9X9数独的已知数字最少个数问题

stonesmith322

很强大啊 这个研究过一阵子 还有有些奇怪的熟读  比如 杀手数独

乌木

我数学很差的，此题不会解答。论坛中数学好的人不少，一起看他们的帖子吧。

WitEden

根据我了解，数独题要多难就可以出多难！

数独在北京开展的很好，国内由数独联盟组织各项比赛，数独联盟是北京晚报集团的一个子公司，

每年举行一次世界数独锦标赛，已经举行四次了，中国参加了3次，第一界中国没有参加！！

数独联盟网站：http://www.sudokuchina.com

WitEden

这个问题很难证明!给你一些英文和中文的资料吧!

《数独背后的四个数学问题》中的一部份

数独初盘最少可以有17个数。

与数独终盘相对应，一个数独游戏给出的初始条件称为初盘。由于规则所限，给出的初盘数字个数必须在32以下。

  一般常见的初盘数字个数在22—28之间，而数独爱好者们常问的一个问题是：最少给出多少个数字，数独游戏才确保有惟一解？具体地说：最少需要在初盘中给出多少个数字，使得移除其中任何一个数字该数独游戏便没有惟一解。

  事实上，这个问题是数独中最有数学趣味的问题之一，并且至今仍未得到解决。但数学家们估计，这个数字很可能是17.17个数字的最小惟一解初盘是由一名日本数独爱好者发现的。澳大利亚数学家GordonRoyle已经收集了36628个17个数字的惟一解初盘，而爱尔兰数学家Gary McGuire则致力于寻找16个数字的惟一解初盘，但至今仍无发现。部分数学家开始退而求其次，转而寻找只有两个解的16个数字初盘。

  统计学家根据一个统计学原理曾随机地构造了大量17个数字的初盘，发现其中有惟一解的初盘只有数个未被GordonRoyle教授发现，这意味着，最小惟一解初盘问题的最终答案可能正是17：因为从理论上说，如果16个数字的惟一解终盘存在，那么每一个必将引起65个17个数字惟一解终盘的增加，而在研究中至今没有观察到这一效应。

The lowest known is 17 givens in general Sudoku, or 18 when the positions of the givens are constrained to be half-turn rotationally symmetric. It is conjectured that these are the best possible, evidence for which stems from extensive randomised searching:

• Gordon Royle has compiled a list of (currently) 36628 17-clue puzzles, each of which is unique up to isomorphism. None of these was isomorphic to a symmetric puzzle, nor contained a 16-clue puzzle.
• An independent construction of 700 distinct 17-clue puzzles found only 33 not already on an earlier, size 32930, version of Royle's list. From that, the MLE estimate of the number of 17-clue grids was c. 34550. If the construction methods were truly random and independent then this would imply a negligible probability of there being a 16-clue puzzle waiting to be discovered -- since any such "16" would give rise to 65 17-clue puzzles, all of which were somehow missed in the search.
• The most fruitful set of clue positions, in terms of number of distinct 17-clue puzzles they admit, from Royle's list have been exhaustively searched for 17-clue puzzles. All 36 puzzles found by this process were already in Royle's list. All 34 puzzles on the next most fruitful set of clue positions were also in Royle's list.
• The most fruitful solution grids (in the same sense) have been exhaustively searched for 16-clue puzzles using CHECKER with no success. This includes one, "strangely familiar", grid that yields at least 29 different 17-clue puzzles.

今夜微凉

psp上的数独游戏，初级需要5分钟，最高级我却要半小时以上~

tm__xk

同意LS..
记得好像做过24还27的....

superacid

有些东西不是很轻松就能证明的，一定会依赖于计算机

Vicki

不清楚~期待乌木老师讲解讲解~

不过我最少也做过30个一直数字的而已~