dailysudoku.com

[someone_somewhere]

Hi,

For me, up to now, this is the hardest Sudoku I ever encountered:

[someone_somewhere]

Hi,
I have found only 1 digit:
8 in r5c5

and after a lot of applying the "double implication chain" technique,
I got up to this:

[someone_somewhere]

Sorry, I think that I copied (the first Sudoku that I have posted) it wrong.
Because of this it could have multiple solutions, which I can not check.

It looks like I have missed the digit 7 in r8c1. This is because I found between I stored puzzles one from Doug Bowman, which looks like:

[David Bryant]

[someone_somewhere]

Hi David,

A big THANK YOU. You made my day.
Could you give me the link to the page of the solver you have used?

Yup, the puzzle with the additional 7 is even so one of the most difficult ones. The 3D Meduza is cnacking it. I used "double implication chains" which are equivalent to 3D Meduza and it is solving it.

for 3D Meduza see:
http://www.stolaf.edu/people/hansonr/sudoku/top95-analysis.htm#medusa

see u,

[David Bryant]

[someone_somewhere]

Hi David,

I told you, that it is "one of the/the" most difficult ones.

The same way one is solving and having fun with classic techniques,
one can have fun using the highly advanced techniques.

You will not need a computer program in order to use the "double implication" chains.
I found at the Internet page (you have mentioned):
http://krazydad.com/sudoku/
the "Super Tough" (Sudoku Puzzles by Jim Bumgardner)
as adequate for training this technique.

The difference is that you work with the "candidate table" instead of the "Sudoku table". Now one has to find the "4 start constellations" or the "5 star constellations" (if possible without writing the double implication chains on the paper, just trying to keep them in the head).

Some/most of them can be cracked after finding only one "star constellation" and this is all the fun.
The problem is from where and which digit to start the double implication chain technique.

The best strategy that I have found, up to now, is to start from the pairs (as I have mentioned in one of my previous messages). This because if one came to a contradiction, than one digit from the pair can be eliminated (unfortunate, not in all cases) and the other digit is the one we where looking for this cell.

Lately, I have found out that for some puzzles, there are "too less" pairs, so I did not know what to do next. I found that it makes a lot of sence (meaning it looks to be a good strategy) to start with a digit from a cell of the candidate table that has more than 2 as candidates, (as I say, from a digit) that when eliminated, an other one from the row/column/3x3 block can be marked as beeing part of the solution.

If you select random a digit and do the "double implication chain" strating from it, you can find out [after a lot of work] that you can eliminate it from the candidate table, but after this ... you will notice that you did not make a substantial progress, meaning that you will have to pick an other one to continue.

Example for puzzles which you can crack after finding one constallation are a challanging nice start for a training.
See Super-Tough example 8 from book 8 from the above link.

I could make a list of examples, for interested solvers, who want to solve Sudoku's beyond the advanced techniques and that have only one "star constellation" after which it can be cracked.

Just let me know (I don't want to work on it, if the market has no need ...)

see u,

P.S. sorry if it was to "chinezee" for some of the readers, but if you take a look at the "double implication chain" techniques, you will understand what I was trying to explain [I am sure].
P.P.S. my message was still shorter than the average ones from Alan

[someone_somewhere]

There is no general limit between "logic" and "trail and error".

The limit is different for every human solver:

"Trail and error" starts from where our "logic and memory" gets to the it's limit.

see u,

[Guest]

ill try it, but it seems that even a computer had to guess to get the final answer

Difficulty score: 4401
Number of guesses required: 4

[Guest]

i put in the revised one and it gave me an even harder difficulty level

Difficulty score: 9610
Number of guesses required: 9

[ravel]

Its a toughie, but with 3 brute force steps not hard enough to add it to my toughest list.
Brute force step means, that by setting a cell to a value, my (rather simple) program enounters a contradiction using singles, k-tuples, locked candidates, x-wing and UR type 1.

Using those eliminations it can be solved with the same techniques:
r2c3<>4, r3c5<>1, r3c2<>9 or
r3c3<>4, r2c3<>4, r3c5<>1
(in arbitrary order)

[ravel]

For the zen sudoku fans: I started a new thread now with ultrahard puzzles: The hardest sudokus