variety. Good work.

Regards, Carcul

Henk · Posted: Thu Jan 26, 2006 11:03 am Post subject:

I guess you won't find any off my puzzles hard, because my solver doesn't use forcing chains or uniqueness tests.

We are rating puzzles different btw. While you are looking at the most difficult technique used and the shortest path, I also take the variety of the used techniques into te rating. But you are right, if I implement more solving techniques, I could generate and rate more difficult puzzles!

I also want to make the rating algoritm configurable, so the player can have influence about how hard a technique is rated.
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Henk · Posted: Thu Jan 26, 2006 9:23 pm Post subject:

I improved the rating system with forcing chains. Nice technique and indeed not to hard to spot. The following puzzle needs this technique to be solved.

..4.6.1..
.........
.219.738.
.1.3.5.4.
..2.9.8..
.6.8.1.9.
.874.326.
.........
..9.8.4..

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graysky · Posted: Fri Jan 27, 2006 11:04 pm Post subject: puzzle #74 has two solutions!

henk -- your puzzle #74 has two solutions:

using my new program which solves sudoku using NO bifurcation -- in fact it uses a solving technique i have developed that investigates all forcing chains throughout the grid -- i call this technique "yinyang" and will write it up soon -- look for it -- it is VERY powerful!! anyway, using my program, i tried to solved your puzzle #74; with starting grid (zeros are not defined):

0 1 0 0 0 0 8 6 0
0 0 5 0 0 0 1 0 4
0 0 8 0 2 9 0 0 0

4 0 1 2 6 0 0 0 8
9 0 0 0 0 0 0 0 0
0 7 0 5 0 0 0 0 6

0 0 0 0 0 0 0 0 0
5 0 0 0 0 0 4 0 1
0 2 0 9 0 4 0 3 0

the computed solution is:

7 1 9 4 5 3 8 6 2
2 3 5 8 7 6 1 9 4
6 4 8 1 2 9 5 7 3

4 5 1 2 6 7 9 5 8
9 6 2 3 4 8 2 1 7
8 7 3 5 9 1 3 4 6

3 8 4 x 1 5 y 2 9
5 9 x y 3 2 4 8 1
1 2 y 9 8 4 x 3 5

where the x and y cells can alternatively be x=6, y=7 or x=7, y=6.

how is it that your program creates sudoku grids with more than one possible solution??

i am looking for really tough-to-solve puzzles that my yinyang program cannot solve. although i can conceptually create a situation that "yinyang" won't catch, i have yet to find one! anyone know of a "unsolvable" puzzle (can't be solved without trial and error)?

Ruud · Site Admin

graysky · Posted: Fri Jan 27, 2006 11:48 pm Post subject: oops!

thanks ruud --

yeah, i guess my "yin yang" still needs a little more tweaking. i'm close though. i'll let you know...

Henk · Last edited by Henk on Tue Jan 31, 2006 10:05 am; edited 1 time in total

eclark · Posted: Sat Jan 28, 2006 4:28 pm Post subject:

Henk I really like your website. Actually right now I am in the middle of implementing a multi user sudoku repository. Where people can store their puzzles and their solutions. Making them either public or private. And it will rate them based upon all of the solvers that I can get my hands on. Right now I have about 2 million in the database. Hopefully the website will be going public soon(and I can handle the bandwidth of people downloading 10000 puzzles at a time.)

So its very much like yours with a few little extras.