Comments for blog.limedaley.com/post/hardest-sudoku-puzzle

Comment #783

2009-03-28T02:40:27Z

Ah, I should have looked it up before commenting. Pattern overlays are not for humans, at least not when you only have 26 numbers filled in.

I let my solver keep going, and it made a number of guesses to remove certain possibilities before it finally found another number using logic. I am probably not going to continue this puzzle, unless I can find another solver that is as nice as scan raid's to explain how it does it.

Comment #782

2009-03-28T02:33:59Z

I came across this puzzle (see the comment about halfway down the page, by 'YH') again, had a photocopy of it lying around somewhere. I haven't done very many sudokus lately, (so might as well start with a hard one, right?)

I actually did much better than I had previously done - I got 8 numbers written in this time, before I plugged it into my favorite sudoku solver. I was happy to see it not find anything I didn't know about, until it got to a new rule, the "hidden unique rectangle" issue, which is an interesting rule, and maybe one I'll be able to keep in my head.

Unfortunately, in this case, it didn't help all that much, just removed one possibility, leaving me stuck again. I was happy to see the solver again not find anything until the "pattern overlay" issue, which I hadn't heard of, and is listed as the hardest issue this particular solver knows how to solve before going to trial and error. Unfortunately, the documentation is being rewritten, and the issue involves looking at 5 squares, none of which are in the same row or column, so too hard for me to guess what the rule is. I'll have to look up the rule elsewhere, and see if I can figure out what it means.

While looking around on his site, I found a Sudoku Song, which is entertaining.

Comment #781

2009-03-15T16:05:52Z

please send me a sudoku puzzle

Comment #780

2007-09-24T14:04:15Z

Which puzzle is that too? I don't see it, but maybe I scanned too quickly.

Also, I assume you mean you did it by hand -- did you see anything interesting - ie. was there one hard square, and then everything else fell into place, or were their multiple "hard" squares? What are your solving methods - do you write out all possibilities right from the start, or do you logically solve "easy" ones first?

I am more interested in the methods than just a simple "did it" comment.

Comment #779

2007-09-23T17:01:31Z

I did it!

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

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

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

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

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

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

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

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

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

Comment #778

2007-08-24T03:04:11Z

like this?

Comment #777

2007-08-23T17:14:01Z

Do you know where I can find blank sudoku puzzles that I can copy and paste and then still write on it.

Comment #776

2007-02-26T15:25:48Z

I added a <pre> tag to your comment, so the table is presented nicer.

Comment #775

2007-02-26T15:15:54Z

oops, i cannot format the grid here. Also the 3 in r4c4 already is eliminated (should be 378). Also note that this solution is much shorter than the one i had manually for gfroyle's beauty.

Comment #774

2007-02-26T15:15:26Z

Thanks for explaining some more.

Comment #773

2007-02-26T15:10:57Z

If you are interested, how the first puzzle *could* be solved, you can either look at Sudoku Explainers solution or do it like this.

With locked candidates, locked sets, a turbot fish and a unique rectangle you come here:

 \*---------------------------------------------------------------\*

| 4 569 1268 | 5789 3 15789 | 25 2567 5679 |
| 1237 359 12 | 6 127 14579 | 8 2357 34579 |
| 23678 3569 268 | 45789 278 45789 | 2345 23567 1 |
|--------------------+--------------------+---------------------|
| 1236 346 1246 | 78 5 13678 | 23 9 378 |
| 123 8 59 | 3479 17 13479 | 6 12357 357 |
| 136 7 59 | 2 168 13689 | 345 1358 3458 |
|--------------------+--------------------+---------------------|
| 68 46 468 | 1 9 2 | 7 35 35 |
| 5 1 3 | 78 678 678 | 9 4 2 |
| 9 2 7 | 35 4 35 | 1 68 68 |
*---------------------------------------------------------------*

r4c4=3 => r4c7=2 (=> r1c7=5) => r5c1=2 => r6c1=3 => r6c7=4 => r2c9=4 => r3c7=3 => r2c2=3 => r2c6=5

Then in row 2 there is no 9 left, so r4c4 cannot be 3.

This gives you a pair 78 and the puzzle can be solved with basic methods.

Comment #772

2007-02-26T13:41:29Z

Correction: the 2nd by YH rated 9.5. For puzzles with rating above 9.0 you need very long forcing or contradiction chains.

But the hardest need contradiction chains inside contradiction chains, so they are classes harder.

Comment #771

2007-02-26T13:30:06Z

While yours is really easy (just needs a hidden pair), the 2 puzzles by YH definitely are very hard ("very easy" was only meant in comparison to the hardest known). The rating by Sudoku Explainer (http://diuf.unifr.ch/people/juillera/Sudoku/Sudoku.html) for both is 9.0 and this is exactly the same as the hardest has, that i personally solved manually, namely gfroyle's beauty:

6.. ... ..3

.7. .8. .9.

..2 ... 5..

... 3.. ...

.8. .1. .7.

... ..2 ...

..5 ... 1..

.9. .4. .8.

3.. ... ..2

Maria45 and Carcul have solved puzzles manually with a rating of up to 10.0.

The current highest rating by SE is 11.4 (for MM's puzzle above)

Comment #770

2007-02-24T16:50:40Z

Well, I agree that the first one ravel posted is the hardest one I have ever seen. I still question whether you did the "VERY EASY" ones by hand or whether you are only comparing on a computer.

Comment #769

2007-02-23T15:10:51Z

I'll have to try your hard ones. I wonder if you actually did the "very easy" puzzles by hand - or you typing them into a computer?

I haven't met anyone who has actually solved the first one by hand yet.

Comment #768

2007-02-23T12:29:58Z

The puzzles i have seen here are VERY EASY compared to the hardest known. According to my current rating this one by Ocean is the hardest:

.....1.2.

3...4.5..

...6....7

..2.....1

.8..9..3.

4.....8..

5....2...

.9..3.4..

..67.....

You can find a list of the current known hardest at

http://www.sudoku.com/forums/viewtopic.php?t=4212&start=587

This by Mike Metcalf is the one with the hardest single step:

5.......9

.2.1...7.

..8...3..

.4.7.2...

....5....

.....6.1.

..3...8..

.6...4.2.

9.......5

Comment #767

2007-01-20T19:08:22Z

Hi. I just found a site where the person has available his collection of 36,628 sudokus of "17 original numbers only". Everyone suspects that 17 is the minimum that will produce a unique solution. Here's the site: http://people.csse.uwa.edu.au/gordon/sudokumin.php Enjoy. Gil Kessler

Comment #766

2007-01-13T15:38:16Z

Hello everybody,
I'm looking for the sudoku with the least amount of already-penned-in numbers.
It doesn't have to be the most difficult (although it can't be EASY by definition), it just has to be the most empty one.
The two above (from October 9 2006) have only 18 numbers in them, and they are, at least for now, the most empty ones I've found.
If anyone knows of a puzzle even emptier, please post its link here.
Thnx :)

Comment #765

2006-12-21T16:02:44Z

heh - the spam filter worked pretty well, though not quite perfectly, I guess. There were about 10 comments made from the same computer (69.151.106.232) this morning, the first one was alright, although his spelling was atrocious. And then he started swearing and insulting me and the rest of the commenters. Once he saw he was blocked by the spam filter, he started removing words one by one until the spam filter let him in. Presumably, since he went back and read the post each time, the badbehavior plugin didn't stop him from trying to post multiple comments.
He eventually got to to four words, and it let him post it, though the comment wasn't all that interesting to read, since he started out so badly, I figured that I might as well delete, though my general policy would be to not moderate people's comments.

I don't know exactly what his point was, no links to any pages, though he did leave a couple email addresses, presumably the last one was real, since it comes from the same network as his computer name.

I wonder how many of his comments were trapped as spam due to more than half of the words being spelled incorrectly.

Comment #764

2006-12-21T14:16:41Z

-- deleted --

Comment #763

2006-12-03T16:09:07Z

That depends on how well the puzzle has been constructed. Proper puzzles should only have one solution but it is of course possible to construct a puzzle with multiple solutions though in general it's an undesirable characteristic. Guesses are simply equivalent to higher forms of logical deduction and the use of a guess does not necessitate multiple solutions.

