Naked Single Technique and Hidden Single Technique can be used to solve simple puzzles. We must apply other techniques when puzzles become more complex. Intersection Removal Technique is introduced as a very common technique to reduce the number of candidates effectively.
Read the following example first:
It can be seen in Block at [A7], digit 9 only appears in the candidates of cells [A9] and [C9]. In addition, both [A9] and [C9] happen to be in Column 9. So in Block at [A7], no matter which cell of [A9] and [C9] will finally be placed with value 9, 9 cannot occur again in other cells of Column 9. Otherwise, there will be more than one 9s in this column. So 9 can be removed from the candidates at cell [E9].
In Block at [G1], only [H2] and [H3] can be filled with number 3. And both of these cells are in Row H. Similarly as in the previous example, no matter which cell will number 3 finally be placed into the other cells in Row H will be deprived of the possibilities for holding value 3. So 3 will be removed from the candidates at cells [H4], [H6] and [H7].
The following two types of Intersection Removal Technique are quite different from the above two. They involve careful comparison of columns and rows against the content of blocks.
There are two occurrences of number 8 in Column 5 at cells [D5] and [F5]. In addition, these two cells both lie in Block at [D4]. Therefore, it is not possible for the other cells in Block at [D4] to have number 8 as one of their candidates. Finally, number 8 is removed from [D4], [E4], [E6] and [F6].
The 6s that exist at cells [E5] and [E6] are the only 6s in Row E. And these cells both lie in Block at [D4]. All other cells in that block can never hold number 6 any more. Therefore, number 6 can be removed safely from the candidates at cells [D5] and [F5].
Now let's summarize the prerequisites for applying Intersection Removal Technique:
In many cases, however, not a single candidate can be removed even if the conditions to apply this technique are satisfied. But any way, this technique is one of the most important techniques and is widely used.
See Also:
