An auto-eroica sudoku

[MattcAnderson]

Hi Math People,

Thanks to Batalov for posting this very hard sudoku puzzle. I worked on it for less than an hour, and my progress should be in the image below.

This puzzle has no 8 and only one 4 in the starting clues. I have a conjecture. Suppose the starting clues of a sudoku puzzle only has 7 of the 9 digits, then there are at least two solutions. I don't know how to prove this, but it seems logical to me.

Also if a puzzle has only 6 of the 9 digits, then there must be at least 6 possible solutions. I imagine '3C2', that is 3 choose 2 is 6.

I also attached the book cover of the New York Times sudoku book. They make three levels, easy, medium and fiendish. I have completed more than 90% of the 150 fiendish puzzles in this book. However, I am obviously outmatched by some of the other sudoku puzzlers who visit this forum.

Regards,
Matt

[R. Gerbicz]

Originally Posted by MattcAnderson

Suppose the starting clues of a sudoku puzzle only has 7 of the 9 digits, then there are at least two solutions. I don't know how to prove this, but it seems logical to me.

If there is a solution then swap the original missing two digits in every place, then you get another solution of the sudoku.

Originally Posted by MattcAnderson

Also if a puzzle has only 6 of the 9 digits, then there must be at least 6 possible solutions.

This is also true. And you can easily generalize this.

[MattcAnderson]

Hi Math People,

The conjecture I proposed above is not true. It is possible for a sudoku puzzle to have 7 of the 9 starting digits and have no solution.

I have a new conjecture. Suppose a sudoku puzzle only has 7 of the 9 starting digits, then it cannot have a unique solution.

Regards,
Matt

[Batalov]

Originally Posted by LaurV

The version of the game which is free will give you a single grid per day per level, but don't be upset about, there are enough levels, and for some of those grids you can work hours...

Anything below Maelstrom is too easy and the android version doesn't have the Mike's "Cancel" level... :-(

So, I think the guy deserved his $2.99, -- the interface is much nicer than any of the other implementations, and now I solve a dozen a day and even they are getting too easy. I should get my 6x6x6 cube off the shelf; it's been gathering dust there for too long...

[LaurV]

Originally Posted by Batalov

Anything below Maelstrom is too easy...

Hahaha, I hope for you that you are serious, I have troubles at lower levels too..
Btw, that grille you put took me ages and it didn't give up without lots of backtrack.

So, I think the guy deserved his $2.99...

I have to confess that it crossed my mind too, but I am still thinking about. Some option to disable the "unique rectangle" hints would worth the money definitively. OTOH, I don't have free time (skill? hehe) to solve the given daily grids, why should I need more?

[LaurV]

I am the fastest in the world at solving sudoku!

I have a proof.
It says "you are faster than 100% of the people solving 'easiest' with autopencil and hints"

I don't think another idiot was even thinking to request hints at "easiest" level, but I tried anyhow... and you see, the results didn't wait for long to show...

[Batalov]

Originally Posted by LaurV

I have a proof.
It says "you are faster than 100% of the people solving 'easiest' with autopencil and hints"

It does feel good to see these, doesn't it? ;-) I am with you. I see these every once in a while too, sometimes a couple times a day.

But I am fine with being merely "faster than 88% of the people solving 'Maelstrom' with autopencil and without hints". (Sometimes a 100%, yes.)

I couldn't reach 70-80-90%-ile for a while, but then I figured what most other players are likely doing (so I do too, now): that is, after eliminating (by contradiction) a long twisted passage almost to the end (and of course remembering the path that I took at a strategically important fork), then instead of backtracking by a few dozen "Undo"s, I do "More Choices" :: "Start Over" and right away pencil out the dead tunnel. Easy-peasy.

[Mini-Geek]

Originally Posted by Batalov

It does feel good to see these, doesn't it? ;-) I am with you. I see these every once in a while too, sometimes a couple times a day.

But I am fine with being merely "faster than 88% of the people solving 'Maelstrom' with autopencil and without hints". (Sometimes a 100%, yes.)

I couldn't reach 70-80-90%-ile for a while, but then I figured what most other players are likely doing (so I do too, now): that is, after eliminating (by contradiction) a long twisted passage almost to the end (and of course remembering the path that I took at a strategically important fork), then instead of backtracking by a few dozen "Undo"s, I do "More Choices" :: "Start Over" and right away pencil out the dead tunnel. Easy-peasy.

I often get 90%-ile on Maelstrom (no autopencil or hints). My current strategy is to keep a log (in notepad or similar) of my recent guesses (what number I guessed and in what cell). Usually that only is 0-2 guesses by the end of a game, but sometimes goes up to 3-5 (i.e. that many guesses I've had to make, that are not yet proven wrong). If I hit a dead end, I use Undo to rewind and continue on from there. The only annoying thing is when I run out of my Undo history, since it has a finite length. If that happens, I'll either give up or restart from scratch. I'll use "Set Bookmark" too, but don't always have one set at a good point.

I started playing this app after seeing it here, bought it a few days later, and now have 74 Maelstrom games completed on it, with fastest time (no pencil/hints) 3:57, avg time of 9:29 (but sometimes if I turn the screen off, it keeps counting time, so the real average should be lower).

[Batalov]

Originally Posted by Mini-Geek

(but sometimes if I turn the screen off, it keeps counting time, so the real average should be lower).

I noticed that you can hit "Game" button before putting it to sleep (it will report "Paused"), then you put it to sleep - and the time will not count.

[LaurV]

Originally Posted by Batalov

But I am fine with being merely "faster than 88% of the people solving 'Maelstrom' with autopencil and without hints". (Sometimes a 100%, yes.)

Man, if you do that without backtrack, or say, no more than 3 (or 5? let's give you 5 ) backtrack moves, then honestly and totally I raise my hat and kneel in front of you!

I can also solve maelstrom quite fast using backtrack, I mean, when I don't know what to do I pick the first cell with two pencil marks and put the smaller number there, and continue to solve it, if it gets to an impossibility (there is a 50% chance, and usually I realize the impossibility after few moves, no need to play it to the end) then I "undo" to starting point and use the other number (edit: which I know it is correct, this time). Doing this on paper would be a big pain...

I usually try to solve it "logical", regardless of the time, that is why I am talking about "hours per day". Sometimes when I am in the "mood" (like waiting in the parking lot during swmbo does shopping) I even try to avoid using colors to mark the active digit, etc. As close to the paper as possible. I don't cheat anybody, but myself, if I try to "cheat"... But I still use autopencil, it saves "routine" time which would be wasted to put them by hand.

Maybe this would be another criteria that would make me pay the money (beside of the checkbox with "don't use the deadly rectangle rules/hints"), to have a limited number of "undo"s, and a top organized by them, like "you solved the xxx level faster than xx% people using autopencil marks and no more than 5 (3? 10?) undos", hehe... Because with unlimited backtrack and enough patience, everybody can solve everything..

About those 88%, you have the time advantage, the tops are still US-time based.

[henryzz]

Has anyone found any good Sudoku generators? I am really looking for large puzzles 25x25+. Killer and other variants would also be nice. Jsudoku almost does what I want but its generator takes too long for large puzzles.