Comment #762

2006-11-28T16:36:07Z

Can anyone answer the question about what are guesses? Does that imply non-unique solutions? Why would you ever need to guess? What happens if you go back and guess a different value than you guessed the first time?

Comment #761

2006-11-28T16:25:23Z

I agree that this original puzzle is NOT hard. I have just written a Sudoku solver in ANSI C based on a very simple algorithm. It finds the solution of the original puzzle without ANY guess.

The 2 puzzles presented by YH are also found to have unique solutions, but require some guessing (7 and 4 guesses, respectively).

If you're interested in the source code, send me an email at humbertoldi at yahoo dot fr.

Comment #760

2006-11-28T02:44:19Z

I am moving the original puzzle to a comment, since I think everyone keeps commenting on this easier one, rather than the hard ones talked about in the comments.

1 3

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

Comment #759

2006-11-28T02:18:40Z

There are palm programs for sudoku. The one I have allowed me to solve this puzzle in 3.5 minutes. It allows the use of pencil marks. The program itself solved the puzzle in 10 seconds.

Comment #758

2006-11-24T00:10:46Z

Never was a sudoku fan myself, I understand the logic but I find the process itself a frustrating, labourious and time-consuming task. I do however enjoy writing programs, which provide the satifaction of logical thinking without any tiresome human inadequacies to get in the way. The program I wrote for this was in basic, and follows the following fool-proof method for solving any sudoku puzzles:

Employs basic logic, to deduce as many squares as possible - similar to a human filling in the possibilities and deducing what must be true.
When first step has been exhausted; eg after an entire repetition no new values have been obtained program selects a square with as few possibilities as possible (bit of a mouthful) and makes a 1st generation guess which it records in an array.
Returns to step 1.
Checks for consistency, eg if any rules have been broken. If ok then 2nd generation guess is made if necessary, if incorrect then erases all current generation guesses and makes new guess. This process can repeat indefinitely moving up and down generations as appropriate if all possibilities in a certain generation have been exhausted.
Blah blah blah you get the idea within a couple of seconds either you obtain a solution to the puzzle or you're informed that the puzzle itself is at fault and there are no solutions.
In this particular case my program only had to resort to a 1st generation guess so by computer standards this puzzle is pretty tame.

Comment #757

2006-11-09T04:53:42Z

Hi - I wrote a solver in Excel (VBA) available at www.bangser.com/sudoku. It solves the puzzles listed here in a second or two; they are in the built-in library as #260, 261 and 262. I'm new to all this and wonder if anyone has a source of more difficult puzzles. Most are solved with logic only. If that's not enough (e.g. try #81 in the solver), it doesn't guess per se, but it does choose sells to "look forward" to see if only one candidate doesn't lead to a conflict elsewhere, or if all candidates lead to the same result in any other cell. I believe these tests are equivalent to more advanced strategies such as chains, coloring, etc.

Comment #756

2006-11-06T21:47:08Z

Oh, or maybe you mean finding just the first number. Yeah - I can't remember how long it took me, longer than that. I might stand corrected - I forget how long it took to me to get the first number on the puzzle posted by YH on October 9th, on this page.

Comment #755

2006-11-06T21:45:46Z

I assume you are talking about a computer solver? If not, I am pretty impressed...

Comment #754

2006-11-06T19:38:27Z

i got it in 3 mins 22secs

Comment #753

2006-10-24T22:40:28Z

I added an "update" to the original post to say that you have to read through the comments to find the harder ones, I realize that the original one I posted is not as hard as I originally thought.

Though I don't think I have seen a puzzle that I took longer to find the first number.

Comment #752

2006-10-24T19:03:39Z

i was happy when i typed in "hardest suduko game" in yahoo search and found this one...but was greatly disappointed when i actually did it...the atlanta constitution offers more of a challenge with its 5 and 6 star puzzles....i might even go as far as to say the 3 and 4 stars are harder than this one....like you said once you find that one it all comes together...the problem i had with it was i found it way to fast...perhaps finding it so fast was just luck but it made the entire puzzle way to easy for my liking.....thanks for the post though...please post more that give you trouble, because next to the monday through friday puzzles in the ajc it was fun doing it

Comment #751

2006-10-21T13:39:09Z

I have talked with a couple people about the possibility of requiring a guess, and we all think that guesses are not needed by definition, because a sudoku is supposed to only have one solution.

