主题：河图洛书，幻方及数独 -- 雨楼

[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。

Sudoku Solving

Basic 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...