Comments on: What Sudoku isn’t

By: Rijk

Rijk — Fri, 07 Apr 2006 12:16:36 +0000

I am addicted to Sudoku! I made an inventory of methods for solving even the most difficult Sudoku. Start with looking for duo’s, it’s an eye opener!
Check http://www.sudokuhints.nl/en/ for details.

Good luck!

By: wim

wim — Tue, 13 Sep 2005 06:40:30 +0000

WIKIPEDIA:
A valid Sudoku solution grid is also a Latin square. There are significantly fewer valid Sudoku solution grids than Latin squares because Sudoku imposes the additional regional constraint. Nonetheless, the number of valid Sudoku solution grids for the standard 9Ã—9 grid was calculated by Bertram Felgenhauer in 2005 to be 6,670,903,752,021,072,936,960 [3], which is roughly the number of micrometers to the nearest star. This number is equivalent to 9! Ã— 72^2 Ã— 2^7 Ã— 27,704,267,971, the last factor of which is prime. The result was derived through logic and brute force computation. The derivation of this result was considerably simplified by analysis provided by Frazer Jarvis and the figure has been confirmed independently by Ed Russell. A paper detailing the methodology of their analysis can be found at [4]. The number of valid Sudoku solution grids for the 16Ã—16 derivation is not known.

Of course, some of the 9Ã—9 grids can easily be transformed into others; by relabelling the numbers, by rotating or reflecting the grid, and by permuting certain rows and columns. Ed Russell and Frazer Jarvis have counted the number of “essentially different” sudoku grids as 5,472,730,538: see the previous link for more details of the calculation.

By: Tom

Tom — Sun, 14 Aug 2005 19:01:37 +0000

It can be beaten by brute-force because there are only a finite number of possibly layouts – and if there’s only one correct answer, it’s not necessary to fill every square on the board to find out you’re wrong – the moment you hit an impossibility, that iteration gets ticked off as a “FAIL” and you go round again.

Of course, the brute force required is pretty massive. My memory of permutations and combinations is failing me, I’m afraid, so I can’t offer a solution to your problem, and calculating the upper bound for “correct” sudokus (rather than for just inserting the numbers 1-9 once in a row of 9 squares) is quite tricky. Still, my point is: it has a finite number of possibilities and clearly defined points for failure, which means an automated system based around brute force – no matter how tricky it is to program – can be guaranteed to work. Unlike, say, trying to reverse-engineer private keys, or MD5 hashes.

I never said it was easy…

By: David Wahlstedt

David Wahlstedt — Sun, 14 Aug 2005 17:54:10 +0000

Tom, you claim that it can be solved with brute-force. Under which conditions do you mean ? No cutting down the search space before guessing ?
Can you give a bound of the number of combinations needed ?
Say there are 25 given numers, then one has to fill in 56 positions with values in [1..9]. Seems to be quite a lot…

Best regards, David

By: DJ

DJ — Sat, 23 Jul 2005 04:58:25 +0000

Check out http://www.el.com/links/sudoku.asp Essential Guide and Links to Sudoku. It is a bridge to an Internet of Sudoku puzzles, sites, solutions, history, etc. etc.

By: xander

xander — Fri, 01 Jul 2005 17:45:42 +0000

A big Dutch Sudoku site:

http://sudoku.jouwpagina.nl

Enjoy!

By: Tom

Tom — Wed, 29 Jun 2005 12:21:58 +0000

Oh, definitely. It was a nonne question, expecting the answer yes. The discovery-by-doing aspect is very much play; indeed, the refining-algorithms-by-doing technique is classic play; taking shorter routes to work each day, refining how late I can get up to a) be clean and b) not miss my train. I like the idea of it as kata. Not just a series of forms/exercises, rules worked through, but applying those rules/kata to a real world problem. The kata are the toolset to approach the problem. There's the meditative aspect of kata which runs in parallel with the practical aspect. And yet it's still not the same as barfight (which is the best way to draw my cryptic crosswords into this analogy). Whittling away; making the ball of mud smoother and shinier; refining the kata rather than learning more. Now there's an idea: backwards Katamari Damacy - where you have a big ball of "stuff" and the goal is not to change its size, but to make it smoother. Dorodango Damacy, as it were.

By: mattw

mattw — Wed, 29 Jun 2005 09:57:47 +0000

sudoku as combinations of kata.

the play for me is discovering new, more complex, patterns of movement to act out, and to perfect the existing ones. discovery by doing: that can be play.

the process of sudoku: hikaru dorodango.