The trick is that you have to know harder and harder rules, so at some point our brains have an easier time just guessing, rather than learning really hard rules.

I have been working on your (YH) first puzzle, and it is pretty difficult. My father has gotten along farther than I have, though I haven't been able to figure out how he made one leap in logic, I think he might have missed something, but it happened to be okay.

Comment #750

2006-10-21T13:16:30Z

I downloaded a sudoku solver program (from Gwerdy software) to see if it worked. After a few tests, I wanted to look for a very hard one. This was the first sudoku I found by searching.
This program (on my computer, which is not really fast) took 1,089 seconds to solve it...

Comment #749

2006-10-09T19:03:59Z

Thanks - I'll try it out. I have not seen any that needed true guesses and I have doubted whether they exist.

Comment #748

2006-10-09T18:29:40Z

My sudokusolver did this one without trial and error (that is without any guessing at all). Hence there is 1 solution only, and the puzzle isnt hard, as i have some that requires up to 10 guesses which i think is the current max of what ive found. (however the number of guesses may be altered slightly by "better" guessing)
This is one Sudoku i has turned out to be one of the hardest (got it from another website)

5
3

(Solved with 10 guesses in total, 0.6 seconds)

This one from the same webpage took 1.2 seconds, but only 9 guesses.

7
8

Id love to see someone post anything more difficult or if they got a non-guessing solution to these :)

Comment #747

2006-08-08T18:36:50Z

Your solver took 12 seconds when I ran it...

But, I do agree that it can be fun to write programs to solve puzzles - unless you just did a brute force sort of method, which it seems that a 12 second method probably is that.

Comment #746

2006-08-08T18:18:01Z

Come on, is it really fun to do a puzzle via a program?

Comment #745

2006-08-08T17:02:43Z

my program took 0.38 seconds to complete it. I used php. I thnk 0.38 seconds is quite good for a scripting language..

Comment #744

2006-08-02T23:25:01Z

It must be because python is superior to all other languages, and nothing to do with your coding style...

Comment #743

2006-08-02T19:52:37Z

.0127 seconds using a python program.

well it did take me a few seconds to copy and paste your puzzle into a string in order to pass it to my program. =]

Comment #742

2006-07-30T12:29:09Z

Yes, I do effectively this operation, although I don't use dots. I write the numbers in different corners of the box, and yes, I occasionally get tripped up by crossing out one number, and assuming it has to be the other -- or not really assuming, but just not thinking.

Maybe I will try the dot method, and see if it helps me make less mistakes as my system also does not distinguish very well between 2 or 3 other choices in the same column/row/box. I started out ignoring the numbers with 3 choices, but now I write them down too, and occasionally make mistakes of that order.

As for why you couldn't get the formatting the way you wanted it, you have to use <br /> html tags to get line breaks. I forget now why I changed it, but there was some reason that having my blog code substitute br tags when the commenter typed a carriage return didn't do the right thing.

Comment #741

2006-07-29T19:39:49Z

MY SUDOKU SYSTEM
from Gilbert Kessler, 7/06
New York City

Hi --

I only began doing Sudoku two months ago, but as a former math teacher, I started with a book of very difficult puzzles and developed my own system. Since none of the books I’ve recently gotten to look at have it, I’ll call it “Gil’s Dots” and pass it on in the hope that it is helpful to others. It seems to take very little extra time, and has usually (not always) solved the puzzles without requiring “guessing”. Of course, I’ve messed up many puzzles, but always due to carelessness.

All the systems put small numbers in squares when you see that only those squares can contain those numbers. In addition, I put small dots or circles next to those numbers as follows:

[A] If the number can only appear in exactly two squares of a row, I put a dot to the right of each of the numbers (e.g. 5• -- I hope this looks like a "filled in dot" in this message). This emphasizes that the two choices are in that horizontal row. If I later discover that one of the squares must have a different actual number, the dot immediately directs me to the square where the actual 5 must go.

If the number can appear in exactly three squares of a row, I use small circles instead of dots (e.g. 5◦ -- I hope this looks like an "empty circle" in this message!). If I later discover that one of the squares must have a different actual number, I fill in the remaining two circles (thus they become the dots previously described). I do not enter any small numbers that can be in four or more squares.

