主题：河图洛书，幻方及数独 -- 雨楼
家园 河图洛书，幻方及数独 偶们滴老祖宗的几千年前就记载了河图洛书，
自豪一下先河图洛书是这个样子滴
外链图片需谨慎，可能会被源头改[QUOTE]相传，上古伏羲氏时，洛阳东北孟津县境内的黄河中浮出龙马，背负"河图"，献给伏羲。伏羲依此而演成八卦，后为《周易》来源。又相传，大禹时，洛阳西洛宁县洛河中浮出神龟，背驮"洛书"，献给大禹。大禹依此治水成功，遂划天下为九州。又依此定九章大法，治理社会，流传下来收入《尚书》中，名《洪范》。《易·系辞上》说："河出图，洛出书，圣人则之"，就是指这两件事。洛书（九宫）的横行竖列斜角总和均为15。有点意思吧。
关于洛书，老祖宗早总结了个口诀，
九子斜排，
3
2 6
1 5 9
4 8
7
上下互换，
7
2 6
1 5 9
4 8
3
左右相更，
7
2 6
9 5 1
4 8
3
四维挺出
2 7 6
9 5 1
4 3 8
简单吧。
数独捏，就是3X3个九宫的组合。类似于填字游戏，给了你一些填好的数字，要求你补全。规则捏，每个行、列、块（九宫）中都只能包含唯一的1-9数字。
听起来简单吧，做起来可不是那么样，绝对需要时间和细心。它是浪费时间的一大工具。至少我是这么认为的。
简单级别的数独，利用基本三原则就能解开，复杂的呢？那就要看有多复杂了，单凭脑力（纸+笔）的话一般人做高级别的会觉得需要升级CPU，扩充内存。。。。
Sudoku SolvingBasic Techniques
Single In Box
When there is only one cell in the box which can contain a certain value, this value can be safely assigned to this cell. Read more...
Single in Row/Column
This technique is based on the fact that every row must contain every value once. Read more...
Moderate Techniques
The following techniques are more difficult to spot because they require that every candidate value is carefully written down. This is a very time-consuming and precise task. Fortunately, this task can be carried out by a computer program. This can spoil the fun of completing the more simple puzzles, but it can still be very challenging when solving more advanced ones.
Naked Single
After writing down all the candidate values into the cells, you can come across a Naked Single, which means that there is only one possible value for that cell. Read more...
Pointing Pair
When a specific candidate value inside a box is restricted to one row or column, you can use the Pointing Pair technique. This means that you can exclude the same candidate value from other boxes in the same row or column. Read more...
Box Line Reduction
When a specific candidate value in a row or column only occurs in one box, this value can be exluded from other cells in the same box. Read more...
Advanced Techniques
Advanced Techniques are based on the same principals as the other techniques. They are generally more difficult to spot. A new term which will be introduced here is the group. A group can be a row, column or box.
Naked Pair
If two cells in the same group contain exactly the same two candidate values, these candidate values can be excluded from other cells in the group. Read more...
Naked Triple
If three cells in the same group contain exactly the same three candidate values, these candidate values can be excluded from other cells in the group. Read more...
Naked Quad
If four cells in the same group contain exactly the same four candidate values, these candidate values can be excluded from other cells in the group. Read more...
Hidden Pair
If two cells in a group contain an identical pair of candidates and no other cells in that group contain those two candidates, then other candidates in those two cells can be excluded. Read more...
Hidden Triple
If three cells in a group contain an identical pair of candidates and no other cells in that group contain those three candidates, then other candidates in those three cells can be excluded. Read more...
Very Advanced Techniques
These Very Advanced Techniques require the player to use the whole puzzle, instead of just parts. Sometimes techniques are chained or multiple techniques can be used together to solve very challenging puzzles.
Remote Pair
When chaining multiple Naked Pairs, a Remote Pair can be used to remove candidate values. Read more...
X-Wing
This is another method of reducing the candidates when two rows have the same candidate only in the same two columns. Read more...
Sword-Fish
Generalisation of the X-Wing pattern. Read more...
XY-Wing
Generalisation of the X-Wing pattern. Read more...
XYZ-Wing
Generalisation of the XY-Wing pattern. Read more...
Empty Rectangles
The Empty Rectangles uses the same logic as the X-Wing technique te exclude candidate values. Read more...
Colors
When a group contains only 2 of the same candidates, at least one of these candidates must have this value. By coloring these pairs, candidates can be excluded. Read more...
MultiColors
Generalisation of the Colors technique. Read more...
Nice Loop
Use strong and weak links to exlude candidates or assign values. Read more...
Forcing Chain
Chain pairs to exlude candidates or assign values. Read more...
Bug
Use the information that the puzzle only has one solution to exclude candidate values. Read more...
Unique Rechtangles
Use the information that the puzzle only has one solution to exclude candidate values. Read more...
Guess
Some puzzles cannot be completed using logic steps only. Read more...
提醒:这东西跟用Super π测计算机性能一样，知道怎么回事就行了，没必要天天开机就先测一边CPU的benchmark，您要是掉里面我不负责捞。
不过您看上边这些技巧，就知道有多少扇子熬过了多少不眠之夜。。。您可悠着点。
家园 九宫格的解法 可以简单推算出中心格是1到9这个等差数列的中间数5如下：
有四条线(两横两纵两对角)从中心格经过，可列式：
3x + 45 = 4 * 15
x = 5
剩下的用两两数的和等于10凑凑就行了。
另外好像有个规律是一条对角线可填连续的三个中间数：
15 = 3*5 = 4 + 5 + 6
奇数个数的等差数列的和是中间数乘数列个数。
家园 行了，下半年有的玩啦。。。 俺是出了名的慢，有时间就来请教一下哈。。。
家园 触景生情,遥望故乡 我是河洛人,看到这个,就想起了我们洛阳...的王城公园...呵呵,在公园里有一块大石头,上面镶的就是河图和洛书.原来的牡丹公园灯会(现在没看过,小时候的事了),这龙马负图可是保留项目~
原来没什么感觉,出来后才发现,在洛阳这地方,古字填充在城市的每一个角落里,浸淫在每一寸土壤里.每一处古迹,每一片遗址,都能娓娓道来一个悠远的故事.
另外说一下那个神龟
那个神龟其实是有名字的,叫赑屃,上古神兽的一种,传说它是龙首,龟身,蛇尾,现在在碑刻下面驮碑的就是它.另外,民间还有一种说法:摸摸赑屃头,一辈子不发愁;摸摸赑屃背,长命又百岁;摸摸赑屃腚,一辈子不生病.