# Solving Techniques 1 (for advanced persons)

The mastery of solution strategies is very important among sudoku friends. Simple sudokus can usually be solved intuitively and through concentrated searching. The two beginner techniques are explained below under "Naked Single" and under "Hidden Single". They are mostly used intuitively and unconsciously when only one number is possible for a particular field or when a certain number fits only in a single field. For more tricky sudokus, scrupulous notes must be taken. We use the method of "candidates". It's the best way to describe the relationships. Some situations in a demanding sudoku require very complex approaches. To explain this easily understandable is an art in itself. We therefore work with graphical examples and hope to facilitate the understanding of the solution techniques.

### 1. Hidden Single

Every number already entered covers a row, a column and a block. Therefore, very often there are situations in which there is only one free field for a given number within a unit * (in block 9, the 7 fits only in the green field).

### 2. Naked Single

The yellow field is in the sphere of influence (same row ** or even block) of eight of the nine possible numbers. Therefore, in this box fits only one number (here: 7).

Naked singles are harder to spot than hidden ones, as each box needs to be examined individually.

### 3. Naked Pair

If the same two candidate values (here: 2 and 4) occupy two squares of a unit * (ie without other candidates), they divide these two squares, and we at least know that they are not in the other squares of this unit can occur further. Therefore, you can remove these two values in the rest of the affected units (here: line 3 and block 2).

### 4. Hidden Pair

If two candidate values (here: 5 and 6) exist only in two fields of a unit *, you can delete the other candidates in these fields, since these two candidates can not be in any other fields of this unit (here: line 4).

* unit = row, column or block - ** a row can be a row or a column

### 5. Naked Triple

If only three different candidates exist in three fields of a unit (here: 1, 3 and 4), these can be eliminated in the remaining fields of this unit (here: Z1).

### 6. Hidden Triple

If a total of three different candidates occur in exactly three fields of a unit (here: 4, 5 and 7), all other candidates in these fields can be removed. (Often exists next to nude threesome.)

### 7. Naked / Hidden Foursome

If there are only four different candidates (here: 4, 5, 6 and 8) in four fields of a unit (here: block 7) exclusively and in total, they can be eliminated in the remaining fields of this unit.

If a total of four different candidates occur in exactly four fields of a unit (here: 1, 2, 3 and 7), all other candidates in these fields can be removed.

### 8. Line-Block Interaction (LBI)

If all candidates of a number (here: 9) are within one block (here: B5) in a row (here: Z4), all further candidates of this value in this block are deleted.

### 9. Block-Line Interaction (BLI)

If in a block (here: B4) all candidates of one number (here: 8) are in a row (here: Z4), all further candidates of that number are removed from this row.

### 10. Extended BLI

This technique is basically the combination of BRC and Hidden Single. If the candidate elimination caused by a BLI (here: B7, Z7) (here: a 4 in B9) results in only one candidate remaining in the block (here: Z9S7 in B9) of the affected value (here: 4), then this is the right number.