[B] I use the same system when examining columns, but I put the dot or circle just above each small number instead (I put my small numbers in the lower part of each square, so I have room above each number for the dot). This emphasizes that the choices are in that column. It often happens that small numbers have both horizontal and vertical markings.

[C] Finally, if I’m examining a (3x3) box and find that a number can only appear in exactly two squares of the box (but those squares are not in the same row or column), I put the dot to the upper right of the number (I can't seem to reproduce this "exponential dot" in this message). That position can later direct me to other squares, but only in that particular box! When there are exactly three choices, I use the small circle instead (e.g. 5˚ -- the circle should look like a "degrees" symbol). In this case, two of the three might be in the same row or column, so you must be very careful about that corner placement of the circle; it directs you to other squares in the box, but does not eliminate possible 5’s elsewhere in the rows or columns. If you eliminate one of those circles later, and the two remaining are in the same row or column, be sure to put in the additional dots (either to the right or above) that indicate this, as that does affect the rest of the row or column.

[D] A few general comments (usually using specific numbers for explanation). Several are well known.

(1) A major error I find is in not seeing a square that a small number could go in, so using the wrong mark. Also be careful that small circles don’t look like dots and confuse things, and that corner marks don’t look as if they’re in the horizontal or vertical positions instead. Small numbers can have as many as three marks on them.

(2) When you enter a small number with horizontal or vertical marks in a single box, that often has implications for the rows or columns of a previously considered box. When entering them anywhere, check if previous entries for that number create an X-Wing or Swordfish (see below).

(3) When you discover that a square actually does contain a 5, cross out any other small 5’s in the corresponding row, column, and box. As you cross off small 5’s, their dots often lead you to more squares where actual 5’s must be put. But when you cross off a small 5, if that square contains another small number, be careful not to assume that the square actually gets that other number!

(4) If two squares in a single row each contain 5• 6•, then those two squares must specifically contain the 5 and 6 in some order (they “use up” those squares). Any other small numbers in those squares must be eliminated. A similar result is true for a single column (using vertical dots), and for a single box if both numbers have corner dots.

(5) The above concept can be extended to three numbers that are within three squares in a row (they “use up” those squares), three that are in a column, or three (even with mixed types of dots and circles) if all are in a single box.

(6) A bit of study shows that if four 5’s with horizontal dots occur in squares that are the corners of a rectangle of any size, then you can give each of them a vertical dot also! You can then eliminate any other 5’s in those columns. This is equivalent to the “X-Wing” concept. [An alternate phrasing of this is that if 5’s with horizontal dots occur in two rows, but within the same two columns, each of them can be given a vertical dot also.] The reverse applies if the original 5’s had vertical dots to start with.

An X-Wing Explanation: Each row must get one of those 5’s, which eliminates the number 5 from that column; this “spreads” the 5’s into the two columns, so no other 5’s can go into those columns.

(7) Similarly, if 5’s with horizontal dots or circles (if there are three) occur in three rows, but within the same three columns, each of them can be given a vertical dot (if there are two vertically) or circle (if there are three vertically) also! You can then eliminate any other 5’s in those columns. This is equivalent to the “Swordfish” concept. The reverse applies if the original 5’s had vertical dots or circles to start with.

A Swordfish Explanation: Each row must get one of those 5’s, which eliminates the number 5 from that column; this “spreads” the 5’s into the three columns, so no other 5’s can go into those columns.

Comment #740

2006-07-21T21:56:54Z

I agree the first number is difficult to find, but after it was found, this puzzle fell quickly. I too started with the 3 in the right collumn. The "5-9" pairs in the upper right gave up the location of the 3. Overall this was a fun one...

Comment #739

2006-07-13T07:08:00Z

this was an easy one i have done harder

Comment #738

2006-07-09T02:38:02Z

Hello all. I am a programmer (both professionally and in my spare time), and I thought it would be a blast to write my own sudoku solver. I just finished it this afternoon and I was in a quest to find the hardest sudoku puzzle.

The program uses 3 complex methods to eliminate any invalid solutions in each cell in the process to solve the puzzle. The methods use a system of direct relations, to slightly indirect relations, and to multiple layers of cross examination to finalize any unqiue values, MOST puzzles I let it crunch away are completely solveable with only these three methods. I have found only a handful that require the last reserved method - a recursive method using all remaining permutations until one solves out. This puzzle has no first answer foudn without recursive permutations, which in lamen terms basically means you'd either have to guess the first value, or you were wrong in thinking you found one without guessing. R2C9 (or R1C8 if you count from zero like me) is the first cell from which a solveable permutation is found. If you guess a 9, you'd be in for a long and painful treat. If you guess a 5, then you guessed correctly, From there on out, all values are either directly relational, or indirectly relational without any cross layered eliminations, in other words, fairly easy.

Comment #737

2006-06-05T23:20:00Z

Yes, if you mean the one I posted, and not the one that sagar linked to.

I have since learned that there are lots of harder suduko puzzles than the ones that typically come in the suduko books and say that they are "hard", it is all relative, I guess.

Comment #736

2006-06-01T21:55:28Z

I didn't think it was very hard -- not even having to use some of the advanced techniques such as x-wing, swordfish, or solving by colors.

I learned these solving techniques by downloading "simple sudoku" from internet and going through the demos.

Comment #735

2006-05-16T23:00:55Z

I choose to solve my sudoku puzzles without guess and check, and if it takes longer i have no problem doing them over the course of a few days. I enjoy seeing if i can find that one clue that will help me solve the entire sudoku puzzle. We all have different ways of solving it and that is fine.

Comment #734

2006-05-16T22:12:17Z

An example (not from this puzzle): "This box can be either a 3 or an 8. If it's a 3, then that box must be a 9, and that box over there must be a 7 -- oops, if that's a 7 then this other box must be a 2, but it can't be a 2, so I've found a contradiction and so the first box can't be a 3." Only in this case it was as if I followed all the logical consequences of the first box being a 3, but never ran into a contradiction. Having actually solved the puzzle, I found my incentive to solve it by a prettier method to be significantly diminished and overwhelmed by my desire to accomplish something else today.

Comment #733

2006-05-16T20:59:33Z

Sudoku puzzles are designed so you dont have to guess and check. You can solve the 976 difficulty puzzles with logical reasoning.

It is hard and sometimes frustrating, but it is fun in the end. That is if you figure it out.

Comment #732

2006-05-16T19:39:59Z

I am not sure if I follow - you had a choice of two numbers, and you just happened to pick correctly?

Comment #731

2006-05-16T19:30:52Z

Well, I solved it -- the 1520 or 976 or whatever. It wasn't that hard to get one number. The puzzle bothered me a little because, unlike other Sudokus I've done, it was not symmetrical. Oddly enough, the first number I found took care of that problem and made it symmetrical. Not that that made it any easier to solve. I didn't ever get a second "for sure" number until I got all the rest. That is, I narrowed it down as far as all my algorithms could do, and then started the "pick a number and follow it until you get a contradiction" rule. In the process I found a few mistakes I had made, but correcting them still did not allow my algorithms to find a certain second number. Nonetheless, after I corrected the mistakes, the first experimental path I chose to follow did not lead to a contradiction but rather to the solution.

Now to get back to real life....

Comment #730

2006-05-15T20:15:59Z

I can't tell what this is, might be interesting.

Comment #729

2006-05-12T19:05:45Z

Hrm. I don't know how that site works. The puzzle is still in the #1 place, but, yes, the score is now lower.

Comment #728

2006-05-12T18:45:40Z

Where is the 1520 puzzle? When I go to the link the highest level I see is 976.

Comment #727

2006-05-12T02:06:46Z

Well, I still say it is more fun to not just write down all the possibilities first, but instead start with doing different algorithms, the 1520 or whatever the score is on the page you (sagar) mention, is pretty tough.

I had other work to do, so I stopped after working on it for a couple hours. I knew a bunch of spaces had to be one or the other, but only had written down one for-sure number.

I submitted it to a sudoku solver and watched it go through each step - the key step was a step it called "swordfish" where it looked at 9 squares at the same time, and then was able to cross out a value in a tenth square.

I was happy to see it go through most of its rules and not find an answer.

Comment #726

2006-05-11T19:17:35Z

Yes, I agree that sometimes you have to write down all the values - it is more interesting to me to find algorithms that simplify this process, instead of just brute-forcing it.

So, I guess the title of this post might be misleading - but if you write down all possibilities, all puzzles are solvable easily enough, right? I will take a look at your example and see what I think of it.

Comment #725

2006-05-11T19:13:59Z

i just checked the difficulty of this puzzle and it is a 126.

Comment #724

2006-05-11T19:11:26Z

sorry i forgot to answer your question. I looked at it for a second after i filled in all the possible values.

Comment #723

2006-05-11T19:10:24Z

You may not like doing that but sometimes it is a must.

Go to this site and try doing any of them without writing anything down. It is hard even with writing all the posibilities down.

http://www.sudokusolver.co.uk/grids_veryhard.html

I think the 1520 difficulty one is new but i beat the second one with a difficulty of 976. Try them and see if you can get it. Its harder then you think. I think that most puzzles in newspapers are around 100-150 for hard puzzles.

Comment #722

2006-05-11T19:01:32Z

You looked at it for a second after you filled in all the numbers, or just looked at it without writing anything down?

I am not interested in solutions that involve writing every single possibility down -- apparently lots of people solve Sudoku puzzles that way - a coworker said he isn't interested in Sudoku puzzles since you can just do that, he doesn't care about making improvements to his algorithm at all.

Comment #721

2006-05-11T18:58:53Z

i havent done it yet, but no really hard ones i also fill in all the possible answers. Getting just one number is really easy in this one. I looked at it for a second and found one. I dont know if it gets harder but finding one is really easy.

Comment #720

2006-05-11T13:06:00Z

When you say "fill in all the possible", what do you mean?

Comment #719

2006-05-10T16:57:51Z

Not a hard one, at least not as hard as I expect. It look clueless at the first glance, but my practise is to fill in all the possible and then it will be easy for you to sort out the possible start. Just like this puzzle, once you do so, it's pretty clear that where the first three numbers can be put down, and viola puzzle solved within 10 minutes.

Comment #718

2006-05-02T10:18:49Z

That's interesting. In one of my parents' Sudoku books, it had a story about some American guy thought it up, and just thought it would be fun to name it a Japanese name or something.

Comment #717

2006-05-02T06:46:51Z

According to Wikipedia, the first Sudoku puzzle was published in America but it first caught on in Japan. Sudoku is a shortened version of the title in Japanese, so that much is for sure Japanese. I didn't see an inventor's name.

Comment #716

2006-05-01T11:42:32Z

I went looking for the story on Suduko creation - some American guy, but I can't find the story at the moment, but I found this puzzle solver, so I typed in the puzzle - it took less than a second to solve it.

It does have an interesting feature of checking whether there is more than one solution to a puzzle, so presumably that means that happens sometimes.

Comment #715

2006-05-01T10:59:03Z

Ah, but you're still correct. I said I was the last in our family to become addicted to sudoku, and doing a few puzzles doesn't count as an addiction. Do you think the name is Japanese? I could spell it in katakana!

Comment #714

2006-05-01T10:52:40Z

Don't believe a word I say. Or at least take it with a grain of salt. I was about to post and say "Am I not a member of the family anymore? since I'm not into sudoku puzzles, but your last post reminds me that I did do a few while on vacation with family. I'm not sure I even remember how to do them now, though. Wow, how short my memory is!

Comment #713

2006-04-29T17:20:29Z

Right, it would have to be a misprint. I did one at Thanksgiving where I think there were two answers. Janet also said something about sometimes having to guess, and just see if it works, and I think that can only be needed if there is more than one solution (or incomplete checking on the person doing the puzzle).

At Thanksgiving, I didn't feel like re-doing the whole puzzle to see if it would have worked the second way too.

Comment #712

2006-04-29T17:06:29Z

Puzzles. Eight minutes is a long time for a computer, but the puzzle was solved. I don't suppose they intentionally publish puzzles for which there is no solution, but it seems that a mis-print might make it impossible.

Comment #711

2006-04-29T16:52:07Z

Insoluble: The puzzles or the methods?

Comment #710

2006-04-29T16:28:39Z

The first thing I do is copy the puzzle to my own grid, which I print out; it's a regular sudoku grid but bigger (most of an 8.5x11 page) to give me more room for writing. (There is not enough room in those tiny boxes in the version in the Orlando Sentinel.) I subdivide (mentally) each blank square into 9 parts, 3 rows of 3: 123/346/789. I generally start with the number that appears most often in the puzzle, and fill in where the missing occurences of that number might be. For example, if there are four 3's given, I write a "3" (in pencil) in the upper right hand corner of every small square where a 3 might go. Then I do the same thing for the other numbers, marking 5's in the middle, 7's in the lower left, etc. (I could just use dots, because I indicate each number in a unique place, but writing the number itself helps reduce errors.) I'm making this sound complicated, but it is a pretty quick process. There's still a lot of work to do, usually, but at least I can see better what I'm doing.

I know Porter works in an entirely different way, and so do you; I wonder how many different approaches there are? Then there's always Mark's.... :) I wonder if any are insoluble?

Comment #709

2006-04-29T15:19:42Z

Oh - do you go through all squares filling in wherever a "1" can go? I do it the other way, going through each square filling in all possibilities for that square. Your way (if it is your way) might be quicker, since it might be easier to skip more squares without a whole lot of thinking.

I have always done an explicit first pass without writing down anything except for numbers that I am sure of. It is a relatively quick process. Last weekend, I developed a new strategy, where I write down little numbers if I know that a "5" has to either be in this square or that square, within any group of 9, though more likely in a box than in a row or column. That rule is how I got the 5 and 9 in this particular puzzle.

I don't like pencils all that much for any kind of writing, so when doing a suduko, one sub-goal is to write down as little as possible, because I won't be able to erase it.

Comment #708

2006-04-29T14:43:34Z

I sort of do a first pass, because I don't fill my grid of possibilities in numerical order, but start with whatever numbers I think will give me the most information, eliminating some of the possibilities. But I do move quickly to writing in the possibilities, since on anything over 2 stars I've found I have to do that eventually anyway. I need an eraser as much as a pencil this way, but marks on paper actually stay there unless erased, unlike my mental images....

Comment #707

2006-04-29T12:50:00Z

Yes, the 5 and 9 on the right column was my first thing as well. But, I had to fill in the top three boxes with all possibilities before I discovered that. My first filled in square was either the same square that you did or else the very bottom row in that column.

I wonder if you find the 3 through 6 stars to be equally difficult because you don't do any "first pass" rules to quickly write down stuff. The level of stars is different depending on which book/paper the puzzle is in, so I don't really pay attention, other than not doing the "easy" puzzles like you said.

Comment #706

2006-04-29T10:43:00Z

Um, Jon -- you might want to censor my answer, since I just realized it's somewhat of a spoiler to someone who wants to do the puzzle....

Comment #705

2006-04-29T10:37:06Z

I was the last in our family to become addicted to Sudoku puzzles, but when I did, I discovered something interesing: 1-stars weren't worth doing, 2 were somewhat interesting because I could do them "in my head," but 3, 4, 5, and 6 stars were pretty much equally difficult! That's not to say I find them easy, just that a 3 is at least as likely to be difficult as a 6. The distiction between "solvable" and "impossible" has been whether or not I make a mistake, since if I do I'm not usually inspired to start over again. I haven't done all that many, however, because I stopped when we stopped getting the daily paper. So this was a nice challenge.

I can't say how long it took me, because I was doing other things (like reading Janet's updates) at the same time. But I didn't find it particularly challenging. The first blank I filled in was the rightmost column, 5th row. After that the middle square of 9 came fairly quickly, and it was all slogging from there.

You won't like my method, however, because it starts with writing all the possibilities in each square. (The order in which I fill in the possibilities depends on the particular set up, so it's not all just slogging.) Once I've done that, certain things jump out at me, such as unique pairs. In this case, I could see that the first two rows of the rightmost columm could only be 5 or 9, so one had to be 5 and the other 9, thus when I found that the 5th row of that column could only be 3, 5, or 9, I knew it had to be 3.

Comment #704

2006-04-29T02:25:09Z

Solved the whole puzzle in just over 8 minutes - using the computer program Mark wrote. No other puzzle has ever been close to a minute. That convinces me not to try it on my own.